Large scale shell model calculations for neutron rich fp-shell nuclei

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1 Large scale shell model calculations for neutron rich fp-shell nuclei Physical Research Laboratory, Ahmedabad , India Collaborators: I. Mehrotra (Allahabad) P.Van Isacker (GANIL, France) V.K.B. Kota (PRL, Ahmedabad) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 1 / 30

2 Structure of neutron rich nuclei as N 40 with Z < 30 Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 2 / 27

3 Experimental status: CLARA-PRISMA setup at Legnaro. Structure of Cr,Mn and Fe isotopes. LISE/VAMOS setup at GANIL. Structure of Ni, Cu and Zn isotopes. RIKEN and MSU. Development of Large Deformation in 62 Cr. N. Aoi et al., PRL 102 (2009) Collectivity at N = 40 in 64 Cr. A. Gade et al., PRC 81 (2010) (R). Collectivity at N = 50: in 82 Ge and 84 Se. A. Gade et al., PRC 81 (2010) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 3 / 30

4 Motivations Neutron rich Fe, Mn, Co, Ni, Cu, Zn isotopes Test the adequacy of the chosen valence spaces, full fp and fpg 9/2. Test the suitability of the best pf effective interactions GXPF1A due to Honma et al. and KB3G due to Poves et al. and the fpg 9/2 space interaction (called fpg interaction) due to Sorlin et al. Onset of collectivity in these neutron rich nuclei as N approaches 40 shell closure. To cheak the importance of the intruder 2d 5/2 and 1g 7/2 orbitals in generating collectivity. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 4 / 30

5 Large scale shell model calculations for Fe isotopes P.C. Srivastava and I. Mehrotra J. of Physics G: Nuclear and Particle Physics 36 (2009) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 5 / 30

6 S. Lunardi et al., Phys. Rev. C 76 (2007) GXPF1A: M. Honma et al., Eur. Phys. J. A 25 (2004) 499. fpg: O. Sorlin et al., Phys. Rev. Lett. 88 (2002) KB3G: A. Poves et al., Nucl. Phys. A 694 (2001) 157. E (MeV) Fe Fe E (MeV) Exp. GXPF1A fpg Exp. GXPF1A fpg Figure: Energy levels of 62 Fe. Figure: Energy levels of 64 Fe. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 6 / 30

7 Fe 2.0 E( ) E (MeV) 1 E(2+) MeV Exp. GXPF1A fpg N Figure: Energy levels of 66 Fe. GANIL Cluster Figure: E( ) in Fe isotopes. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 7 / 30

8 Fe 56 Fe 58 Fe 52 Fe 60 Fe Fe Fe 62 Fe B (E2) (W.u.) Dimensions in m scheme Fe 64 Fe Fe 66 Fe 0 N A Figure: B(E2) in Fe isotopes. Figure: Dimension Table: Excitation energies, quadrupole moments and B(E2) for Fe isotopes. 62 Fe 64 Fe 66 Fe E( )(MeV) E( )(MeV) Q( )(efm 2 ) B(E2)(W.u.) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 8 / 30

9 Table: Main configurations in the wave functions of the ground state and the first exited state for Fe calculated with GXPF1A interaction. Nuclei J π Wave function Probability Neutron Proton 62 Fe 0 + gs (0f 7/2 ) 8,(1p 3/2 ) 4,(1p 1/2 ) 0,(0f 5/2 ) 4 (0f 7/2 ) Fe gs 7/2 3/2 1/2 5/2 (0f 7/2 ) 8,(1p 3/2 ) 4,(1p 1/2 ) 2,(0f 5/2 ) 4 7/2 (0f 7/2 ) (0f ) 8,(1p ) 4,(1p ) 0,(0f ) 4 (0f ) Fe 1 (0f 7/2 ) 8,(1p 3/2 ) 4,(1p 1/2 ) 2,(0f 5/2 ) 4 (0f 7/2 ) gs (0f 7/2 ) 8,(1p 3/2 ) 4,(1p 1/2 ) 2,(0f 5/2 ) 6 (0f 7/2 ) (0f 7/2 ) 8,(1p 3/2 ) 4,(1p 1/2 ) 2,(0f 5/2 ) 6 (0f 7/2 ) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 9 / 30

10 P.C. Srivastava and I. Mehrotra, Phys. At. Nucl. 73 (2010) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 10 / 30

11 Results and Discussion Experimental data is very well reproduced for 62 Fe and the agreement is better than the earlier calculations carried out in fpg space. For 64 Fe the results are almost same as those obtained with fpg configuration space. The agreement gets worse for 66 Fe showing the inadequacy of the chosen configuration space. The negative parity states of 61 Fe can be well reproduced with GXPF1A interaction in full fp space without truncation but for 63 Fe the correct ordering of levels is not reproduced. The structure of the wave function for the ground state and the first excited state of odd Fe isotopes suggest that the orderings of the single particle energy levels gets modified due to monopole correction. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 11 / 30

