NEW PHENOMENON IN EXOTIC NEUTRON-RICH Sn ISOTOPES : ROLE OF 3-BODY FORCE S. Sarkar, M. Saha Sarkar Bengal Engineering and Science University, Shibpur, Howrah - 711103, INDIA Saha Institute of Nuclear Physics, Kolkata 700064, INDIA E-mail: ss@physics.becs.ac.in 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Experimental Chart of Nuclei 132Sn 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Introduction: 132Sn region Nuclei with 50 Z 56 and 82  N  88 in the (gdsh) (hfpi) valence space above the 132Sn core lie on or close to the path of astrophysical r-process flow. Their structure,particularly the binding energy (BE), low-lying excited states and beta decay rates at finite temperatures are important ingredients for nucleosynthesis calculations. Sn isotopes are of particular importance. Even Sn isotopes, say 136Sn, is known to be the classical "waiting point" nucleus in A=130 solar system abundance peak under typical r-process condition. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Experimental Status Spectroscopic information, such as BE and low lying spectrum, is known experimentally only for 134Sn. Recently half-lives of 135-137Sn have been measured through -n decay process. No other information exists.Lifetimes of these nuclei are very small and production rates are also very low presenting challenges to spectroscopic studies. Reliable theoretical results are therefore necessary and useful. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS E(2+1) of Sn isotopes(A=102-134) 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Theoretical Endeavours Shell Model Calculations: Few valence particle nuclei above the doubly closed magic 132Sn core are generally described in the valence space consisting of Proton (1g7/2, 2d5/2, 2d3/2, 3s1/2 and 1h11/2) and Neutron (1h9/2, 2f7/2, 2f5/2, 3p3/2, 3p1/2 and 1i13/2) orbitals. Remarkably good results for isotopes of Sn, Sb, Te, I, Xe, Cs with different interactions for 134 A 138 and 50 Z  56. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Interactions used Primarily two types of interactions used: realistic and empirical Empirical interactions : the interaction derived from 208Pb region (Chou & Warburton) which fails for N > 84: specific matrix elements are tuned to reproduce known experimental levels (S. Sarkar and M. Saha Sarkar) Realistic interactions obtained starting with a G matrix derived from the CD-Bonn nucleon-nucleon interaction using the Q-box method (B.A. Brown, M. Hjorth-Jensen, T. T. S. Kuo, and E. Osnes, + F. Andreozzi, L. Coraggio, A. Covello, A. Gargano) 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Structure of even-even A = 138 isobars and the yrast spectra of semi-magic Sn isotopes above the 132Sn core, S. Sarkar and M. Saha Sarkar, PHYSICAL REVIEW C 78, 024308 (2008) SMPN CWG 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Casten-Sherill Systematics Casten and Sherill have pointed out that, although [E(2+1 )Sn − E(2+1 )Te] 400 keV for a given neutron number over most of the N = 50–82 shell, the difference is only 119 keV for N = 84 R. F. Casten and B. M. Sherill, Prog. Part. Nucl. Phys. 45, S171 (2000). The difference for N = 86 is 108 keV with SMPN. It is consistent with the trend discussed by Casten and Sherill. (Casten-Sherill Systematics) For CWG, this difference is 733 − 356 = 377 keV for N = 86, which deviates from the trend. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Present Work We have used extended the calculations for more neutron rich 140Sn The shell model codes OXBASH and NUSHELL@MSU have been used The results are The E(2+1 ) for 140Sn is 1949 keV showing a sudden increase for N=90, indicating a shell closure With CWG interaction, the 0+1 - 2+1 spacing remains nearly constant at around 750 keV for 136−142Sn, except for a small increase at 140Sn To understand the implication of these completely different trends in the results using these two interactions, the theoretical results for these experimentally unobserved nuclei have been compared with the E(2+1) values of neutron rich nuclei in other mass regions for which experimental data are available. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Comparison with neutron-rich isotopes 140Sn 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS The shell closure at N=90 In order to put forward further evidence and to understand the shell closure at 140Sn more precisely, the effective single-particle energies (ESPE) for the neutron orbitals for the two Hamiltonians have been compared. The ESPE is defined as bare single particle energy (spe) added with the monopole part of the diagonal two body matrix elements (tbme). 