Application of Nuclear Data and Measurement Techniques in Nuclear Reactor and Personal Neutron Dosimetry1 Donald L. Smith Senior Physicist Special Term Appointee Nuclear Engineering Division Argonne National Laboratory, U.S.A. Digitized by: Shruthi T M (Manipal) and Shivashankar B S2 (PhD Student, Department of Statistics Manipal University, Manipal India.)

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Reference to this lecture notes: D. L. SMITH, Application of nuclear data and measurement techniques in Nuclear reactor and personal neutron dosimetry, Lecture Notes, Argonne National Laboratory. available at: https://drive.google.com/file/d/0B6lfYGCxTKOBLWhkOGtpcnY4MFU/view?usp=sharing 2 Kindly inform the suggestions and corrections to: [email protected]

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Contents 1 Introduction and Overview 1.1 What role does neutron activation play in basic neuclear science? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 What role does neutron activation play in various applications technologies? . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 What are the basic considerations associated with neutron activation measurments? . . . . . . . . . . . . . . . . . . . . . 1.4 Integral versus differential measurments. What are the issues? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 What is the status of development of the techniques associated with neutron activation measurements? What are the limitations? . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 7 8 9 12 14

2 BASIC ISSUES ASSOCIATED WITH THE MEASUREMENT OF NEUTRON REACTION RATES, ACTIVITIES AND CROSS SECTIONS 19 2.1 The formulas used for cross section and reaction rate detrminations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Magnitudes of the various observable parameters and limitations which they impose . . . . . . . . . . . . . . . . . . . . 20 2.3 The need for data corrections and the procedures used . . . 21 2.4 What are the important measurements to make for applications? The issue of sensitivity . . . . . . . . . . . . . . . . . 22 2.5 What are the factors which limit the achivable accuracy for activation and cross section measurements? . . . . . . . 24 2.6 Numarical analysis, modeling and simulation: The relationships between measured quantities and desired parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3 FEARURES OF RADIOACTIVE DECAY AND THE IMPACT ON ACTIVITY AND CROSS SECTION MEASUREMENTS 29 3

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CONTENTS 3.1 The details of correcting data for radioactive decay . . . . . 31 3.2 Uncertainties introduced by radioactive decay corrections . 33 3.3 Comments on the status of radioactive decay half-life information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.4 Cyclic activation technique . . . . . . . . . . . . . . . . . . . . 34

4 THE NATURE OF NEUTRON SOURCES AND THE INFLUENCE OF NEUTRON SOURCE PROPERTIES ON ACTIVATION AND CROSS SECTION MEASUREMENTS 39 4.1 How neutron fields are produced . . . . . . . . . . . . . . . . 39 4.2 The energy range of interest for most technologies . . . . . 41 4.3 Basic characteristics of neutron sources . . . . . . . . . . . . 43 4.4 Integral neutron fields . . . . . . . . . . . . . . . . . . . . . . . 43 4.5 Differential neutron fields . . . . . . . . . . . . . . . . . . . . . 45 4.6 Correction of activation and cross section data for spectrum features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.7 Energy scale considerations associated with activation and cross section measurements-basic issues . . . . . . . . . . . . 48 4.8 determination of neutron energy spectra for differential measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5 NEUTRON FLUENCE MEASUREMENT AND STANDARDS 5.1 Absolute neutron fluence determination . . . . . . . . . . . . 5.2 Relative neutron fluence determination. . . . . . . . . . . . . 5.3 The hydrogen standard . . . . . . . . . . . . . . . . . . . . . . 5.4 Fission standards. . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Activation standards and neutron dosimetry . . . . . . . . .

57 57 59 60 61 62

6 SAMPLE PERTURBATION EFFECTS ON THE NEUTRON FIELD 69 6.1 Sample absorption and correction procedures. . . . . . . . . 69 6.2 Neutron multiple scattering and correction procedures . . . 71 7 MEASUREMENT OF SAMPLE ACTIVATION AND CORRECTIONS 79 7.1 Types of activity and radiations . . . . . . . . . . . . . . . . . 79 7.2 Principles of detection . . . . . . . . . . . . . . . . . . . . . . . 80 7.3 Standard sources . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.4 Calibration and standardization . . . . . . . . . . . . . . . . . 83 7.5 Sample absorption, scattering and related corrections . . . . 84 7.6 Sum coincidence effects . . . . . . . . . . . . . . . . . . . . . . 85 7.7 Detector deadtime and related perturbations . . . . . . . . . 86

7.8

Background and other interferences in measurements . . . 86

8 GEOMETRIC EFFECTS AND THEIR INFLUENCES ON ACTIVITY AND CROSS SECTION MEASUREMENTS 95 8.1 Finite sample size-typical sample shapes . . . . . . . . . . . . 95 8.2 Interaction between finite sample size and neutron field inhomogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 8.3 Finite sample size effects in activity counting . . . . . . . . . 96 8.4 Geometric effects in ratio measurements . . . . . . . . . . . . 97 9 CHEMICAL AND PHYSICAL PROPERTIES AND THEIR EFFECTS 9.1 Chemical impurities and related effects . . 9.2 Thermo-mechanical effects . . . . . . . . . . 9.3 Sample inhomogeneity and related effects . 9.4 Sample assay . . . . . . . . . . . . . . . . . . 10 STATUS OF THE DATA BASE TIONS 10.1 Experimental information. . . 10.2 Evaluations . . . . . . . . . . . 10.3 Directions for future work . .

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OF SAMPLES 101 . . . . . . . . . . 101 . . . . . . . . . . 102 . . . . . . . . . . 102 . . . . . . . . . . 103

FOR ACTIVATION REAC105 . . . . . . . . . . . . . . . . . . 105 . . . . . . . . . . . . . . . . . . 106 . . . . . . . . . . . . . . . . . . 107

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Chapter 1 Introduction and Overview 1.1

What role does neutron activation play in basic neuclear science?

1. Since atoms and nuclei are so small, all observations of neuclera static and dynamic properties are indirect. (a) Mainly it involves study of the interactions of electromagnetic radiation and particles with nuclei and detection of emitted particles and electromagnetic radiation from unstable nuclei

a + B → c + D∗ ; D∗ → E, E∗

(1.1)

2. Radioactivity is either natural (long-lived or cosmic ray induced) or artificial - produced by energetic reactions in the laboratory (reactors, accelerators, plasma devices, etc.). 3. Nuclei are said to be radioactive if the decay half lives are considerably longer than nucleon transit times within the nuclei, i.e., the time required for a nucleus to reorient itself into a lowest (stable) nuclear energy state. This time is ≈ 10−21 − 10−20 sec. (a) The range of nuclear lifetimes is enormous, i.e., ≤ 10−21 sec to ≥ 1010 years. 4. The existence of nuclei in excited states, either in nature or induced artificially, provides rich opportuinities for examining nuclear structures and dynamics. (a) The size of nuclear potentials and their strengths can be deduced indirectly from nuclear decay lifetimes, e.g., alpha decay. 7

(b) Level structures (excitation energies, spins, parities, etc.) can be deduced by observing the emitted photons, beta particles that are emitted as the nucleus reorients itself and emits excess energy as it seeks the lowest possible energy configuration. (c) The shapes of nuclei in various energy states can be deduced by the nature of the emitted radiation patterns (largely electromagnetic radiation), including anisotropies, emission strengths, radiation angular correiations, etc. (d) The nature of particle unstable states can be examined by observing delayed neutron emission following nuclear fission into highly excited fission product nuclei. (e) The behavior the nuclear fission process can be studied by examining the specific nature of the decay of highly excited but still particle stable fission fragments. (f) The decay of radioactive nuclei produced by artificial transmitation provides a mechanism for measuring nuclear reaction rates and thereby studying nuclear dynamics.

1.2

What role does neutron activation play in various applications technologies?

1. Radioactivity plays many roles, both beneficial and detrimental, in applied technologies. Here are just a few to consider: (a) Radiotherapy: Co-60 is used for cancer therapy. Radio-iodine is used for treating thyroid conditions, etc. (b) Medical diagnostics: radioactive materials are used for a variety of diagnostic purposes, e.g., locating tumors, cardiovascular studies, etc. (c) Nuclear waste: The presence of radioactivity in spent nuclear fuel, including both actinides and fission products, is a liability of the nuclear power option.We are still wresting with the technical, social and economic issues which are raised. (d) Reactor safety: The issue of reactor operational safety involves two main factors-criticality and shutdown afterheat. The latter problem has been responsible for most nuclear accidents (e.g., Three-Mile Island) and it is largely governed by the radioactivity of fission products. 8

(e) Measurements on radioactive byproducts from nuclear reactions provide a means for determining important reaction rates (e.g., cross sections). (f) Nuclear assay: A variety of complex radiochemical assay techniques are useful in measuring very small quantities of critical materials and impurities in materials, e.g., neutron activation analysis in forensics, airport security, etc. (g) Nuclear reactor dosimetry: The intensities, energy distributions and geometric profiles of neutron fields in fission and fusion reactors can be measured by observing the activities induced in specially selected foils of dosimeter material. (h) Radiation damage studies: Induced activities in materials irradiated in reactors can provide information that is useful in assessing radiation damage.

1.3

What are the basic considerations associated with neutron activation measurments?

1. The difficulty of ease with which various neutron activation measurements can be made in the laboratory depends on several factors: (a) Neutron flux intensity: If it is too low, insufficient activity will be produced for convenient measurements. If it is too high, the samples will be too “hot”, detectors will be "swamped", etc. (b) Impurities and competing activities: If one is looking for a weak activity in the presence of competing activities which complicate the spectrum and affect statistics, or if the presence of impurities complicates identification of the origins of the observed activity (e.g., 511-Kev annihilation radiation from plural origins), then accurate measurements are difficult. (c) Background: The presence of background radiation can have multiple effects-it can interfere with the radiation observed (peak obstruction). It can contribute to poor statistical accuracy (when a small peak "sits" on a continuum background, etc. 9

(d) Due to detector limitation, radiation absorption, and the basic nature of the radiation ineractions with matter, some activities are much more difficult to measure than others. i. Photons: 100 KeV - 2 MeV (realatively easy) < 100KeV (moderately difficult, absorption, detectors) > 2MeV (progressively difficult, complex detector interactions). ii. Betas: Generally difficult to measure accurately. Continuous spectra, absorptionand scattering perturbations. iii. Alphas: Not too difficult to measure for very thin samples. Essentially impossible for thicket samples. Can detec accumulated helium if the concentration is high enough (HAFM). (e) Half life: N = N0 e−λt . Law of radiactivity decay. A = abs(dN/dt) = λN0 e−λt . Short half life → large λ → A large for short time. Long half life → small λ → A small for a long time. (f) This affects ease of measurement in several ways: i. Very short half lives are hard to measure by conventional techniques because it is not possible to build up adequate statistics. However, background is not a problem. ii. Very long half lives are difficult to study because activity is low. Need very efficient detectors. Background interference is a real problem. Need low background counting facilities. (g) half life < 1 minute. Need special techniques, e.g., cyclic activation. i. half life from 1 minute to 5 years. This is the range of conventional activation measurments technique. ii. half life > 5 years. Need special techniques, e.g., chemical separations, high-efficiency detectors, low-background counting, etc. (h) Detectors: There is a wide variety-limited only to the cleverness of the experimenter. Basically, all involve detection of induced ionization energy in the form of collected charge or emitted light. i. Gaseous ionization chambers (collect charge). 10

ii. Scintillation detectors (light is produced and then detected by photo multiplier tubes or equivaient photosensitive devices that convert light to charge). iii. Solid state ionization detectors (collect charge). (i) The issues are: i. Efficiency. high efficiency is generally desirable but only if the signal-to-background ratio is enhanced or at least is maintained at an acceptable level. ii. Resolution: Good resolution aids in discriminating the desired radiation from what is unwanted. iii. Intrinsic discriminatory power - some detectors, e.g., geiger counters, respond in about the same way to most radiations, while others, e.g., Ge detectors, have a high degree of discriminatory power. iv. Cost, stability, ease of use, etc., are also factors to consider. (j) Sample material: The nature of the sample has a strong impact on ease of activation measurements. Some of the issues are: i. Purity: Pure materials offer fewer possibilities for competing activities. Sample mass is easily determained. ii. Chemical properties: Stable, non-toxic, non-explosive, nonhygroscopic, etc. Need for encapsulation? Effect or activation of other elements of the compound. Well defined stochiometric properties, i.e., determination of precise content of the element considered. iii. Physical properties: Powder, liquid, gas, metalic, melting point, boiling point? Determines ease of preparing activation samples, applicationsin high temperature environments (reactor) or low temperature environments (cryostats, space, etc.). iv. Homogeneity and other geometric properties: Since radiations from radioactive materials are absorbed to varying degrees, it is important that a sample be homogeneous and possess a well defined geometry [See Fig. 1.1, On Page 16]. (k) Decay scheme properties: Detailed and precise knowledge of the parameters of the radioactive decay process, including energies, branching factors, angular distributions, etc., is generally needed in order to make accurate activation measurements. Much of this information is either lacking, known with 11

poor accuracy or just plain wrong. This is especially true for very long-lived activities or for short-lived activities far from the line of stability on the chart of Nuclides. (l) The accuracy levels to which radioactive decay parameters need to be known depends upon how they are used. If knowledge of the activity over a range of several half lives is requried, then the decay constant needs to be well known because the effect of the error is magnified. (m) If the reaction rate is very small, then measurements are difficult because of poor statistics, interfering activities, etc. If the reaction rate is large, the activity may be too large to measure and a waiting period is requried before counting. Chemical separations and low level counying facilities are useful techniques for handaling small reaction rates and low activities. (n) Radiation absorption and scattering: The interactions of primary radiations (e.g., neutrons) with the sample to produce the activated nuclei, and the interactions of secondary (decay) radiations with the same sample have an influence on the measurments.