12 Large scale shell model calculations for Mn isotopes Model space for fpg-interaction In this an inert core of 48 Ca is considered and the valence space chosen is the whole fp shell for the protons and the 1p 3/2, 0f 5/2, 1p 1/2 and g 9/2 orbitals for the neutrons,more accurately 40 Ca core with eight f 7/2 frozen neutrons. In fpg we used truncation by allowing up to a total of six particle excitations from the f 7/2 orbital to the upper fp orbitals for protons and from the upper neutron fp orbitals to the g 9/2 orbital. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 12 / 30

13 D. Steppenbeck et al., PRC 81 (2010) S.N. Liddick et al., PRC 72 (2005) ; PRC 73 (2006) Recently D. Steppenbeck et al., have reported many high-spin states of 58 Mn above 1338 kev. In this experiment they observed four levels within 500 kev above 1338 kev. They make plausible arguments that these levels may be negative-parity states. This is an indication of at least one particle in 0g 9/2 orbital. P.C. Srivastava and I. Mehrotra, Eur. Phys. J. A 45 (2010) 185. For low-lying states up to 1MeV, both KB3G and GXPF1A are good. Above 1 MeV, both for high-spin positive- and negative- parity states it is necessary to include the 0g 9/2 orbital. The results of the present fpg interaction indicate that a further modification of its present form is required. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 13 / 30

14 (7) (6) Mn Energy (MeV) ( ) ( ) ( ) ( ) ( ) (3 + ) (3 + ) ( ) ( ) ( ) (5) (4) Experimental GXPF1 GXPF1A KB3G fpg Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 15 / 27

15 Many high-spin states for 60 Mn above 2223 kev, reported by D. Steppenbeck et al. these levels may be negative-parity states. For low-lying states up to 1 MeV, the KB3G interaction is better than GXPF1A interaction. The fpg interaction predicts more compressed levels for negative-parity states and also they lie very low in energy Mn 2.5 (7) (9) (6) (7 + ) Energy (MeV) ( ) ( ) + (3 + ) (2 ) Experimental GXPF1 GXPF1A KB3G fpg Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 15 / 30

16 Experimentally, for 62 Mn there is an uncertainty in assiging the ground-state spin to be,3 + or. The fp and fpg interaction predicts as a ground state. The predicted results of fpg interaction may be relevant. However, the experimental data is very sparse, thus it is not possible to make any definite conclusions regarding the prediction of fpg interaction. Dimension for 62 Mn 10 7 in fpg space. Energy (MeV) (3 +,, )? 0 Expt. GXPF1A KB3G fpg GANIL-PRL Cluster 62 Mn Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 16 / 30

17 Table: The extent of configuration mixing involved in Mn isotopes for different states. For each state the numbers quoted are S, sum of contributions from particle partitions each of which is contributing greater than 1%; M, maximum contribution from a single partition, and N, total number of partitions contributing in S. J π Mn 33 J π Mn 35 S, M, N S, M, N GXPF1A gs 74.7, 25.9, 16 gs 82.9, 34.7, , 22.2, , 39.6, , 22.0, , 23.0, 17 KB3G gs 79.0, 35.4, 17 gs 82.3, 42.3, , 28.1, , 36.5, , 36.4, , 35.4, 15 J π Mn 37 S, M, N fpg gs 69.5, 13.8, , 14.1, , 15.6, 20 Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 17 / 30

18 Results and Discussion For low-lying states in 58 Mn both KB3G and GXPF1A predict good results and for 60 Mn, KB3G is better than GXPF1A. For 62 Mn, the predicted results of the fpg interaction may be relevant. A key feature yet to be identified in the neutron-rich odd-odd Mn isotopes is the location of the negative parity levels that could signify the presence of 0g 9/2 orbital. Influence of the νg 9/2 orbital on level structures of neutron rich 61,62 Mn 36,37 - C. J. Chiara et al.,prc (2010) in press. More experimental data on higher neutron-rich Mn isotopes are needed to discuss the onset of the collectivity while approaching N = 40. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 18 / 30

19 Shell-model results in fp and fpg 9/2 spaces for 61,63,65 Co isotopes: D. Pauwels et al., PRC 78 (2008) (R). D. Pauwels et al., PRC 79 (2009) P.H. Regan et al., PRC 54 (1996) The large scale shell model calculations for 61,63,65 Co have been carried out with different effective interactions and valence spaces. Full fp shell calculations for 63,65 Co and a truncated one for 61 Co, using two recently derived fp shell interaction GXPF1A and KB3G with 40 Ca as core. Second set of calculations using fpg interaction due to sorlin et al., Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 19 / 30

20 D. Pauwels et al., PRC 78 (2008) (R) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 20 / 30

21 P.C. Srivastava and V.K.B. Kota, Phys. At. Nucl. 74 (2011) in press. 61 Co 19/ (19/2 ) 4802 (17/2 ) /2 17/ /2 17/ / Energy (kev) (15/2 ) 3657 (13/2 ) 3471 (15/2 ) 3126 (13/2 ) 2374 (11/2 ) / / / / / /2 11/ / / /2 13/2 11/2 9/2 15/ / / /2 13/2 9/ / /2 13/2 11/ /2 0 Experimental 7/2 0 7/2 GXPF1A 0 7/2 0 KB3G fpg Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 21 / 30

