High spin structure of
35Cl
and the sd-fp shell gap
RITESH KSHETRI Nuclear and Atomic Physics Division, Saha Institute Of Nuclear Physics, Kolkata, INDIA.
Plan of the Talk 1. Introduction & Motivation. 2. Experimental Details. 3. Experimental Results: * DCO & Polarization measurements. * Analysis of experimental sidefeeding intensity pattern. * Lifetime analysis using DSAM. * Level scheme. 4. Theoretical predictions with Shell Model. 5. Summary & Conclusion.
Introduction – Some issues of mass 40 region Indications of breaking of a semimagic shell closure (near N = 20) far from stability have been Phys. Lett. B 346 (1995) 9, observed in 31Na, 32Mg - in the "island of inversion”.
Phys. Rev. Lett. 99 (2007) 072502
→ Inversion of spherical closed shell and intrinsically deformed 2p-2h intruder configuration. → Consequence of reduced sd-fp shell gap.
Important for nuclei relatively close to stability line
Charge radius measurement of 40, 42, 44, 46, 48Ca nuclei Phys. Lett. B 522 (2001) 240
More studies of stable nuclei are needed before arriving at a general consensus Superdeformation in 40Ca & 36Ar, Violation of Mirror Symmetry observed.
Phys. Rev. Lett. 87 (2001) 222501 Phys. Rev. Lett. 92 (2004) 132502
Nuclei in this mass region have low level density ⇒ sidefeeding to a level may be substantial which presents great problem for measurement of lifetime of a level especially in the singles mode.
Need for DSAM from coincidence spectra
Motivations for studying 35Cl: a) probe high spin states, b) search for low-lying deformed states observed in neighbouring nuclei
36, 38Ar, 40Ca.
Earlier HI works on 35Cl: a) Warburton et. al. {Phys. Rev. C 14 (1976) 996}: Eex ~ 9 MeV, J ~ 13/2, angular distribution and lifetime measurements. b) Vedova et. al. {LNL Annual Report (2004) 7, AIP Conf. Proc. 764 (2005) 205, Phys. Rev. C 75, 034317 (2007)}: Eex ~ 22 MeV, J ~ 29/2, no detailed information on intensity, spin assignment and lifetimes
Experiments using fusion evaporation reaction INGA setup at TIFR, Mumbai (1) 28Si (70 MeV) + 12C (50µg/cm2), (Au backed ~ 10mg/cm2) − Seven angles (30°, 60°, 65°, 90°, 105°, 120°, 145°) – Fourteen NaI multiplicity detectors – BARC-TIFR Pelletron
INGA setup at IUAC, New Delhi (3) 28Si (88 MeV) + 12C (50µg/cm2), (Au backed ~ 10mg/cm2) – Two angles (80°, 136°) – Ten-element charge particle detector array – Four neutron detectors – IUAC Pelletron
Electronic setup at IUAC using INGA Clover modules and CANDLE data acquisition software
Eγ, Tγ were recorded. 34,35 Cl, 37,38 Ar, 38,39 K 17 18 19
Effect of Inverse Kinematics Phys. Rev. C. 7 (1973) 1120
For same Eex of CN (Ecm = 26.4 MeV)
( 12C, αp ) 35Cl β = ( 2.5 ± 0.4 ) % βspread = 17 % angular spread = 31ο 28Si
( 28Si , αp ) 35Cl β = ( 5.8 ± 0.4 ) % βspread = 7 % angular spread = 13ο 12C
Due to reactions that produce large recoil velocities & Array with better energy resolution. --- Doppler shift » FWHM --- Doppler Broadening is less due to small angle scattering of recoils.