1.4

Integral versus differential measurments. What are the issues?

1. A distinction is commonly made between integral and differential measurments. Let’s understand what is meant. (a) Differential measurments are made using neutron fields which are approximately monoenergetic, or at least the dominant neutron yield falls in a narrow energy band. EXAMPLE D(d, n) neutron source. Approximately monoenergetic deuterons [See Fig. 1.2, On Page 16]. (b) Broad, continuous spectra emerge from 3-body "bresakup" reactions whereas "monoenergetic" neutron always come from 2-body reactions. (c) Li-7 (p.n) Be-7 is not a truly monoenergetic reaction, even discounting the breakup continuum component. This is because, except at the lower few hundred KeV of energy, there are two 12

distinct neutron groups. However the high-energy group (n) is dominant at all energies. (d) Usually, for "monoenergetic" sources the yield of higher energy neutron is discrete while the continuum neutrons have lower energies. This allows a "bootstrap" approach to differential measurments which we will discuss later in more detail. R i. Y ∼ σ(E)φ(E)dE+σ(E0 )φ(E0 )There is a discrete and continuum term in the yeild R equation. Therefore, σ(E0 ) ∼ [Y − σ(E)φ(E)dE]/φ(E0 ). ii. In this analysis, φ(E) is the breakup spectrum, σ(E) in the vicinity of of φ(E) is known from work, at lower energy. φ(E0 ), relative to φ(E), is known as. So... σ(E0 ) is determained. This is roughly the idea. In reality, things are more complicated. (e) Integral sources are continuum sources with no pretense at having a dominant neutron energy. - Nuclear reactors (fission spectra). Photo-nuclear sources. - Thick target sources. - Spallation sources. ...etc. EXAMPLE Two common integral spectra which are widely encountered in applications: [See Fig. 1.3, On Page 16] R (f) The yeild equation is given by Y ∼ σ(E)φ(E)dE. No attempt is made (or is possible) to identify and separate the yeild for a dominant neutron energy. (g) Differential measurements with quasi-monoenergetic neutron sources can yeild fairly detailed information about the energy dependence of a cross section. EXAMPLE Typical measurement of differential cross section. [See Fig. 1.4, On Page 17]. (h) A single integral measurement can provide practically no information about the shape of a cross section. If the shape is well known, an integral measurement can fix the normalization. (i) A sequence of integral measurments in diverse spectra can provide shape information by statistical unfolding. Here is how: [See Fig. 1.5, On Page 17]. 13

(j) Main point: The response function φσ has a different shape for a fixed σ and various φ. Different regions of σ(E) are R "examined" by the integral data I = σφdE. (k) The method of unfolding would-in principle-be capable of giving a lot of information about differential cross sections. The main problem lies in the nature of the integral (continuum) neutron fields. There is limited variety and hence limited capacity for selectively "examining" the different energy regions of the differential excitation function.

1.5

What is the status of development of the techniques associated with neutron activation measurements? What are the limitations?

1. The techniques are well developed-for the most part-but there are some serious organizational problems that affect the ability for needed work to be accomplished. (a) The techniques are so diverse that no one laboratory has the developed capabilities to address them all. (b) There is limited cooperation and collaboration between various labs in addressing those complex problems. This happens because of national boundaries and the tightly controlled nature of program funding in most countries. (c) Some of the useful techniques are actually being lost because of lack of use, program reductions, etc. Among the victims: - Coincidence measurement procedures. - Radiochemical separation techniques. - Precision beta counting ...etc. 2. Many of the fundamental measurements that remain to be made of cross sections and decay properties (half lives, level schemes, branching, etc.) could be accomplished using existing techniques. But there are problems: (a) The key problem is a lack of motivation in both the basic research and technology sectors of the scientific establishment. 14

- Basic nuclear scientists are interested in other areas (e.g., heavy ion physics, mesons, etc.) - Applied scientists are bound by restrictive programmatic endeavors and are allowed little leeway to address such matters. (b) Also, there is a critical shortage of manpower. Skills, interest, etc., are being lost as a generation that developed the field in more "prosperous" times move into retirement. (c) The computer has moved onto center stage, replacing experimental science as the main attractive force in program definition. Analytic work is drawing the attention of more and more young scientists. 3. There are some areas where development of new capabilities and techniques would benefit neutron activation work. At present these are limitations: (a) More intense, tailored accelerator neutron sources would enable investigations to be carried out for both shorter and longer half lives, for reactions with small cross sections, for a wider range of energies, for very rare sample materials, for rare isotopes, etc. (b) More work is needed to refine the techniques of cyclic activation for short half-life studies, particularly using pulsed accelerator facilities.

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Figure 1.1: Sample Geometry

Figure 1.2: Neutron spectrum of D(d, n) Neutron source.

Figure 1.3: Two common integral spectra which are widely encountered in applications.

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Figure 1.4: Typical measurement of differential cross section.

Figure 1.5: A sequence of integral measurments in diverse spectra.

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Chapter 2 BASIC ISSUES ASSOCIATED WITH THE MEASUREMENT OF NEUTRON REACTION RATES, ACTIVITIES AND CROSS SECTIONS 2.1

The formulas used for cross section and reaction rate detrminations

1. There is obviously a limit as to how much detail can be discussed on such highly technical matters during this lecture. The intent here will be to outline the the key issues and show some of the formulas used in the analysis. 2. The basic definition of a cross section is our starting point [See Fig. 2.1, On Page 27]. (a) We will assume the following: i. ii. iii. iv.

Parallel beam of monoenergetic neutrons. Very thin sample (homogeneous)-a foil. Mono-elemental, mono-isotopic sample. Uniform (constant) neutron fiuence.

Let Y = number of reaction product atoms produced. n = number of sample atoms per cm3 . σ = cross section. φ = neutron fluence 19

per cm2 incident on the sample (normally incident). A = sample area. X = sample thickness. The reaction is A(n,X)B. This leads to the formula.

Y = φAXnσ (basic formula for the cross section)

(2.1)

(a) The important point is that in this very simple model, all the parameters scale multiplicatively, e.g., double the flux φ double the yield of the reaction product B. (b) This simple formula is the starting point for all analyses involving neutron activation cross sections, reaction rates, etc. i. I know. I have written it down myself countless times. ii. All realistic analyses, no matter how complicated, are merely embellishments on the formula. (c) This approach applies to reaction processes involving other incident radiations, e.g., photons and charged particles, but we will limit this lecture to neutrons.

2.2

Magnitudes of the various observable parameters and limitations which they impose .

1. Let’s look at the formula Y = φAXnσ and put in some typical numbers. EXAMPLE-1: Suppose the material has density 5gm/cm3 and mass number A=30. Then, each atom weighs ≈ 30 × 1.6 × 10−24 gram = 4.8 × 10−23 gram. So, n = 5/(4.8x10−23 ) ≈ 1 × 1023 atoms/cm3 . For conveinience, let A = 1cm2 and x = 0.1 cm. his is thin enough sT the neutron absorption is pretty small unless the cross section is very large. This means the sample has ≈ 0.5 gram total mass. Let us suppose that σ ≈ 100 millibarn. i.e., σ = 100 × 10−3 × 10−24 cm2 = 10−25 cm2 . Let us consider Y/φ = AXnσ = (1)(1 × 1023 )(10−25 ) = 0.001. This is an interesting number. It states that only 1 out of every 1000 neutrons passing through this particular sample ever interacts with the sample to cause a nuclear reaction. 20

(a) It takes a lot of neutrons to activate a sample of material. Most are wasted. Fortunately, neutrons are pretty abundant from reactors and accelerators. i. From an accelerators, one can obtain, typically, fluxes in the range ∼ 106 to 1013 n/sr/sec fairly routinely, depending upon the size and type of accelerator, energy range, etc. Some accelerator concepts have been developed or proposed that offer fluxes up to ∼ 1014 to 1016 n/sr/sec. ii. From a reactor, one is typically able to obtain much higher fluxes, say ∼ 1013 to 1016 n/cm2 /sec or even higher. Notice that for a reactor we have used different units for flux. A reactor is not a point neutron source whereas most accelerators are. iii. We reconcile these differences in units by considering 1 n/sr/sec to equal 1 n/cm2 /sec at a distance of 1 cm from the point source. EXAMPLE-2: Following up on the preceding example, suppose that the measurement was made with a flux of ∼ 109 n/cm2 sec. Then Y ≈ (0.001)(109 ) ≈ 106 reaction product atoms/sec produced. Run for ≈ 103 sec (≈ 2.8hours). Then, Y ≈ 109 total number of reaction product atoms. Thus Y/(A × n) = 109 /[(1)(0.1)(1023 )] = 10−13 . Thus, the fraction of atoms in the sample which are transmuted by neutron induced reactions is indeed almost minuscule compared to the total number of tartget atoms present in the sample.

2.3

The need for data corrections and the procedures used .

1. Obiously, the model above is far too simple to provide a realistic realtionship between cross section and the other parameters which enter into consideration. Corrections must be made to the data and new parameters, etc., time-related ones, must be introduced. (a) In general, the correction procedures involve mathematical simulation of the physical situation at hand, making use of differentials. integrals, factoring, etc., in order to extract what is truly desired fromm what is measured. 21

i. There is no unique way to approach these issues. ii. Computer analysis is required in order to carry through the details in a practical way. (b) Here are some of the more common issues that must be examined: i. Neutron absorption when the sample is not thin. Flux depression. ii. Nuetron multiple scattering must be considered when neutrons interact through neutron emission processes within the sample or nearby before the reaction takes place. This perturbs the neutron field. iii. Neutron flux anisotropy or inhomogeneity (a particular problem with point sources). iv. Decay of radioactive reaction products(half life). v. Absorption and scattering of decay radiation. vi. Detector efficiency for measuring decay radiations. vii. Decay radiation sum coincidence effects. viii. Sample impurities. ix. Background radiation and interfering radiations. x. Neutron spectrum properties. xi. Detector deadtime effects. xii. Various geometric effects. xiii. Features of the decay scheme for reaction products. xiv. Loss of sample material. xv. Standard cross sections for neutron fluence measurment.

2.4

What are the important measurements to make for applications? The issue of sensitivity

1. Ideally, one ought to know with very good accuracy all of the decay schemes, half lives and cross sections which figure in nuclear applications. In practice, this never has happened and probably never will. (a) Realistically, scarce and expensive resources will be focused to perform measurements on the most critical nuclear parameters, 22

i.e., the scope of work is narrowed by the following considerations: i. What technologies require the data? Reactors, fusion, medical diagnostics and therapy, nondestructive assay, etc.? ii. What particle and energy range is important? e.g., for reactor physics, the neutron is important and the energy range is from thermal to a few MeV (< 10 MeV anyway). For fusion, the interest is in charged particle and neutron reactions. For neutrons, 14-15 MeV is an important range, though lower energies need also be considered. iii. What materials are important, e.g., for reactors we need to consider the fuels (actinides), fission products, structural materials, dosimetry materials, shielding, etc. Likewise for fussion. iv. Which isotopes are important? Abundance is an important consideration, but that must be weighted by the cross sections and important of the reaction product or secondary radiations produced. v. The generation of nuclear waste is a factor in activation data requirements. Long-lived, low-level activities dominate the storage concerns for waste depositories after a few years. vi. Cross section for producing activities must be considered in assessing the importance of nuclear reactions. 2. Even if a particular process is potentially relevant to a certain technology, we must examine how critical the dependence of that technology actually is with respect to the process in question, i.e., the issue of sensitivity must be considered. Example Dosimetry reaction. Fission spectrum. respose function. [See Fig. 2.2, On Page 27] (a) The integral response I to differential cross section σ in spectrum φ is trhe shaded area under the curve. There is relatively little sensitivityof I to the details if either σ or φ at the higher energies. Neither σ or φ need to be very well known in this region. The critical region is near threshold. This region is also the most difficult to measure differential σ. 23

2.5

What are the factors which limit the achivable accuracy for activation and cross section measurements?