22 PRL, HPC Cluster Dimension Co 19/ /2 19/2 17/ / / /2 Energy (kev) (19/2 ) 4167 (17/ (17/2 ) 3610 ) (15/ ) (15/2 ) 3203 (13/2 3034(13/2 ) 3007 ) (11/ ) 11/ / / / / / /2 13/ / / / /2 13/ / / / / / /2 11/ / / / / /2 9/ / / / /2 0 7/2 0 7/2 0 7/2 0 Experimental GXPF1A KB3G fpg Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 22 / 30

23 65 Co (15/2 ) / / /2 15/ Energy (kev) (13/2 ) 2669 (11/2 ) 2479 (3/2 ) 1997 (11/2 ) 1642 (9/2 ) 1479 (3/2 ) 1223 (1/2 ) 1095 (3/2 ) /2 13/2 9/ / / / / / / / /2 3/ / / /2 9/ /2 3/2 3/ /2 3/ / /2 596 (7/2 ) 0 7/2 0 7/2 0 7/2 0 Experimental GXPF1A KB3G fpg Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 23 / 27

24 For 61,63 Co the GXPF1A and KB3G are reasonable. For 65 Co, the results in the extended model space i.e. in fpg 9/2 space does not reproduce correct experimental finding. Further with monopole correction by reducing the gap between f 7/2 -f 5/2, the 1/2 is still high and 11/2 1 is low. Thus it appear to be necessary to include the intruder 2d 5/2 orbital while approaching N 40. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 24 / 30

25 fpg 9/2 d 5/2 effective interaction: Island of inversion around 64 Cr S.M. Lenzi, F. Nowacki, A. Poves and K. Sieja PRC 82(2010) pf shell for proton and f 5/2 pgd 5/2 shell for neutrons. Dimension for 64 Fe Onset of deformation in Fe and Cr. Co istopes around N = 40 F. Recchia et al. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 25 / 30

26 Neutron rich Ni, Cu, Zn isotopes Effective single particle energies in Sc isotopes using pfg9 interaction Energy HMeVL g 9ê2 0f 5ê2 1p 1ê2 1p 3ê2 0f 7ê Neutron number N Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 26 / 30

27 Effective single particle energies in Sc isotopes using pfg9a interaction 10 5 Energy HMeVL g 9ê2 0f 5ê2 1p 1ê2 1p 3ê2 0f 7ê Neutron number N Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 27 / 30

28 3 Ex SM Ex SM Ex SM Ex SM Ex SM Ex SM 3ê2-1ê2 - Energy HMeVL ê2-7ê2-7ê2-1ê2-5ê2-3ê2-9ê2-7ê2-7ê2-1ê2-5ê2-3ê2-7ê2-9ê2-7ê2-1ê2-3ê2-5ê2-9ê2-7ê2-1ê2-9ê2-7ê2-1ê2-3ê2-3ê2 -? 5ê2 -? 5ê2 -? 7ê2-5ê2-69 Cu Cu Cu Cu Cu Cu (With P.Van Isacker) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 28 / 30

29 Future directions: Three-body interactions A.P. Zuker, PRL 90 (2003) T. Otsuka et al., PRL 105 (2010) P. Van Isacker and I. Talmi, EPL 90 (2010) Pairing plus quadrupole-quadrupole plus quadrupole-pairing interaction Projected shell model description for high-spin states in neutron-rich Fe isotopes Y. Sun et al., PRC 80 (2010) Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 29 / 30

30 Summary It is necessary to generate, good fpg 9/2 and fpg 9/2 d 5/2 space effective interactions (with 48 Ca core) for neutron rich Fe, Mn and Co and also for Ni, Cu and Zn isotopes. For neutron rich fp-shell nuclei, the neutrons excited to the sdg orbitals coupled to the unfilled 1f 7/2 proton orbital generate deformation. Collectivity is more important as N approaches 40 for fp shell nuclei. The fpg interaction adopted in the study is inadequate and also point out that it is necessary to include orbitals higher than 1g 9/2 for N > 36 isotopes. Imprtance of the role of three body forces. Large ( Physical scale shell Research model calculations Laboratory, Ahmedabad-380 for neutron rich fp-shell 009, India) nuclei 30 / 30

SHELL-MODEL RESULTS IN fp AND fpg 9/2 SPACES FOR

SHELL-MODEL RESULTS IN fp AND fpg 9/2 SPACES FOR 61,63,65 Co ISOTOPES P.C. Srivastava 1, * 1, ** and V.K.B. Kota 1 Physical Research Laboratory, Ahmedabad, India arxiv:1004.4443v2 [nucl-th] 18 May 2011