Analysis Results Energy and Efficiency calibration was done with
60Co, 152Eu
and 66Ga (τ1/2 = 9.41 hr) sources. 52Cr (16O
(55 MeV), pn) 66Ga
833 keV
Multipolarity measurement of gamma-rays
γ
I 1 at θ=90ο gated by γ2 at 120ο RDCO = γ1 I at θ=120ο gated by γ2 at 90ο
11/2− 5407 2244 7/2−
γ
I 1 : Αrea corrected by efficiency
3163
γ1 (keV) γ2 (keV) RDCO (γ1 )
3163 3/2+
(gate)
0
+
20
3163
2244
0.9 (1)
2244
3163
1.0 (1)
L=2
+
2 6 4 6 k e V (7 /2 -> 3 /2 ) E2
N(00)
0
O
O
N(90 )-N(0 )
10
-1 0 -
3 1 6 3 k e V (7 /2 -> 3 /2 ) M2
-2 0 -3 0 2500
+
3000
E n e rg y (M e V )
3500
N(900)
52Cr (16O
1 .5 1 .4
Polarisation Measurement of gamma-rays
(55 MeV), pn) 66Ga {t1/2 = 9.41 hr} 833 keV
1 .3 1 .2
a
1 .1 1 .0 0 .9
Estimation of normalization factor a(Eγ)
0 .8 0 .7 0 .6 0 .5 0
500
1000
1500
2000
2500
3000
E n e r g y (k e V )
Measured Asymmetry values for different γ transitions
NIM A 423 (1999) 16
3500
4000
4500
5000
Mixing ratio
Analysis of side-feeding intensity pattern Observed lifetime (τeff ) of a Nuclear Level includes: 1. effect of actual lifetime (τ ) of the level 2. contributions (τd) from discrete transitions from above 3. contribution (τsf) due to side feeding. If τd & τsf » τ ⇒ τ & τeff are different If τd or τsf » τ ⇒ τ & τeff are different depending on Id & Isf Measure ⇒ Fractional side-feeding Intensity ( νsf ) νsf = ( Iout – Iin ) / Iout = [I3 – (I1 + I2)] / I3
Unknown Discrete Feeding
τd2
Direct Feeding
τd1
1 τsf
2 τ
3
Formulation using the statistical model CASCADE*: *F. Puhlhofer, Nucl. Phys. A 280(1976)267
Input contains adopted level schemes of all residue nuclei
CASCADE Output contains for each residual nucleus – population distribution over a matrix in Eex & J For a residual nucleus – using adopted level schemes & experimental branching ratios, we distribute these theoretical populations and calculate νsf of a level.
Double peaked nature E x p e rim e n ta l d a ta T h e o ry 1 .0
0 .8
νsf
0 .6
0 .4
0 .2
0 .0 3
4
5
6
7
8
E x (M e V )
⇒ seems promising & work still in progress
9
Formulation of coincidence Doppler Shift Attenuation Method Extracting τ from GTA spectrum: step 1: γ1 gated, observed γ → τeff measured (SF excluded, SF1 included). step 2: γ gated, observed γ1 → τdeff measured (SF1 included). step 3: from step1 & step2 ⇒ subtracted effect of SF1 → τ extracted
τ – not effected by SF
SF1
τd
SF γ1
τ γ
Extracting τ from GTB spectrum: If step 1 is not possible because of insufficient statistics of γ1 then putting gate on γ2 gives limit for lifetime:
τ < τeff τ – effected by SF
τa γ2
Examples of Doppler Shifted gated spectra
80
Data Lineshape Background
− 2179
Lineshape o
60
40 0 120 o
Entirely shifted
80
120
τ < 0.5 ps
40 0 160 120 80
o
90
40 0 2100
2150
2200
Energy (keV)
2250
Doppler-shifted spectra for 1059 keV γ-ray
Results of Lifetime Measurements (τmean) NNDC
Level Scheme of
35Cl
Case I
Theoretical Predictions with Shell Model
Valence Space - full sd for positive parity states and 1p-1h excitations for negative parity states
35 Cl 17 18
After depressing f7/2 & p3/2 spes by 1.5 MeV
Case II Valence Space – same for both parity states After depressing f7/2 & p3/2 spes by 4 MeV
Different amounts of reduction are needed in the two truncation schemes. ⇒ Strong dependence of the reduction on the truncation involved.
Wave function structure * For both truncation schemes, the wave functions show a single particle nature. * For the negative parity states upto 17/2−, the 1p−1h sd→fp excitation is dominant. * The positive parity states upto 9/2+ can be explained by full sd shell calculations while higher spin states show a dominance of two particle excitation to the fp shell.
* Ritesh Kshetri et. al., Proceedings DAE-BRNS Symposium on Nuclear Physics (India) 47B, (2004) 40; 50 (2005) 235 and 237. * Ritesh Kshetri et. al., Proceedings International Workshop on Nuclear Structure Physics at the Extremes: New Directions (India) {To be published in Narosa Publishing House; ISBN: 978-81-7319-897-7}, http://arxiv.org/abd/nuclex/0507019
35Cl
Discussion New levels, Jπ, δ, τ new
8
9
6
Interpreted by Shell Model 9
Excitations to fp shell - essential to reproduce even the positive parity higher spin states.
9
sd-fp shell gap has to be decreased to reproduce levels of both parities. This reduction apart from being real - may be due to the effective interaction used and/or the particular truncation scheme involved.
9
Shell structure changes for neutron-rich nuclei, but the observation of a reduced shell gap in the present case of a stable nucleus (along with 36S, 30, 34P ) indicates the importance of this issue for both stable and neutron-rich nuclei.
Acknowledgements • •
Mr. Pradipta Kumar Das for preparing the target. Accelerator staff at the BARC-TIFR Pelletron Accelerator Facility, Mumbai and the IUAC Pelletron Accelerator Facility, New Delhi for their sincere efforts in delivering the beams.