1. Technique and care for the details of experimental measurements is essential to coax the best data possible from an experiment. However, even if all precautions are taken, there are certain aspects of modern experimental measurement procedure which limit ultimate achievable accuracy. Here are a few important error sources: (a) Statistics. This is not a problem for experiments with high count rates, but in measuring very short half lives where the activities die away rapidly, or for very long half lives where the true event rate is low, and must be separated from background, it is an unavoidable problem. (b) Neutron fluence measurment and standard cross sections. Very few activation experiments involve absolute neutron fluence measurements. Usually, a cross section ratio is measured. Then, two factors enter: (1) the accuracy of the standard cross section. (2) the manner in which the ratio is determained. There are enough differences in the unknown and standard sample irradiations, e.g., geometry, absorption factors, energy differences, etc., that errors creep in. (c) Energy scale uncertainty, espicially near threshold. If σ = σ(E), ∆σ = (∂σ/∂E)∆E. This is very difficult to estimate because ∂σ/∂E and ∆E are speculative in many experiments in just the region where the greatest sensitivity is encountered. (d) Neutron field perturbations. Neutron absorption and multiple scattering effects are sample geometry and mass dependent. Under certain conditions, these effects can be substantial. Sometime it is possible to measure this effects, but such approaches inevitably involveother perturbations, e.g., geometric once which must be separated out. Usually they are calculated. i. Calculations involve scattering and absorption cross sections which are incompletely or inaccurately known. ii. Modeling involves various geometric and energetics approximations which lead to inaccuracies. (e) Detector calibrations. Again, very few absolutely calibrated detector systems are used in experiments. So... calibration 24

standards are required and this leads to error. Furthermore, the conditions of the actual measurements (energy, geometry, etc.) are usually enough different from the standard measurement used to establish the calibration that errors arise. (f) Fundamental nuclear constsnts. Most measurements of activation processes draw upon such basic data as decay half lives, level excitation energies, decay branching factors, etc. Knowledge of these parameters is uncertain to varying degrees and this impacts upon the activity measurements. (g) Time. This is a strange one, but ultimately the time available to do an experiment limits the achievable accuracy. Shortcuts have to be taken in deriving complex corrections. There are limits on the number of repetitions of a particular measurement that are feasible.

2.6

Numarical analysis, modeling and simulation: The relationships between measured quantities and desired parameters

1. The anatomy of a typical correction: (a) Let’s look at a fairly simple correction, namely, neutron absorption for a simple slab geometry, monoenergetic neutrons, homogeneous material, uniform and normally incident neutron flux.

Basicformula : Y = φAXnσ (see above) ∆X = X/m, Xi = (i − 1)∆X

(2.2) (2.3)

Absorption factor for layer i:

ηi = exp(−nσt Xi ) where σt = neutron total cross section. (2.4) ∆Yi = φηi A∆Xσ. Yield from ith layer. 25

(2.5)

Therefore

Y = Σi=1,m ∆Yi = Σi=,m φηi A∆Xσ = φAXnσ[(1/m)Σi=1,m ηi ] = φAXnσ < η > .

(2.6)

i. So... the correction factor for neutron absorption in the sample is a multiplicative factor Fa =< η >, equal to the average absorption in the sample, i.e.,

Y = Fa (φAXnσ)

(2.7)

2. Even though data corrections are usually not calculated that way, it is possible, through mathematical manipulations, to represent most for the important data corrections as multiplicative factors. Thus,

Y = (Πk=1,q Fk )(φAXnσ)

(2.8)

3. The most fundamental problem with all of experimental science is that one can never measure exactly what one needs to know and, furthermore, the act of measurement itself perturbs the system being observed.

26

Figure 2.1: Schematic diagram of cross-section measurement.

Figure 2.2: Dosimetry reaction, fission spectrum and reaction function.

27

28

Chapter 3 FEARURES OF RADIOACTIVE DECAY AND THE IMPACT ON ACTIVITY AND CROSS SECTION MEASUREMENTS The basic nature of radioactive decay. 1. Radioactive decay is exponential in nature. This follows directly from the nature of poisson statistics. (a) Poisson statistics applies because each decay is an independent event and decay is usually a rare event. Remember from a preceding example that the number atoms in a sample which are active is relatively very small in a much larger matrix of stable atoms. However, what really counts is that the probability of a single atom decaying in a small time interval (small compared with the half life) is usually very small. Let λ = decay constant. The probability that no decays will occur from time 0 to t, followed by a single decay from time t to t + ∆t, where ∆t << (1/λ), is given by

∆p = [(λt)0 exp(−λt)/0!][(λ∆t)1 exp(−λ∆t)/1!] ≈ λexp(−λt)∆t.

(3.1)

This is obviously the exponential decay law, with λt the mean number of decays in time t, or λ the mean number of decays per unit time. 2. Limitations imposed by various ranges of half life. 29

(a) Let B be the formation rate (atoms/sec) of radioactive reaction product atoms in a sample during steady neutron bombardment. At t=0, the sample is not radioactive, N(0). i. The differential equation govering this process is

dN/dt = B − λN

(3.2)

The first term deals wuth the formation of active atoms through nuclear reactions. The second term deals with their decay. ii. The solution N(t) which satisfies the requirment N(0) = 0 is N(t) = (B/λ)[1 − exp(−λt)]. This equation is the basis for examining the major limitation of the measurement process, namely, the limited availability of radioactive atoms whose decays are to be measured. The appearance of the solution is shown in the following sketch: [See Fig. 3.1, On Page 36] iii. For large t, N(t) saturates at B/λ. for very small t, N(t) ≈ BT . iv. The deacy constant is a scale parameter which scales time. 3. Suppose λ is very large (short half life). Than, the saturation atom density for a given formation rate is relatively small. It is like pouring water into a container with a hole in the bottom. The steady state level of water will be low! [See Fig. 3.2, On Page 36] (a) When B/λ is small, then the maximum number of decaying atoms which can be measured subsequent to discontinuation of the radiation is small, even if the counting covers several half lives. Let te be the exposure time, with te λ >> 0. Then, N(t) = (B/λ)exp(−λt) for t > te and dN/dt = -Bexp(−λt). Although initially the disintegration rate is B, it drops fast and not many counts can be recorded in total. 4. If λ is very small, then B/λ is large, but N(t) ≈ Bt for all times up to t = te , the exposure time. The longer te , the more active atoms reside in the sample, i.e., activity is proportional to irradiation time if B is constant. (a) When Bλ is large, then for t = te , N(t) = Bte , and for t > te , N(t)Bte exp(−λt) and dN/dt = −Bte λexp(−λt). So, the 30

disintegration rate for a given te gets smaller as λ decreases. Then, problems arise in counting (background, etc.). 5. There are obvious limits to the exposure times and counting times of neutron activation studies, but they can cover broad ranges from seconds to years depending on the experiment. Ultimately, low count rates (with attendant background) or too low a number of total activated atoms, are the origins of limitation in these experiments. λ is fixed by nature. To mitigate the problem, we need B as large as possible.

3.1

The details of correcting data for radioactive decay

1. First, let us relate the number of actual counted atoms Nc during count time tc to the total number of activated atoms Y produced during an irradiation at steaby state flux for time te . The sample “cools ”for a time tw after irradiation. The time record is: [See Fig. 3.3, On Page 36] (a) The basic expression is

Y = (Nc /)T (λ, te , tw , tc )

(3.3)

Where it is assumed that  combines both detector efficiency and activity decay branching factors. No deadtime effects, sum-coincidence effects, or other perturbations should influence the counting in this formalism. T is the correction fator which corrects Nc/ for decay effects. (b) The formula for T is:

T (λ, te , tw , tc ) = λte [1 − e(−λte ) ]−1 e(λtw ) [1 − e(−λtc ) ]−1

(3.4)

2. In reality, the formation rate often cannot be considered essentially constant during the irradiation because of various facility perturbations. This is especially true for accelerator neutron sources. Let’s consider a variable formation rate and discuss how to treat that scenario. (a) Approximate true situation by a series of histograms [See Fig. 3.4, On Page 37]. 31

3. If we adopt a histogram approximation, we can apply the basic formula above a number of times (n) and rely on the principle of superposition. Again, wait time tw and count for time tc after t = te . (a) Let Qi be the fraction of the total fluence delivered during time interval ∆ti = ti − ti − ti − 1. Require that Σi=1,n Qi = 1 for proper normalization. Also, let = te − ti . (b) Then, we can show that

Y = A(te )[Σi=1,n Qi ∆ti ][Σi=1,n Qi [1 − e(−λ∆ti ) ]e−λti ]−1

(3.5)

Where

λ (3.6) A(te ) = (Nc )exp(λtw )[1 − exp(−λtc )]−1  i. This formula is somewhat more complicated than before but not decidedly so. It reduces to the previous formula when n = 1.

4. No detector recording system is able to process a high incoming signal rate without losses. At very high count rates, the analysis can be complicated but basically there are two effects to consider: (a) Analog pulse pileup. Signals have a finite duration in detector circuitry. If they arive to close, they add (“pileup ”). This lead to spectrum distorations and loss of true events (e.g., pulses are thrown out of the full-energy peak of a Ge detector). We shall not deal further with this effect, but it must be sought by looking for spectrum distortions during data taking. (b) Simple deadtime of a spectrum recording device (e.g., multichannel analyzer) comes about because the circuitry is paralyzed for a short while when a signal is being processed (“deadtime ”) [See Fig. 3.5, On Page 37]. i. Most modern multicahnnel analyzers keep track of “clock time ”and system “live time ”. Livetime = Clocktime Deadtime. Deadtime = n∆t, where ∆t is the deadtime during each pulse processing, while n is the number of counts during the count time interval from t = “start ”to t = “stop ”. (c) Let tc = clocktime and t1 = livetime. Then a new data correction factor is needed. We have to write.

A(te ) = (Nc λ/)e(λtw ) [1 − e(−λtc ) ]−1 d. 32

(3.7)

where −1

d = 1−λλ0 (tc − t1 )[1 − e(−λtc −λtc ) ](λ + λ0 )[1 − e(−λtc ) ][1 − e(−λ0 tc ) ] (3.8) is a correction factor that accounts for the fact that tc > t1 . In this formula, we note that λ is that decay constant for the particular activity we are interested in while λ0 is that decay constant for the dominant activity affecting the detector deadtime. These may be the same or different. If λ0 is time dependent, becouse there is no single dominant activity, then things are much more complicated. Numerical integration is needed.

3.2

Uncertainties introduced by radioactive decay corrections

1. For the most part, the models used to provide decy corrections (formulas, etc.) are very realistic. There is no reason why they should not be since the fundamental nature of decay (poisson statistics and exponential history) is well substantiated. In correcting data, approximations should not be made in this realm of perturbations because there is no need to do so. Computers can be used to model the decay accurately, if need be. So... there is no cause for model error here. 2. The uncertainties due to decay effects must than come mainly from the parameters which appear in the formulas above. They can be estimated from error propagation using a computer. (a) λ, λ0 : Sensitivity to λ is significant, particularly if te , tw , tc ≥ (1/λ). Sensitivity to λ0 enters only if t1 differs significantly from tc . Effect is not necessarily linear-often it is not. (b) te , tw , tc : These can be measured quite accurately if the experimenter takes precautions. Usally, they are not a source of significant error unless any one is very small and λ is very large. 33

3.3

Comments on the status of radioactive decay half-life information

1. One would think that half lives for most known radioactive nuclear species are well known. The truth is that there are many regions in the chart of the Nuclides where unacceptable half life uncertainties persist. (a) This truth emerged recently from a comprehensive examination at Argonne National Laboratory of nuclear data for fusion energy applications. (b) Let’s list some reasons why half lives are not known well. i. Rare isotopes that are not produced easily. ii. Very short lived species relatively far from the line of stability. iii. Difficult decay properties (radiations are hard to detect, etc.). iv. Very long hlaf lives not amenable to measurement. v. Simple lack of interest or attention. 2. The international ENSDF project addresses such issues, bur progress is modest because of limited (actually shrinking!) resources to do the work. Also, inflow of new data is limited because of declining nuclear programs world-wide, e.g., in the U.S.A., Europe and Japan. 3. Knowledge of the decay half life affects many other areas of nuclear science and technology: standards, cross sections, waste storage, personnel radiation dosimetry, decay after heat in reactors, etc.

3.4

Cyclic activation technique

1. We have indicated that when the half life is very short, the maximum number of activated atoms that are present in the sample, when the production rate is B, is B/λ (saturation). Short half life implies large λ, B/λ is small. (a) In a single irradiation it is usually not possible to build up enough concentration of active atoms to make measurements feasible-the measured yield will simply be too low. 34

2. A technique known as cyclic activation allows for repeated irradiations with periods of counting in between. This is best applied when the half life is of the order of a few seconds or less. There are two basic methods: (a) Pulse the sample i.e., move the sample into a neutron field, irradiate brifly, transport to counter, count for a while, then repeat the cycle. Usually this involves a shielded source, shielded detector and “Rabbit ”for transport. Commonly used in reactor environments or 14-MeV generators [See Fig. 3.6, On Page 37]. (b) Pulse the neutron source! This requires a pulsed accelerator to produce the neutrons. A pulsed charged particle beam on a neutron producing target yields neutron pulses. Duration is usually a few milliseconds up to a few tence of milliseconds. during the quiet period between pulses, allowance is made for a “cooling ”period followed by a short count and dealy time to reset the system. The detector (or source) must be shielded for this work to avoid detector damage (or pulse overload). The approach works best for measuring gamma-ray activity [See Fig. 3.7, On Page 38]. 3. The advantage of cyclic activation techniques is that no matter how short the half life (within practical limits), sufficient data can be accumulated by the detector to yield good statistical precision. All that is required is to run enough cycles. The only disadvantage is that the experiments are more complicated, more equipment is required, and the data analysis is more difficult. (a) We shall not delve into the details of the data analysis, but the concepts have already been discussed. Mainly, one needs to carefully handle the time histories.

35

Figure 3.1: Basic nature of radioactive decay.

Figure 3.2: Illustration of saturation atom density for a given formation rate.

Figure 3.3: The time record of irradiation, wait and counting time.

36

Figure 3.4: Approximate true situation by a series of histograms.

Figure 3.5: Correcting data for radioactive data.

Figure 3.6: Shielded source, shielded detector and “Rabbit”for transport.

37

Figure 3.7: Pulsed neutron source.

38

Chapter 4 THE NATURE OF NEUTRON SOURCES AND THE INFLUENCE OF NEUTRON SOURCE PROPERTIES ON ACTIVATION AND CROSS SECTION MEASUREMENTS 4.1

How neutron fields are produced

1. Neutrons do not exist free in nature. They must be produced by nuclear reactions. Typically, the binding energy of a neutron in a nucleus is ≤ 10 MeV. That is not to say that 10 MeV of energy is required to release every neutron. Were that true, there would be no nuclear power! (a) In fact, many neutron producing reactions are exoergic, i.e., they produce energy. i. Some examples are: U − 235(n, f) → Fission products plus nu-bar neutrons (nu-bar is ≤ 3). Be − 9(d, n)B − 10.... (b) Neutrons themselves are responsible for releasing other neutron through certain nuclear reactions. e.g., Co− 59(n, 2n)Co− 58, U, Pu, Np(n, f)F.P. neutrons, etc. (c) Let’s look at some nuclear reaction processes that produce neutrons, but within the context of specific applications and 39

technologies. Doing this will provide us with a framework for thinking about what otherwise is an incredibly complex pattern of possibilities: i. Accelarator neutron production [See Fig. 4.1, On Page 51]. ii. Some of the more common “monoenergetic”sources A. Li-7(p,n)Be-7 B. H-2(d,n)He-3 C. V-51(p,n)Cr-51 D. H-3(d,n)He-4 iii. Intense sources of continuum neutron fields A. Be-9(p,n) thick target B. Be-9(d,n) thick target C. Li-7(p,n) thick target D. Li-7(d,n) thick target E. e− + Ta,W,U → γ + Ta,W,U → n (photoneutrons) F. p + Ta,W,U → n (spallation) iv. As a basic rule, accelerator neutron sources are net users of energy. Their purpose is to produce well defined neutron fields for research purposes. However... v. Schemes have been proposed for spallation neutron production on subcritical actinide target assemblies that, in principle, are capable of producing net energy, e.g., p + U,pu,Th→ n + U,pu,Th → nu-bar neutrons + F.P. This concept is undeveloped but is being proposed by Los Alamos National Laboratory. (d) Fission reaction neutron production. i. Reactions of the form n + Fissionable material → nu-bar neutrons + F.P. can produce more neutrons than consumed and, if a critical mass is present of the fissionable material, will lead to self-sustained neutron production at a steady state plus net energy release. This is the basic principle of a nuclear reactor. (e) Fission reactors are the most prolific neutron sources which have been developed so far on Earth. However, there is not much latitude in the spectra which can be produced [See Fig. 4.2, On Page 51]. 40

(f) Reactor spectra are degraded by inelastic scattering to energies considerably lower than a pure fission spectrum. There is noy much latitude available for tailoring fission reactor neutron spectra because of the fixed nature of the source term! Almost all interactions which alter the primary spectrum lead to its degradation in energy. (g) Secondary neutron sources. i. A number of reactions of the general category A(n,n)A, A(n,n0 )A∗ and A(n,Xn)B influence the neutron field in a neutron radiation environment. Elastic scattering is a mechanism for transport, energy degradation and energy conversion. Inelastic scattering is a primary mechanism for energy degradation and energy conversion. The (n,2n) reaction is important because it helps to make up for the neutron losses which occur due to (n,γ), (n,α), (n,p), etc.

4.2

The energy range of interest for most technologies .

1. It is important in the study of neutron activation processes that we consider what areas are important for technological applications so we can limit our research attention accordingly. (a) There are a lot of known nuclei: ∼ 106 known elements, many isotopes for each elements (including radioactive ones). (b) Each element is capable of undergoing a wide range of interactions from (n,γ) capture to fission and/or spallation. (c) The energies we can be concerned with range from sub-eV to TeV (1012 eV). 2. Nuclear fission: In principle, the concern is for neutrons from subeV to ∼ 200 MeV. But... in practice the greatest interest is in the range from thermal to a few tens of KeV, with secondary interest extending to perhaps ≤ 10 MeV. Beyond 10 MeV, there are so few neutrons present that there are only a few possibilities for concern. This is true to some extent even for fast reactors. 41

3. Nuclear fusion: The source reactions for fusion that are being considered are H-3(d,n)He-4 and H-2(d,n)He-3. The former releases ∼ 16 MeV of energy with about ∼ 14 MeV going to the neutron. The latter releases ∼ 3.3 MeV with ≤ 3 MeV going to the neutron. This is for incident deuterons of plasma temperatures (∼ KeV to 10’s of KeV). Other source reactions have been suggested but they won’t be exploited in our lifetimes. In the most critical regions of fusion devices (first wall, blanket, multiplier, etc.) the mean neutron energy is much higher than that for a fission reactor (several MeV). Farther away from the plasma, the spectrum of neutrons is degraded so that it is much like a fission reactor spectrum and similar engineering problems are encountered. 4. Biomedical-isptope production: Most isotope production occurs either by using charged particles from acceleators for transmutation or thermal neutrons from a reactor. (a) For accelerators, C.P. + Target → Radioisotope. The C.P. energy range is typically 10-100 MeV, and it is chosen empirically to optimize the yield of the desired radioisotope. (b) In reactors, capture reactions, (n,γ) arehe main source for isotope production. A(n,γ)B∗ → c∗ + X. Either B∗ is desired, or a daughter product C∗ from the decay of B∗ . What is of interest here are the thermal and resonance region energies up to a few KeV. 5. Biomedical-neutron therapy: Neutron therapy is not all that common. It is carried out only at a few hospitals and research centers with the special facilities to do so. In general, fast neutrons are desirable because of their greater penetration and less disruptive effects on healthy tissues. The interactions of primary interest are elastic and inelastic scattering and the energy deposition (Kerma) which this entails. An exception is born capture therapy with thermal neutrons. Boron (B-10) is ingested, migrates selectively to tumors, then n + B − 10 → α + Li − 7. The α’s are quite energetic, have a short range, and generally release their cell-destructive potential in a very localized way. The yield is optimal at thermal neutron energies. 6. Space applications: The concern is mainly for personnel in space who are exposed to solar and cosmic radiations. The needs here 42

are really rather poorly established but may represent an area of some interest in the future.

4.3

Basic characteristics of neutron sources .

1. In the determination of cross sections, in the apllication of of neutrons to various technologies involving irradiations, and in the operation of nuclear devices such as fission and fusion reactors, we are required to consider various features of neutron sources in the analysis. Here, we define these consideration for the sake of future discussions: (a) Energy spectrum: If we examine a small region space and consider all the neutrons which pass by, generally we find that they are not all of the same energy for a combination of two reasons. i. The source processes which give birth to neutrons produce them at varying energies rather than at a unique energy. ii. Elastic and inelastic scattering of neutrons leads to broadening of the spectrum toward lower energies than at their origin. iii. The degree to which the energy spectrum of a neutron field in a particular region is relatively broad or narrow has traditionally been the basis for assigning the labels “integral ”or “differential ”to the spectrum.

4.4

Integral neutron fields .

1. Let us consider what are typically referred to as integral fields: (a) Fission reactor neutron spectra: At birth, the neutrons are emitted in a continuum spectrum which closely resembles a Maxwellian energy distribution with average energy ∼ 2 MeV (depending on the fissionable element). 43

i. The source term spectrum qualifies as an integral spectrum, with neutrons present from the eV range to over 200 MeV (though very few are at these extremes). ii. Elastic and inelastic scattering plus (n,2n) reactions in the bulky structures of the reactor degrade the spectrum in energy, but still it is broad-even in a thermal reactor. (b) Fusion blanket spectrum: A Maxwellian distribution of H-2 and H-3 atoms in a hot (several KeV or more) plasma leads to ∼ 14 MeV neutrons with some energy spread, though in this region they qualify as relatively monoenergetic. However, in the outer regions of a fusion device (such as the blanket), elastic and inelastic scattering and (n,2n) reactions lead to a degraded spectrum which qualifies as “integral ”[See Fig. 4.3, On Page 51]. (c) Thick target accelerator sources: Even an accelerator neutron source which is “monoenergetic ”for kinematic reasons broadens to an effectively integral neutron source if the incident charged particles are slowed down and stopped in the target. Neutrons are produced by C.P.’s of all energies from the maximum to zero or to the threshold energy, as appropriate [See Fig. 4.4, On Page 52]. (d) Radioactive sources: Sources of neutrons can be obtained from radioactive materials. There are two common typesi. Spontaneous fission neutron sources. The predominant one is Cf-252. These are very convenient and widely used in applications. They are very compact and can be quite intense. The spectrum is basically a Maxwellian fission neutron energy distributin. ii. Secondary reaction sources. Typically, an intense alpha emitter such as Am, Pu or Ra is mixed intimately as a powder with a light element such as beryllium. The process is (Am,Pu,Ra) decays with alpha emission, then α − Be.... → n+ reaction product. Such sources are somewhat more bulky than Cf-252 and are not as widely used any more. iii. Radioactive neutron sources can be quite accurately calibrated for absolute neutron source intensity. This can be quite useful for some applications. 44

(e) Photoneutron sources: Electron linac accelerators, operating in the several tens to 100+ MeV energy range with high-current electron beams produce bremsstrahlung photon fields which are extremely intense when the electrons impinge on a high-Z target (Ta,W,U). In turn, these photons produce neutrons from the target due to γ+(Ta, W, U) → n via photoneutron reactions. Such sources produce copious neutrons at low energy, but also neutrons up to fairly high energies are emitted. (f) Spallation sources: Energetic protons of several hundred MeV incident on high-Z targets (Ta,W,U) lead to production of intense continuum neutron fields with strong representation at high as well as low energy.

4.5

Differential neutron fields

1. There are several considerations to producing differential neutron fields-namely neutron spectra in a particular region of space which are essentially monoenergetic. (a) Choose a reaction which is two-body and has a single reaction channel with a well-defined reaction Q-value. a + A → n + B + Q (Q = energy release-pos. or neg.). (b) Constrain the geometry so that kinematic broadening influences the spectrum to a minimal amount [See Fig. 4.5, On Page 52]. (c) Keep the target as thin as possible because ionization energy loss (a is usually a charged particle) broadens the neutron spectrum accordingly. 2. The only differential neutron sources attainable are those produce by accelerators using certain specific reactions. Even then, these sources are truly monoenergetic for only a narrow range of incident charged particle energy. Beyond these ranges, usually above a certain energy threshold, new reaction channels open up and the source is no longer truly monoenergetic [See Fig. 4.6, On Page 53, and see Fig. 4.7, On Page 54]. (a) and so on. There are really not very many convenient “differential neutron sources ”. 45

3. Even if a second group or “Breakup ”continuum appears in the spectrum, we tend to consider the source as differential so long as the primary group is predominant (has the most neutrons) (a) Under these conditions, it is possible to correct the data for the secondary neutrons. This is facilitated by the fact that mostly the secondary neutrons tend to have lower energies than the primary neutrons. 4. There is a particularly difficult range to access with conventional neutron sources. That is the 10-14 MeV range. (a) One special technique which has been developed to overcome this is to accelerate the heavy C.P. rather than the light one, i.e., “A ”instead of “a ”in the reaction a + A → B + n. i. This takes a higher energy accelerator and more difficult ion source technology, but it is feasible. ii. The reactions H-3 (p,n)He-3 and Li-7 (p,n)Be-7 have been exploited in this way with considerable success, particularly the former at Las Alamos National Laboratory. 5. Production of differential neutron fields requires considerable expertise in the fabrication of thin targets. (a) Solid targets must be either evaporated or electroplated on high-Z backings, where the latter contribute negligibly to neutron production. (b) Gaseous targets (such as deuterium) require short cells, high-Z beam stops and thin entrance windows of uniform material to minimize C.P. beam straggling and minimal production of extraneous neutrons [See Fig. 4.8, On Page 54]. 6. Why there is no such things as a truly “monoenergetic ”neutron source. (a) It should be evident from the preceding discussion that a purely monoenergetic source φ0 δ(E − E0 ) is not attainable in the laboratory, even with a two-body reaction with single Qvalue open channel. The reasons are: i. Incident C.P. beam energy spread and straggle. ii. Target perturbation effects. iii. Kinematic broadening. iv. Sample perturbation effects (scattering, etc.). 46

4.6

Correction of activation and cross section data for spectrum features.

1. This is a complex issue. Basically, if we assume a spectrum is φ0 (E) when, in fact, it is φ(E), the general approach is to write

φ(E) = φ0 (E) + [φ(E) − φ0 (E)]. From the basic yield equation, Y = φAXnσ, we have Z Y = φ(E)AXnσ(E)dE Z Z = φ0 (E)AXnσ(E)dE + [φ(E) − φ0 (E)]AXnσ(E)dE R [φ(E) − φ0 (E)]σ(E)dE R = AXn < σ >0 +AXn < σ >0 φ0 (E)σ(E)dE Where

(4.1)

(4.2)

Z < σ >0 = φ0 (E)σ(E)dE

(4.3)

For the idealized spectrum φ0 (E) we wish to consider. Thus

Y = AXn < σ >0 [1 + Correction factor]

(4.4)

(a) The correction factor has to be calculated from estimates σ(E).φ0 (E) and φE. each of which is known to varying degrees of accuracy. So long as “correction factor ”is small, then we do not need to know any of these very accurately. However, if the “correction factor ”is large (i.e. ≥ 1), then we need to know σ(E)φ0 (E) and φ(E) quit well, or we need to rethink the approach and treat φ(E) directly as our spectrum of interest, not φ0 (E). (b) EXAMPLE. “Monoenergetic ”measurements using Li-7(p,n)Be7 as a neutron source. Assume Ep > 3.68 MeV. Two discrete groups and a “Breakup ”component [See Fig. 4.9, On Page 55]. The basic formula is Y = φAXnσ. Assume that all other factors which complicate the analysis are ignored. Focus on spectrum aspect. Two discrete groups R and a continuum. Therefore. Y = AXn[φ1 σ(E1 ) + φ2 σ(E2 ) + φ(E)σ(E)dE]. We assume σ(E) ≈ constant for E ≈ E1 orE2 . our objective is to determine σ(E1). Formally 47

σ(E1 ) = [Y/AXnφ1 ]/[1 + Correction R Factor], with Correction Factor = [φ2 σ(E2 ) + φ(E)σ(E)]/φ1 σ(E1 ). In this framework, knowledge of φ1 is necessary and unavoidable. Otherwise, whatRare needed are the ratios. φ2 σ(E2 )/φ1 σ(E1 ) and φ(E)σ(E)/φ1 σ(E1 ) Usually, enough information is available on φ1 , φ2 and φ(E) for such estimates to be made, so long as the Correction Factor is not to large. Now, σ(E2 )andσ(E) for E < Em is usually obtained by the “bootstrap ”method from lower energy measurements, since Em < E2 < E1 . In that domain, the corrections are smaller. A rough estimate of σ(E1 ) can be obtained from σ(E1 ) ≈ (Y/AXnφ1 ) (neglect corrections). In general, this is how we approach the problem of such corrections. This bootstrap approach can be improved by iteration to improve the accuracy, if need be.

4.7

Energy scale considerations associated with activation and cross section measurements-basic issues .

1. Since σ(E) is energy dependent, an uncertainty in determination of energy E by ∆E will lead to a discrepancy in the interpretation of σ by an amount ∆σ = (∂σ/∂E)∆E. (a) This is a source of correlated error if the uncertainty ∆E vs. E is systematic. It will usually be systematic because of the way calibration procedures are used to determine C.P. energy and, thus, indirectly, neutron energy [See Fig. 4.10, On Page 55]. i. This can be called the error in σ due to misinterpreting E. 2. Another different problem in determining monoenergetic cross sections has to do with the factthat the neutron spectrum is never truly monoenergetic. We wish to interpret the experiment as follows: Y1 = φ1 AXnσ(E1 ). Where φ1 is the total neutron fluence in the group and E1 is a “point ”energy for the group. In reality, the relationship is R Y1 = AXn φ(E)σ(E)dE = AXn < σ >. 48

Where φ(E) R is a narrow spectrum. We Rcan reconcile this by assuming E1 = φ(E)EdE =< E > and φ1 = φ(E)dE. We can reconcile the problem by the following method: Y = AXn < σ >= AXnφ1 σ(< E >)[< σ > /σ(< E >)]/φ1 . The factor in [...] is a correction factor that enables us to relate Y to the point cross section σ(< E >). In order to calculate the correction factor. We need to know the shape of σ(E) in the vicinity of E =< E >. If φ(E) is very narrow, such that σ(E) is approximately linear in E in the region where φ(E) > 0, then Correction Factor = [...] = 1. However, if this is not so, then we need to have some knowledge of the shape of both σ(E) and φ(E) in order to calculate the factor. This is usually possible, but that is a subject requiring detailed study.

4.8

determination of neutron energy spectra for differential measurements .

1. One way to address this issue is by direct measurement of the neutron spectrum from the target. (a) This can be accomplished by time of flight if the spectrum is produced using a pulsed acceleator. In fact, it is very important that this be done for any neutron source that is to be used for precision activation measurements. 2. Certain aspects of the effective neutron spectrum in a Sample can be deduced via calculations directly from more fundamental considerations. Here is how it can be done: [See Fig. 4.11, On Page 55] (a) The important point is that φik1 , as a function of θk1 , Enik1 , etc., can be calculated from a basic knowledge of the neutron source reaction, kinematics. C.P. energy loss in the target. etc. Also, the basic flux profile in the sample vs. Enik1 can be calculated, e.g., the flux associated with Enik1 is basically (φik1 /d2k1 )sinθk1 . 49

Where the factor sin θk1 is a solid angle factor. it is assumed that the neutron source reaction is a single Q-value, two body reaction that produces a discrete group. However, the source spectrum broadening occurs because of C.P. energy loss in the target and Kinematic broadening. Calculations carried out on numerous occasions at Argonne National Laboratory show that the “monoenergetic ”spectrum looks roughly as follows: [See Fig. 4.12, On Page 56] These are never symmetric spectra or particularly Gaussianlike. They exhibit considerable tailing, particularly for the H2(d,n)He-3 reaction.

50

Figure 4.1: Accelerator neutron production.

Figure 4.2: Reactor neutron spectrum.

Figure 4.3: Fusion blanket spectrum.

51

Figure 4.4: Thin and thick target accelarator sources.

Figure 4.5: Kinematic broadening influence on neutron spectrum.

52

Figure 4.6: Neutron spectrum of differential neutron source.

53

Figure 4.7: Neutron spectrum of differential neutron source (Continued).

Figure 4.8: Gaseous targets (such as deuterium).

54

Figure 4.9: Correction of activation cross-section data for spectrum features.

Figure 4.10: Energy scale considerations associated with activation and cross-section measurements.

Figure 4.11: Calculation of effective neutron spectrum in a sample.

55

Figure 4.12: Mono-energetic neutron spectrum.

56

Chapter 5 NEUTRON FLUENCE MEASUREMENT AND STANDARDS 5.1

Absolute neutron fluence determination .

1. There are basically three ways to establish absolute neutron flux fields. Having said this, it should be pointed out that most nuclear activation measurements do not rely on absolute neutron flux determinations. (a) Calibrated “standard ”neutron sources are radioactive sources (not a reactor or accelerator). The number of neutrons emitted per unit time are determained either by physical chemistry means (e.g., mass of the material) or by comparisons with standard sources via techniques such as the “manganese bath ”. i. Cf-252. Since nu-bar and the half life are well known, all that is required to make an accurate determination of the neutron emission intensity is to carefully weigh the material in the source sample. ii. Am-Be, Ra-Be, Pu-Be radionuclide sources rely on a two step process: X → Y ∗ + α : α + Be → n. These sources are usually calibrated by comparison with a standard source of like composition and geometry, under similar geometric configurations for comparison. The satndard sources, e.g., at NIST in the U.S.A. there is a 57

Ra-Be standard, have been calibrated for total yield of neutrons by capture of all the neutrons in a large tank of water containing a solution of salt, generally manganese or vanadium. The raections Mn-55 (n, γ)Mn-56 and V51(n, γ)V-52 are typical reactions. The concentration of Mn-56 or V-52, knowledge of the half life, etc.. enables us to determine the neutron intensity quite accurately. There are corrections and technical considerations which have to be handled, however. No technique is completely straightforward. (b) Associated particle method. This works with reactions such as H-3(d,n)He-4, H-2(d,n)He-3 or Li-7(p,n) Be − 7∗ (γ) Be-7. The key point is that for every neutron released there is an associated particale, e.g., He-4, He-3, or γ, which is much easier to detect and measure reliably than the neutron. i. In the case of H-3(d,n)He-4, this technique is not too difficult to execute and is used quite frequently. Because of kinematic considerations, the cone of detected alpha particles (solid angle subtended) is directly correlated with the corresponding neutron cone [See Fig. 5.1, On Page 65]. (c) This possibility of defining the “cone ”of neutrons Ωn , and keeping absolute track of their numbers by detecting the associated α-particales one-to-one, is what gives this method great power. i. The limitations of the associated particale method are mainly due to a need for precise control of geometry and of dealing electronically with the high count rates that are often encountered in the associated charged particles (or photons) which are detected. (d) Absolutely calibrated neutrons detectors. We don’t wish to get into the details of detector technology, but it is possible to calibrated certain detectors in such a way that they can be used for absolute neutron fluence measurement. Uaually, such detectors have relatively high efficiency and flat efficiency response over a reasonably wide range of energies [See Fig. 5.2, On Page 65]. i. Long counter, BF3 counter imbedded in a paraffin cylinder with cadmium wrapping. No timing capability [See Fig. 5.3, On Page 65]. 58

“Black ”neutron detector. Fast timing capability [See Fig. 5.4, On Page 66]. Measure scintillations from recoil protons. H(n,n)H.

5.2

Relative neutron fluence determination.

1. Because of the difficulty in determining neutron fluence directly, and the limited technical opportunities for doing so, most measurements with neutrons are relative, in the sense that one process (the “unknown ”) is measured against a second process (the “known ”or “standard ”) in such a way that knowledge of the absolute neutron fluence is not required. (a) In the simplest sense we have the following: Unknown: Yu = φu Au Xu nu σu Standard: Ys = φs As Xs ns σs Suppose φu = Cu φ and φs = Cs φ where Cu and Cs are simply factors to scale for differences in exposure time, etc., but basically the “u ”and “s ”irradiations are carried out in the same neutron environments. Then, Ratio = σu /σs = (Yu /Ys )(As Xs ns Cs /Au Xu nu Cu )φ cancels!! i. So... the Ratio −σu /σs is directly determained from what is known and/or measurable. ii. To determine σu , we must known σs . This is why standard cross sections are so important to nuclear science. (b) In reality, things can get more complicated and a lot of corrections are needed. To keep this corrections minimal, here are steps which can be taken [See Fig. 5.5, On Page 66]: i. Choose process “s ”, the standard, so there are similarities to process “u ”the unknown, e.g., comparable half lives, comparable thresholds (if applicable), similar decay radiations (γ 0 setc.). ii. Irradiate “u ”and “s ”simultaneously to insure equal irradiation experience. iii. Keep the irradiation geometries as simple as possible. Keep the samples small and contiguous. 2. Suppose the objective is actually to determine the relative neutron fluences in two environments (e.g., at the two locations in a reac59

tor). We can turn on the arguments above (where fluence cancels) around completely. (a) Foils 1 and 2 have the same material and thus the same reactionb process, described by σ [See Fig. 5.6, On Page 66]. Then, Y1 = φ1 A1 X1 n1 σ1 and Y2 = φ2 A2 X2 n2 σ2 . Thus, φ1 /φ2 = (Y1 /Y2 )(A2 X2 n2 /A1 X1 n1 ) (b) In reality, things can get much more complicated if the spectrum shape of φ1 and φ2 differ somewhat (as is usually the case). i. Other corrections may also have to be considered. Life is hardly ever easy!

5.3

The hydrogen standard

1. The elastic scattering of neutrons from hydrogen is a primary standard of nuclear science for several reasons: (a) Up ot rather high energies, there are only two interaction processes for neutrons with hydrogen. i. Elastic scattering: H(n,n)H ii. Radiative capture: H(n,γ)H-2. A. Of these, elastic scattering is the dominant process, particularly at higher energies. (b) The H(n,n)H cross sections and scattering angular distributions are very well known. i. There have been extensive measurements. ii. They can be calculated accurately from basic nuclear theory. iii. The integrated elastic scattering cross section is probably known to an accuracy of ∼ 1several 10’s of MeV. A. However, even here there are some imperfections, e.g., some uncertainties at a several percent level persist in the angular distribution details. 2. Much of the importance of the hydrogen standard stems from its role in various neutron detector schemes. 60

(a) Proton recoil detector [See Fig. 5.7, On Page 67]. (a) knowledge of the H-atom number in the foil and the hydrogen elastic scattering cross section is essential for calibration of this detector. (a) It can serve as an absolute neutron fluence monitor for both monoenergetic neutrons or fast-pulsed neutrons with a continuum spectrum. For the latter, time of flight techniques are needed to sort out the flux at various energies. (a) hydrogeneous scintillators. i. Recoil protons produce ionization and light is emitted. Neutrons can scatter from 0 - 90 degrees in the laboratory. The result, for monoenergetic neutrons, is a spectrum of the form [See Fig. 5.8, On Page 67] ii. Depending upon the bias setting, the detector efficiency has the form [See Fig. 5.9, On Page 67] iii. The corrections are substantial, and computer techniques are requrid, but the efficiency can be calculated from the H(n,n)H cross section and ionization light output tables reasonably well.

5.4

Fission standards.

1. The fission cross section for the major isotopes of U and Pu are of great importance for the influence they have on the behavior of nuclear reactors. These cross sections have been measured many, many times, and are carefully evaluated. U-235(n,f) is essentially a primary standard, i.e., it is known almost as well as H(n,n)H. (a) The U-235(n,f) cross section is known with accuracies of 1 to a few % from thermal to several 10’s of MeV (excepting in the vicinity of certain resonances). (b) U-238(n,f) is known to few percent accuracies from a few hundred KeV above threshold to a few 10’s of MeV. (c) Pu-239(n,f) is known as well or better than U-238(n,f) in the MeV range, and is known to thermal energies. 61

2. The fission cross section of U and Pu, and of Th and Np as well, are very useful-also-because of the roles they can play in neutron detectors. Why is this the case? (a) Each neutron induced fission releases a lot of energy (≥ 200MeV). Most of this energy goes into kinetic energy of two fission fragments. They are very easy to detect above background noise, α particles, recoil protons, beta emission, etc., in detectors which employ (n,f) reactions [See Fig. 5.10, On Page 68]. (b) Fission detectors are easy to make and operate. The signals are large and easy to distinguish from noise and competing reactions. The detector geometries are simple and easy to model for data analysis purposes. (c) There are several drawbacks: i. The efficiency is quite low relative to many other neutron detector concepts. ii. For ansolute efficiency calibration purposes, it requires a variety of special techniques to determine the exact amount of material on the deposite. The amount of material is too small for direct measurement (from microgram to a few milligrams of fissionable material). iii. Fission fragments, in spite of their relatively high energies can straggle or be absorbed in the layer of fissionable material. iv. One of the most commonly used methods of fission deposit assay is the measurement of α spectra from the deposits. These spectra can be perturbed by contaminants or “blurred ”(resolution affected) by deposite non-uniformity. A. All-in-all, the foil assay issue requires careful attention to details by knowledgeable specialists. It is not a job for amateurs.

5.5

Activation standards and neutron dosimetry

1. Foils, wire, or other forms of sample material can be activated by neutron irradiation. This is a very common way to measure neutron fields in a reactor and also in cross section studies. There 62

are a number of activation reactions which are sufficiently well known, i.e., the differential cross sections σ(E) are known over an energy range for which the response function R(E) = φ(E)σ(E) is significantly different from zero, to enable these materials to be used for neutron dosimetry. A wide range of neutron fields and intensities can be studied. (a) Examples of such reactions are: Ni-58(n,p)Co-58, Al-27(n,σ)Na24, In-115(n,n0 )In-115m, In-115(n,γ)In-116m, Fe-54(n,p)Mn-54, etc. The collection of all such reactions is often designated as a dosimetry file, accenuating the fact that they are used for just that, determination of neutron fluences... and spectra! (b) The important issue in the response range. Let’s focus on continuum spectra because “dosimetry ”for “monoenergetic ”fields is relatively easy. R R Ij = dEφ(E)σj (E) = dERj (E)/(j = 1, n). The Ij are integral reaction rates for a collection of n dosimeter reactions. i. Often, foil-sample bundles are plated at various places around a neutron radiation environment in order to measure the neutron field intensity and spectrum shape at these various locations. ii. The response range (E1j Ehj ) for the activation dosimeter with cross section σj (E) is defined such that 95% of the area under Rj (E) is contained in this range with equal amounts (2.5%) at higher and lower energies [See Fig. 5.11, On Page 68]. iii. Thus, for several (n) activation dosimeters we have an assortment of response ranges, i.e., A. These provide “coverage”of the spectrum [See Fig. 5.12, On Page 68]. NOTE: Non threshold reactions such as (n,γ) activation have broad response ranges. 2. Spectral shapes in neutron dosimetry can be studied by a process called “spectrum adjustment ”. (a) Let the continuous quantities φ(E) and σ(E) be represented by group R values. Thus, Ij = dEφ(E)σj (E) ≈ Σk=1,m ∆Ek φk σjk (j = 1, n). 63

One starts with a trial spectrum φ0 (E), usually based on calculations, convert it to a collection of group values φ0k (k = 1, m). Then... using the method of least squares, one adjusts all the φ0k → φk so the set of equations is best satisfied for a given collection of measured integral reaction rates Ij and associated dosimeter cross sections σjk . (b) In this manner, good approximations to both the spectrum shape and the neutron field intensity can be deduced. Modern neutron dosimetry is a combination of measured reaction rates, standard activation cross sections, reactor modeling and statistical analysis.

64

Figure 5.1: Kinematic considerations showing correlation between detected α-particles and neutron cone.

Figure 5.2: Absolutely calibrated detector.

Figure 5.3: BF3 counter imbeded in a paraffin cylinder with cadmium wrapping.

65

Figure 5.4: “Black”neutron detector.

Figure 5.5: Good and poor sample geometry.

Figure 5.6: Relative fluence determination.

66

Figure 5.7: Proton recoil detector.

Figure 5.8: Recoil proton spectrum for mono-energetic neutrons.

Figure 5.9: Recoil proton detector efficiency.

67

Figure 5.10: Fission detector and its spectrum.

Figure 5.11: Activation standards and neutron dosimetry.

Figure 5.12: Activation dosimeters and its response range.

68

Chapter 6 SAMPLE PERTURBATION EFFECTS ON THE NEUTRON FIELD 6.1

Sample absorption and correction procedures.

1. The neutron absorption by materials is the simplest correction of this category. Basically, to analyze the correction one need to have knowledge of: (a) The sample geometry and composition. (b) Energetics and geometry of the neutron field. (c) The applicable neutron total cross section. (a) We must know that the straight absorption of neutrons is governed by the exponential law. For monoenergetic neutrons in a parallel beam with one element present [See Fig. 6.1, On Page 74]: φ = φ0 e(−nσt x) = φ0 e(−Σt x) . (6.1)

nσt = Σt (macroscpic total cross section) i. Suppose we have a broad neutron spectrum [See Fig. 6.2, On Page 74].

dφ(E) = φ0 (E)dEe[−Σt (E)X] . 69

(6.2)

So...

Z

Z dEφ(E) = dEφ0 (E)e[−Σt (E)X] .

(6.3)

Thus, Z Z Z Z [−Σt (E)X] dEφ(E)/ dEφ0 (E) = dEφ0 (E)e / dEφ0 (E)

=< e[−Σt (E)X] >0 .

(6.4)

(b) Suppose φ is not too broad (say ∼ 100 KeV width at a mean energy of 3 MeV). RThen, it is temptingR to say that,R if φ = R dEφ(E) and φ0 = dEφ0 (E) and = EdEφ0 (E)/ dEφ0 (E), then φ = φ0 e[−Σt ()X] , (6.5) i.e., that

< e[Σt (E)X] >= e[−Σt ()X] .

(6.6)

i. This assumption is fundmentally wrong! If Σt (E) is very smooth over the region of significant flux in φ, then it s not a bad approximation. If there are reasonances or other significant structure, this assumption can lead to significant error [See Fig. 6.3, On Page 75]. (c) Suppose we have a uniform foil of material, a continuum spectrum and a point source of neutrons which is both monoenergetic and isotropic (too ideal to be true). What are the effects of neutron absorption on the total yield of activated atoms if the point source is close enough to the foil that geometric effects have to be considered. Assume the foil is a disk with thickness 1 and radius R » 1 (thus neglect edge effects) [See Fig. 6.4, On Page 75]. σ = reaction cross section, n = sample atom density, Z = path length in material, δ = distance to dV from point source, φ0 = Source strength/sr, Y0 = yield without absorption, Y = yield with Rabsorption, R Y0 = dVcosθ(φ0 /δ2 )nσ. Y = dVcosθ(φ0 /δ2 )nσe(−Σt X) i. Here, the factor cosθ corrects for the angle with which the laminar volume element dV presents itself to the incident neutrons. When dV is “normal ”to the incident neutrons, the yield per unit volume is the largest, i.e., the solid angle is the largest. 70

The integrals involve the variables r (0 → R) and X (0 → 1), We have in these formulas the following expressions: dV = 2πdrdX, Z = X/cosθ, δ = (y + X)/cosθ. So, the fluence depression factor is Fa = Y/Y0 . (d) If we go to continuum spectra, more irregular sample geometies, isotropic sources, e..g., the conditions found in a reactor, then the analysis becomes even more complex and must be carefully thought out. Not a back of the envelope task! 2. Suppose the sample is not homogeneous and has several elements and isotopes? (a) It is essentially impossible to deal with inhomogeneous samples (voids, incompletely mixed chemicals, etc.). For this reason, it is essential to demand that the samples used be homogeneous. There is no fundamental reason why this should not be possible. (b) Samples which are chemicals and/or mixtures involving several elements and/or isotopes simply need to have this reflected in the macroscopic total cross section. Suppose there are m different species in the material with concentration nk for the Kth one and total cross section σtk (E). Then, the proper macroscopic cross section for the material is Σt (E) = n1 σt1 (E) + ... + ni σti (E) + ... + nm σtm (E). So long as the material is homogeneous, we can calculate absorption of neutrons for composite materials in the same way as for single component materials. 3. We conclude from all this that even the conceptually simple process of correcting for neutron absorption can become very complicated owing to realistic features of neutron fields, geometry, etc.

6.2

Neutron multiple scattering and correction procedures .

1. The neutron fluence at any point within a sample is always somewhat larger than one deduces from simple geometric and absorption effect analyses. The reason is multiple scattering. 71

(a) Multiple scattering effects can be categorized in two ways [See Fig. 6.5, On Page 76]: i. Scattering from the external environment to the sample. ii. Scattering from one portion of the sample to another. 2. The analysis proceeds as fallows: Let Y = total reaction yield in a sample, Yo = primary yield, Ye = yield from external scattering and Ys = yield from sample scattering. If the possibility of scattering externally as well as internally for the same neutron is negligible, then Y = Yo + Ye + Ys = Yo 1 + [(Ye + Ys )/Yo ]. The term (Ye + Ys )/Yo is called the multiple scattering correction term. (a) The calculation of this term is-even in simple cases- a very complicated process involving scattering cross sections, analytic geometry and Monte Carlo simulation. (b) If the calculation of Ye and Ys involves analyzing all events in which a neutron can scatter once before producing a reaction in the sample, but not more than once, we are said to be considering “single scattering ”corrections only [See Fig. 6.6, On Page 76]. i. The “single scattering hypothesis ”is applicable in “clean ”experiments where external objects that are potential scatterers are minimized and kept low in mass, and the samples are kept relatively small. ii. The “single scattering ”condition is very important because it allows the principle of superposition to be invoked. Higher order scattering effects violate the principle of superposition and make analysis extremely difficult and dependent upon specific geometry conditions. 3. Here are some basic considerations associated with multiple scattering: (a) Neutron elastic and inelastic scattering cross sections and angular distributions need be known, as well as total neutron cross sections, for all the scatterer materials. At higher energies, (n,2n), (n,np), etc., also are required. These need to be known as a function of neutron energy from the maximum energy down to much lower energies (thresholds). 72

i. Multiple scattering analysis is always very demanding of nuclear data. (b) In general, neutron multiple scattering analysis cannot be addressed using simple analytical techniques. Monte-Carlo simulation is essential. i. Older techniques, such as effective path lengths, which were practiced when the available computing power was very limited, are no longer viable. (c) Neutron scattering kinematics must be handled carefully and in exhaustive detail in order to obtain reliable results. The multiple scattering perturbations are very sensitive to energetics [See Fig. 6.7, On Page 77]. i. If the reaction cross section at energies < E are small, then the multiple scattering corrections to data at energy E will be much smaller than if the cross sections for energies < E are large compared that at E. (d) When making ratio measurements, multiple scattering corrections tend to cancel if the reaction thresholds and shapes of the standard and unknown cross sections are similar. (e) This is an important consideration in selecting the standard reaction to use for a given measurement. 4. In examining old data from the literature for evaluations purposes, one often notices that the values tend to be too large. This very probably is due to underestimation of the neutron fluence due to the defacto fluence enhancement by multiple scattering. Thus, Y ∼ φσ. Yfixed → σ ↑ asφ ↓

73

Figure 6.1: Sample perturbation effects on the neutron field-1.

Figure 6.2: Sample perturbation effects on the neutron field-2.

74

Figure 6.3: Sample perturbation effects on the neutron field-3.

Figure 6.4: Sample perturbation effects on the neutron field-4.

75

Figure 6.5: Neutron multiple scattering-1.

Figure 6.6: Neutron multiple scattering-2.

76

Figure 6.7: Neutron multiple scattering and its correction.

77

78

Chapter 7 MEASUREMENT OF SAMPLE ACTIVATION AND CORRECTIONS 7.1

Types of activity and radiations

1. The basic decay processes leading to radioactive emission of radiations from materials are: (a) α decay (mainly heavy nuclei). (b) β− decay (throughout periodic table). (c) electron capture -EC- (throughout periodic table). (d) β+ -positron- decay (throughout periodic table). (e) Electromagnetic -EM- decay (throughout periodic table). i. There are two mechanisms for electromagnetic decay of excited nuclei. One is direct photon emission. The second is internal conversion (IC), whereby the excitation energy goes into ejecting an electron from the atom (usually from an inner shell). The unstable atomic structure then rearranges itself and, in the process, emits X-rays. 2. Nuclei can de-excite in more than one manner, with a well defined probability or branching factor for each process. It is very important that the details of decay are quantitatively understood in order to be able to perform accurate radioactivity measurements. Decay information is available from the following sources: 79

(a) The literature. (b) Charts of Nuclides. (c) Nuclear Data Sheets. (d) Radioactivity handbooks. (e) ENSDF (computerized decay data files). 3. Processes such as σ, β−, EC or β− are very often followed by electromagnetic decay with associated gamma rays, conversion electrons and X-rays. The spectra can be simple or complex but, again, the details need to be known to make accurate radioactivity measurements.

7.2

Principles of detection .

1. The detection of radioactivity reduces essentially to detecting αparticles, β-particles, β− particles, gamma rays or X-rays. Occasionally, internal conversion electrons are measured but this is rare now in an age where beta spectrometers are hardly ever found in laboratories. 2. α-particle detection. (a) α particle emission is very commonly measured for very thin actinide deposits as a means for sample assay. i. The detectors are usually either proportional counters (rare these days) or solid state surface barrier detectors. (b) There are two types of alpha detectors: i. High efficiency-poor geometry (Ω = 2π, 4π, etc.) [See Fig. 7.1, On Page 89]. ii. Low efficiency-good geometry (small Ω) [See Fig. 7.2, On Page 89]. A. Good geometry detectors can be calibrated very accurately for absolute efficiency (by geometric means) and the alpha spectra can be quite clean because the alphas that reach the detector all leave the deposite perpendicularly. The only requirement is a uniform deposit [See Fig. 7.3, On Page 89]. 80

3. β− , β+ particle detection. (a) This is rapidly becoming a lost art science β emission is usually (though not always) followed by electromagnetic transitions (which are easier to measure). (b) β spectra are always continuum spectra because of the presence of the neurino. This makes precise measurements difficult compared to α particle or photon measurements [See Fig. 7.4, On Page 90]. (c) Samples for β measurements do not need to be as thin as for α particle measurements, but still need to be quite thin and uniform to get good quality spectra. Chemical separations and preparation of very thin deposits by evaporation of solutions on blotter paper is a good method if the activity is high enough to make measurements with very small quntities of material. (d) Gaseous proportional counters are frequently used for β measurements. i. The details of these techniques are too extensive to cover in this lecture, but they are well documented in the literature. 4. Gamma-ray detection. (a) There are two methods which are in common use today to detect gamma rays: (1) scintillation detectors (sodium iodide, bismuth germanate, barium fluoride, organic scintillation detectors). Let’s look at some different types. i. Sodium iodide detectors [See Fig. 7.5, On Page 90]. A. Time honored method for detecting gamma rays. B. Typical spectrum for monoenergrtic gamma ray spectrum [See Fig. 7.6, On Page 91]. C. These detectors are still widely used because they are simple to use, reliable and efficient. Also, they do not require a caryogenic environment. ii. Bismuth germanate, barium fluoride detectors. A. These detectors are very expensive and do not give particularly good resolution. However, they are very efficient. Used as a substitute for organic scintillation detectors in capture gamma ray detection experiments. iii. Organic scintillation detectors [See Fig. 7.7, On Page 91]. 81

A. Usually used to detect neutrons are reject gamma rays. However, they are useful for measuring gamma rays from (n,γ) reactions with fairly high efficiency. They, it is the scattered neutrons which are rejected. iv. Germanium solid state detectors. A. Require cryogenic equipment (liquid nitrogen). B. Photons produce ion pairs in the crystal (either Lidrifted to ultra high purity germanium-the more modern approach). The small amount of energy required to produce ion pairs leads to a large number of pairs and therefore give good statistics and high resolution. C. Modest efficiency (less than NaI) Example Co60 γ-rays. E=1.17 and 1.33 MeV. Compare NaI and Ge detector spectra [See Fig. 7.8, On Page 91]. 5. X-ray detection. (a) On the whole, X-rays have much lower energies than gamma rays. The principle detection methods are proportional counters, scintillators (mainly NaI or CsI) and germanium or silicon solid state detectors. i. Proportional counters are not widely used for direct spectometry but may be used as detectors in crystal spectrometers or equivalent dispersion devices. ii. Thin scintillation detectors are fairly widely used but are on the decline. iii. Germanium and, mainly, silicon, solid state detectors are becoming the detectors of choice. The reason is their good efficiency and, mainly, good resolution. They require cryogenics equipment (liquid nitrogen).

7.3

Standard sources .

1. With the exception of large scintillation detectors and alpha particle detectors, most radiation detector systems are not 100% efficient for detecting the incident radiations. Therefore, calibrated sources are prepared for measuring the efficiencies of these detectors. 82

(a) This is too vast a subject to address in this lecture in any detail. (b) Almost all experimental laboratories possess a collection of standard radioactive sources. Standard gamma ray sources are the most commonly used. (c) Standard sources are available to be purchased from standards laboratories in several countries, e.g., NIST (USA). LMRI (France) and PTB (Germany).

7.4

Calibration and standardization .

1. Again, this is a complicated subject which cannot be addressed in this lecture in detail. (a) Intercomparison of unknown sources to existing standard sources in a well defined geometry. (b) Produce a source from a carefully prepared batch of sample material. Weigh carefully. Activity can be deduced from the mass of the material and decay constant. (c) Coincidence counting. Suppose that a particular source produces two coincident radiations R1 and R2 during decay. Suppose that B1 is number of R1 emitted per decay and B2 is the number of R2 emitted per decay (i.e., branching factors). Let S = source strength. Look at the source with two detectors. D1 and D2 . D1 measures R1 and D2 measures R2 . Measure coincidences between D1 and D2 . 1 and 2 are the singles efficiencies [See Fig. 7.9, On Page 92]. N1 ∼ S1 B1 . N2 ∼ S2 B2 . Nc ∼ S1 B1 2 B2 C. Where C = angular correction for R1 and R2 . Measure N1 , N2 and N1 . Then, (N1 N2 /Nc ) = S/C(1 , 2 , B1 and B2 cancel). Thus, S = N1 N2 C/Nc . i. Of course, there are some corrections not mentioned here which need to be made. Things are never quite as simple as shown here. ii. On the whole, it is a powerful technique because, in principle, it allows for absolute calibration of a source without reference to detector efficiencies or decay properties. 83

7.5

Sample absorption, scattering and related corrections .

1. Just as in the case of neutron scattering perturbations affecting the production of radioactivity in samples, the radiation emanations from decaying nuclei in samples can interact with the sample and effect the interpretation of the counting data. (a) The assumption is that the count rate C in a detector is given by the formula C = S, where  = efficiency and S = absolute activity (decay events per unit time) of the detector and sample, respectively. Suppose that there is absorption of radiation in the sample. Let’s consider how the analysis would go [See Fig. 7.10, On Page 92]. Let σ be the radiation absorption cross section. For this slab geometry. Assume  is the efficiency for a massless point source. The counts from layer dX are (−nσX)(S/A1) dC = (dX)Ae (volume = A1). Thus, R (−nσX)/1 C = S[ dXe ] = S < π >, where π = e(n−σX) Since π < 1 → < π > < 1. So... the absorption effects is to reduce the count rate, which is equivalent to reducing the counting efficiency. (b) Now, consider scattering of the radiation by the sample [See Fig. 7.11, On Page 92]. Thus, C = S < π >] + Cm is a contribution to the count rate from multiple scattering. Now Cm > 0. We can write C = S[< π > = (Cm /S < π >)] = S (Correction Factor). The correction factor adjust the effective efficiency for counting. The multiple scattering term must be calculated just as in the case of neutrons. The calculations are generally complicated and rely on Monte Carlo simulation. The difference from neutrons is that generally the decay radiation interaction cross sections with matter are well known. EXAMPLE. Measure gamma rays from radioactive decay of a sample. Use a high resolution Ge detector. Measure yield of full energy (F.E.) peaks in the spectra. If a photon interacts with an atom, it will either be absorbed by the photoelectric effect, scatter elastically (Raleigh scattering), scatter inelastically (Compton scattering), Pr produce β − /β+ 84

pairs. So, only Rayleigh scattering need be considered in this case. Raleigh scattering is sizable only for low-energy photons and high Z materials 2. Most detector efficiencies are given for point sources since they are developed from standard sources which are often point (massless) sources. Geometric effects certainly affect the counting [See Fig. 7.12, On Page 92]. S = total sample activity. V = sample volume. Thus, 2 2 dC = (S/V)dV(l 0 /lv ), thus R 2 C = S[l0 dV(l/l2v )/V]. The Correction Factor [...] adjusts for the different path lengths of the radiation from various parts of the sample to the detector, relative to some selected reference distance l0 .

7.6

Sum coincidence effects .

1. If the radioactive decay involves the emission of two or more radiations simultaneously, then simultaneous detection of these (within a small resolving time) can influence the counting of any one of them. (a) This is a complex subject, but let’s look at a simple case to see how the issue arises. Example . Measurement of Co-60. The 1.17 and 1.33 MeV radiations are emitted simultaneously due to the decay scheme, so they can be in coincidence. If the efficiency for detecting both of these radiations is high, then a “sum ”peak with effective energy of 1.17 + 1.33 = 2.50 MeV appears in the spectrum. When such “sum coincidence ”effects occur, they do so at the expense of losses of events from the singles peaks. Since coincidences can involve both full energy events and Compton events, the analysis is complicated. Often, it is best to simply avoid the effect by keeping the efficiency low, or by calibrating the detector system in such a way that sum coincidence effects are included experimentally is the overall efficiency determination [See Fig. 7.13, On Page 93]. 85

7.7

Detector deadtime and related perturbations .

1. We have already discussed the complex interplay between detector deadtime and the half life of radioactive decay, in discussing halflife related issues. (a) We also discussed the origins of deadtime in detector systems. 2. It remains to emphasize how we actually determine true count rate per unit time in radiation measurements. (a) Let us suppose, for the sake of orgument, that half life effects are not very significant, i.e., that the fraction of the total radioactive atom inventory of a sample which actually decay is small. That is, tc << (1/λ), where tc is the counting time and λ is the decay constant. Let tl be the time that the detector is available to count during time tc . tc − tl is the time lost to processing the counts accepted during tl . Let Y be the observed counts. Then, the true count rate is C = Y/tl , not C = Y/tc . i. Most modern measurement recorders of data, such as multichannel alyzers, or computer-based data acquisition systems, keep track of both tc and tl , as well as the absolute start and stop times. (b) Only if tc ∼ (1/λ), and tl is significantly less than tc , do we need to keep track of the more complex livetime/deadtime issues discussed previously.

7.8

Background and other interferences in measurements .

1. We have mentioned background as a consideration in previous sections. Here, we simply look at a couple of basic issues as “food for thought ”for the student. Basically, there are two types of “background ”to consider: 86

(a) Background inherent to properties of the spectrum of the primary radiation one is trying to measure. i. Here, we are concerned with how to analytically distinguish the events we wish to count in the spectrum from those we don’t. Example . Photon counting with NaI or Ge detectors [See Fig. 7.14, On Page 93]. A. It is much easier to separate out the unwanted contributions of the 1.33 MeV F.E. peak and Compton continuum for a Ge detector than for an NaI detector, when making measurements of the F.E. peak yield of 1.17 MeV gamma rays. ii. There are physical and/or semi-empirical models which assist the experimenter in this task. The important thing is to truly understand the nature of the physical processes which govern the counting. iii. However, the single most useful technique is to treat both unknown and calibration standards in the same way for such analyses. Then, the effects of any particular choise of data analysis method will tend to cancel to first order-even if the method selected has some built in flaws. (b) Background from external sources. i. The most obvious way to deal with this issue is to perform sample-in and sample-out measurements, then take the difference of the results (corrected for count times, decay, etc.) as the “true ”sample count rate. A. This is a reasonable approach so long as• The background does not vary significantly during the counting periods. • The presence of the sample does not perturb the background measurement process by altering the geometry, affecting absorption and scattering, etc. If the sample is small, this will be the case. 2. Other interferences in radiation measurements. There are a number of issues which arise in experimental measurements. Perhaps the most important of these to consider are instrumental effects. (a) All radiation detection and recording devices are subject to 87

failures. We can’t go into all the possibilities, but here are some to consider. i. Gain drifts or jumps. ii. Noise bursts (loose connectors, bad H.V. supply, etc.). Can show up as distortions in the spectrum or abnormally high deadtime relative to what should be expected for a particular source and detector [See Fig. 7.15, On Page 93].

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Figure 7.1: α detectors, high efficiency-poor geometry.

Figure 7.2: α detectors, low efficiency-good geometry.

Figure 7.3: α spectra (Good geometry).

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Figure 7.4: β spectra.

Figure 7.5: Sodium iodide detector.

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Figure 7.6: Sodium iodide detector γ-ray spectrum.

Figure 7.7: Organic scintillation detector.

Figure 7.8: NaI and Ge detector spectra.

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Figure 7.9: Coincidence counting.

Figure 7.10: Sample absorptoion.

Figure 7.11: Scattering in sample.

Figure 7.12: Different path lenghts of radiation from various parts of sample.

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Figure 7.13: Sum coincidence effects (Ex: Co-60).

Figure 7.14: Photon counting with NaI and Ge detectors.

Figure 7.15: Instrumental effects.

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Chapter 8 GEOMETRIC EFFECTS AND THEIR INFLUENCES ON ACTIVITY AND CROSS SECTION MEASUREMENTS This subject has been discussed extensively throughout this lecture. Here, we will stress a few general points to re-emphasize their importance.

8.1

Finite sample size-typical sample shapes .

1. Measurements with point neutron sources. The neutron fields across the sample are generally not uniform, but there tends to be azimuthal symmetry even if the distance and polar homogeneity is broken. For this reason, thin circular disks are the best choices for sample shapes. It simplifies the analysis associated both with sample irradiation and counting. (a) Samples tend to be somewhat larger in these types of experiments to enhance the mass so as to compensate for reduced neutron flux. 2. Measurements in high neutron intensity environments which have more nearly homogeneous, isotropic fields, and can utilize very small samples, allow much more latitude of sample shape (e.g., 95

wires, chips, powder samples, etc.) because the geometry effects are much reduced, both in irradiation and counting applications.

8.2

Interaction between finite sample size and neutron field inhomogeneity

1. This issue was touched upon earlier. There are two basic considerations: (a) If the sample is fairly extensive in its dimensions, compared to the natural variations of the neutron field (e.g., a point neutron source and a sizable disk sample nearby), then the analysis must take into account flux variations across the sample [See Fig. 8.1, On Page 98]. (b) If the sample is also fairly massive, then its presence will perturb the basic neutron field structure due to scattering and absorption effects [See Fig. 8.2, On Page 98]. i. The neutron field at point X has a deficit of neutrons directly from the source due to absorption, but an added component of scattered neutrons-that are not directionally correlated-due to scattering by the sample.

8.3

Finite sample size effects in activity counting .

1. Basically, the principles are the same as for neutron irradiation, but perhaps just reversed. Consider it as a symmetrical problem to neutron transport. (a) In neutron irradiations, the sample geometry effects the way neutrons emanating from a source reach the sample and produce reactions. (b) In sample counting, the sample geometry affects the way radiations from the activity decay in the sample reach the detector. 96

8.4

Geometric effects in ratio measurements .

1. The important point to stress here is that by the use of ratio experiments, and careful choice of the experimental design, the effects of geometry, absorption, etc., can be greatly minimized. This point can be illustrated as follows for the case of a neutron irradiation involving a point neutron source: [See Fig. 8.3, On Page 99].

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Figure 8.1: Interaction between finite sample size and neutron field inhomogeneity.

Figure 8.2: Sample perturbations.

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Figure 8.3: Geometric effects in ratio measurements.

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Chapter 9 CHEMICAL AND PHYSICAL PROPERTIES OF SAMPLES AND THEIR EFFECTS 9.1

Chemical impurities and related effects .

1. There are two basic reasons to be concerned about the chemical composition of samples: (a) One needs to know the total numbers of atoms in a sample of the particular species of interest, in order to perform accurate activation and cross section measurements. i. The sample weight is important. Furthermore, for unstable materials (volatile, oxidizable, etc.) this may change with time. ii. The stohiometry of the sample is important. One needs to know the precise chemical composition and, also, know that it is stable with time. EXAMPLE. Proton recoil detectors employ hydrogenous materials which are often polymers of the sort HX Cy . X and Y must be known accurately to determine the hydrogen atom content of a particular radiator film or deposit. iii. The isotopic abundances are also important. For rare isotopes, knowledge of these parameters is often uncertain by several percent. For some materials like Boron, Lithium or Uranium, that may have been artificially enriched or 101

depleted of a particular isotope, knowledge of the sample history is essential. (b) The second reason one needs to know sample composition is the effect of background or competing radiations. Certain impurities may produce intolerable levels of such unwanted radioactivity. i. This is especially a problem with reactor irradiations where very large thermal or resonance integral cross sections involving a minor impurity can completely destroy an experiment. EXAMPLE. Desired activity is β+ decay. However, a contaminant also decays by β+ emission. To get proper data, one needs to correct for this effect by either knowing the abundance of the contaminant and its activation cross section, or by distinguishing on the basis of half life, or by chemical separation.

9.2

Thermo-mechanical effects .

1. Irradiation environments can be quite harsh. (a) Moisture can be present which oxidizes the sample or is absorbed hygroscopically. (b) AT high temperatures, samples can melt or vaporize, or undergo chemical reactions. This can cause loss of material or changes in the geometry which affect sensitive measurements.

9.3

Sample inhomogeneity and related effects .

1. It was already pointed out that sample inhomogeneity is intolerable in many experiments because it destroys the possibility for modeling sample geometry, absorption and scattering effects, both in neutron irradiations and in sample counting. 102

(a) The opportunity for such modeling is essential to allow reliable data corrections to be made.

9.4

Sample assay

1. The starting point is to employ research grade materials, obtained form reliable suppliers and possessing certified documentation on composition and physical properties. Such materials can be costly, but they avoid a lot of grief. 2. If other materials are used, then some of the batch ought to be subjected to spectrochemical analysis. If isotopic composition is an important issue, then one needs to know the history of the material. 3. If one is concerned about possible radioactivity interferences from a particular impurity, then trial irradiations and counts of that material, and perhaps other samples with various concentrations of that impurity, can provide very useful information for sorting out the effects of that contaminant.

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104

Chapter 10 STATUS OF THE DATA BASE FOR ACTIVATION REACTIONS 10.1

Experimental information.

1. Certain reactions which play important roles in technology are adequately known for most applications, while others are perhaps acceptably well known in one context (e.g., fast fission reactors) but not for another (e.g., fusion). (a) One should never assume that knowledge is adequate for a particular application without examining the exiting experimental data base. To do this, one can refer to cross section data compilation plots (e.g., BNL-325), data inventories (e.g., CINDA) or data archives (e.g., CSISRS-EXFOR system). (b) One ought to perform some from of sensitivity analysis to determine just how accurately one has to know the pertinent parameters. (c) As a general rule (with numerous exceptions, of course): i. Measurements at the 15-20% accuracy level are not too difficult to meke. Many corrections can be ignored. ii. Measurements at the 10% level require attention to the details, but many corrections need to be labored over too much. Rough approximations may suffice for a well-designed experimenat. iii. Measurements at the 5% level require careful attention to detail and accurate corrections. Things must not be overlooked. While a sigle experiment may fix a parameter to 105

5% accuracy with reasonable confidence, verification by other experiments with different techniques are very desirable and probably necessary. iv. Measurements at the 1% level require years (perhaps decades) of effort, attention to minute details, and input from many different laboratories. Very few nuclear parameters are known to this accuracy level.

10.2

Evaluations .

1. We do not have the resources (time and data) to examine the status of evaluations available for this reactions in this lecture. That job could cost any individual, with training and access to all the needed information, months or perhaps years of toil. (a) Instead, we will focus on some general considerations about which one ought to be aware when dealing with this problem. 2. Users of cross section or decay data ought to employ evaluated information, not individual data sets, in any analysis which involves such parameters. There are some very fundamental reasons for this: (a) From a statistical point of view (Lectures 4.2.a and 4.2.b), no one single set of data (though, in reality, it might be closer to the “truth ”than any other) has the higher probability associated with it of being the “wisest ”choise. Evaluated information, which makes use of all available information, carries a lower risk factor associated with its use. (b) Applied scientist ought to resort to common data sets, or at least no more than a few well-documented sources of evaluated information, in their analyses. Only in this way can “data ”be eliminated as a source of disagreement between workers. 3. Anyone who uses evaluated data from file ought to spend some time examining the origins of the evaluation (documentation, comment cards, etc.). Only in this way can the probable reliability be properly assessed. 106

4. If there are no experimental data available, or few data, and a complete evaluation is available, one can be sure that it results from nuclear model calculations. (a) This may be superior to having no information at all but, in view of the wide disparities of such calculated results for many reactions over wide energy ranges (i.e., factors of 2 to 10), one ought to be quite skeptical of the quality of evaluations based entirely on nuclear models. Large errors have to be assigned in many cases. i. For example, activation cross section files exist with many thousand of reactions included. For most of these entries, the results are highly speculative. 5. One needs to be very careful in dealing with uncertainties of evaluations. (a) In many instances, no uncertainty information is provided. One is then forced to speculate on the uncertainties, for the purpose of performing sensitivities studies, or for such applications as dosimetry spectrum unfolding-where the mathematical procedures demand uncertainty information. (b) If uncertainty information is provided, the quality needs to be examined. Is the information adequate or will the deficiencies actually thwart any process which attempts to use it? EXAMPLE. Suppose an uncertainty file says the following for a threshold dosimetry reaction: 3.3-5.0 MeV: 25% error. All errors are 100% 5.0-9.0 MeV: 8% error. correlated within an 9.0-14 MeV: 15% error. energy block but are 14-15 MeV: 5% error. totally uncorrelated 15-20 MeV: 20% error. between blocks. So... the errors between 5.5 and 8.0 MeV are 100% correlated but between 6.2 and 9.1 MeV they are totally uncorrelated! i. This is quite artificial and probably unrealistic. It can lead to problems in dosimetry analyses.

10.3

Directions for future work . 107

1. Future progress in this field will be modest for the foreseeable future because of diminished resources. 2. Emphasis in the dosimetry reaction area should be placed on improvig the accuracy and reliability of those reactions which are already in common use, rather than opening up a lot of alternativebut probably equivalent-possibilities. (a) One exception is the need for threshold reactions with lowenergy response in the 100 keV to 1 MeV range. This could be achieved by developing more inelastic scattering reactions, (n,n), which excite isomers in medium to heavier mass nuclei. This should be further exploited. 3. It should be established that thoroughly “modern ”evaluations have been done on the important reactions, i.e., that optimal use of the experimental information has occurred, that these data have been properly adjusted for standards, corrections, etc., wherever possible. (a) Also, modern statistical methods should be used in the evaluations. 4. If nuclear models have to be used, than the calculations should be done systematically by people who truly understand the codes, parameters and procedures. Extensive benchmarking against data will improve reliability. 5. A continued measurement effort, worldwide, is required in order to address acknowledged deficiencies and to respond to new needs as they develop. 6. Education: Workers in the field who would do the experiments and/or evalutions, as well as users of the information, need to be aware of the modern techniques for (a) Designinng experiments. (b) Analyzing the data and applying corrections. (c) Statistical analysis procedures. (d) Extracting and using information from computer files (data inventories, archives, evaluated files, etc.). 7. Progress in this field has been and will continue to be evolutionary rather than revolutionary ! 108