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Neutron ESPEs with CWG and SMPN interactions for increasing neutron numbers 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Origin of this new shell closure Spin-tensor decomposition of the two body matrix elements (tbmes). - central, antisymmetric spin-orbit (ALS), spin-orbit (LS) and tensor parts of tbmes identified For SMPN, the central and ALS part for 2f7/2- 2f7/2 tbmes account for majority of the downward shift of the ESPE of 2f7/2with increasing valence neutron number (n). tbmes involving 3p3/2 - dominant contribution from the central part. The central parts of 2f7/2 and 3p3/2 vary with similar slopes for increase in n. Variation in ALS part is primarily responsible for this observed shell gap at N=90. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Decomposition 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Decomposition of USD tbmes for oxygen isotopes 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

The implication of ALS term? ALS component in the tbmes corresponds to those LS-coupled matrix elements which have SS, i.e., terms non-diagonal in S (spin). Do not conserve total spin of the matrix elements. But the interactions which are parity conserving and isospin conserving must also conserve the total spin. Bare nucleon- nucleon force contains no ALS term. But effective interaction is not simply related to bare nucleon-nucleon force. Core polarisation corrections to the G-matrix give rise to non-zero but small ALS matrix elements. A characteristic feature common to many empirical effective interactions is strong ALS components in the tbmes. It usually arises from inadequate constraint by the data. It indicates the important contributions from higher order renormalisation or many body forces to the effective interactions. In empirical SMPN such many - body effects might have been included in some way through the modification of important tbmes. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Features of Realistic Interaction Two-body realistic interactions derived from the free nucleon-nucleon force fail to reproduce some shell closures. increase of the 1d5/2 - 2s1/2 gap for Z=8 and 1f7/2 - 2p3/2 gap for Z=20 (as a function of neutron number), required to explain empirical data are not obtained in the calculations with these interactions. It has been shown that the three-body forces have to be taken into account to reproduce these shell gaps. Otsuka et al. have proposed a three-body delta-hole mechanism to explain these shell gaps and they have shown that three-body forces are necessary to explain why the doubly-magic 24O nucleus is the heaviest oxygen isotope Zuker showed earlier that a very simple three-body monopole term can solve practically all the spectroscopic problems in the p, sd, and pf shells those were hitherto assumed to need drastic revisions of the realistic two-body potentials. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Three body forces and CWG interaction A simple three-body monopole term in CWG as prescribed by Zuker Corrections in 2f7/2-2f7/2 and 2f7/2-3p3/2 tbmes similar to those in KB3 for 1f7/2-1f7/2 and 1f7/2-2p3/2 tbmes. Included the effect of mass scaling. By (40/132)(1/3) factor. This factor reduces the effect of three - body correction on CWG compared to that in KB3. The correction terms included in the tbmes are V J,T=1ffff (CWG3M)= V J,T=1ffff (CWG)−74 keV, for J=0,4and 6; V J=2,T=1 ffff (CWG3M)= V J=2,T=1ffff (CWG) − 208 keV and V J,T=1 frfr (CWG3M)= V J,T=1 frfr (CWG)+201 keV for J=2, 3, 4 and 5. f stands for 2f7/2 and r stands for 3p3/2. The correction factor will be effective for nuclei for which the valence neutron number n≥ 3. A shell gap for N=90 now appears with CWG3M which is very close to that with SMPN. The E(2+1 ) energies of 136,138Sn are 0.639 and 0.633 MeV, respectively. The E(2+1 ) energy of 140Sn predicted by CWG3M (1.889 MeV) is close to that predicted by SMPN (1.949MeV). 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Comparison with neutron-rich isotopes 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Neutron ESPEs with CWG interactions for increasing neutron numbers 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Wavefunction structure for CWG 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Wavefunction structure for SMPN 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Wavefunction structure for CWG3M For CWG3M, the wave function composition for the 0+ g.s is (70.4%) from the ν(2f7/2)8 partition, similar to SMPN (75.8%) But due to overestimation of the up-sloping trend of ν(3p3/2) ESPE and for non-inclusion of corrections for other spes, for 2+1 state, 29.0% originates from the ν(2f7/2)6(1h9/2)2 and 9.6% from ν(2f7/2)6(2f5/2)2. The effective energy gap between ν(2f7/2) and ν(2f5/2) (the lowest orbital which contributes to the composition of 2+ state) single particle orbitals is 2.370 MeV. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Conclusion A new shell closure at 140Sn has been predicted. ALS term in empirical interaction SMPN is found to be responsible for the gap observed in SMPN results. A simple three-body monopole term has been included in CWG to get CWG3M, which predicts a shell gap at N=90 for Sn isotopes as well as decreasing 2+1 energies for 136,138Sn, similar to that from SMPN. This also indicates that three body effect plays an important role for shell evolution in neutron rich Sn isotopes above 132Sn, as also observed in sd and fp shells. The anomalously depressed 2+1 states in Sn isotopes having N=84-88, and the new magic number for N=90, might have interesting consequences for the r - process nucleosynthesis. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Construction of the new Hamiltonian Modification of the CW5082 [W.T. Chou and E.K. Warburton, Phys. Rev. C 45, 1720 (1992)] Hamiltonian in the light of recently available information on binding energies, low-lying spectra of A=134 Sn,Sb and Te isotopes. The spes of the single particle orbitals of the valence space above the 132Sn core have been replaced by the recently measured ones. The details of this modification procedure have been given in [Sukhendusekhar Sarkar, M. Saha Sarkar, Eur. Phys. Jour. A 21 (2004) 61]. The new Hamiltonians work remarkably well in predicting binding energies, low-lying spectra and electromagnetic transition probabilities for N=82,83 and even for N >= 84 isotones of Sn,Sb,Te,I,Xe and Cs nuclei. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS References O. Sorlin, M. G. Porquet, Prog. Part. and Nucl. Phys. 61, 602 (2008). Takaharu Otsuka et al., Phys. Rev. Lett. 95, 232502 (2005). http://www.nndc.bnl.gov. M. P. Kartamyshev, T. Engeland, M. Hjorth-Jensen, and E. Osnes, Phys. Rev. C 76, 024313 (2007) and references therein. S. Sarkar, M. Saha Sarkar, Phys. Rev. C 78, 024308 (2008). Sukhendusekhar Sarkar, M. Saha Sarkar, Eur. Phys. Jour. A21, 61 (2004) and references therein; S. Sarkar and M. Saha Sarkar, Phys. Rev. C 81, 039803 (2010). B.A. Brown, N. J. Stone, J. R. Stone, I. S. Towner, and M. Hjorth-Jensen, Phys. Rev. C 71, 044317 (2005). Sukhendusekhar Sarkar, M. Saha Sarkar, Phys. Rev. C 64, 014312 (2001) and references therein. L. Coraggio, A. Covello, A. Gargano, and N. Itaco, Phys. Rev. C 72, 057302 (2005) and references therein. R. F. Casten and B. M. Sherrill, Prog. Part. Nucl. Phys. 45, 171 (2000). B.A. Brown et al., Oxbash for Windows PC, MSU-NSCL Report No. 1289, (2004); Nushell@MSU, B. A. Brown and W. D. M. Rae, MSU-NSCL report (2007). M.W. Kirson, Phys. Lett. 47B, 110 (1973); Kenji Yoro, Nucl. Phys. A 333, 67 (1980); B.A. Brown, W A Richter and B H Wildenthal, J. Phys.G: Nucl. Phys. 11, 1191 (1985); K. Yoshinada, Phys. Rev. C 26, 1784 (1982). A. Poves and A. Zuker, Phys. Rep. 70, 235 (1981); [26] A. P. Zuker, Phys. Rev. Lett. 90, 042502 (2003). Takaharu Otsuka, Toshio Suzuki, Jason D. Holt, Achim Schwenk, and Yoshinori Akaishi, arXiv:0908.2607v2, 25 Jan 2010. S. Sarkar, M. Saha Sarkar, arXiv:0910.2119v1, v2 [nucl-th], 12 Oct 2009. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS THANK YOU 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Onset of deformation for nuclei (Z54) Shell closure at N=90 with SMPN for Sn isotopes Does it contradict the experimentally observed fact that N=90 is suitable for onset of deformation for nuclei with Z  54, like Xe, Ba etc.) ? The neutron ESPEs for SMPN does not show much variation with increasing proton number at N=90 for Z > 50. The proton ESPEs for SMPN favours the onset of collectivity at N=90 for Z > 50. Evidenced by the substantial reduction of the (1g7/2) and (2d5/2) energy gap with (1g7/2)8. This is very similar to the appearance of the new shell gaps for the oxygen isotopes which disappears at larger Z values 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Proton ESPEs with SMPN interactions for increasing proton numbers for N=90 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Proton ESPEs with SMPN interactions for increasing proton numbers for N=90 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Neutron ESPEs with SMPN interactions for increasing proton numbers for N=90 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

132Sn region :Shell Model calculations It has been pointed out that there should be many points of similarity between the spectroscopy of the doubly closed shell regions around 208Pb and 132Sn. The single particle orbits above and below the shell gap in the two cases are similarly ordered. Every single particle orbit in the 132Sn region has its counterpart in the 208Pb region, with same radial quantum numbers but one unit larger in angular momentum l and j values. As a consequence, effective interactions in the Sn region can be estimated from the corresponding well studied effective interactions constructed for nuclei in the 208Pb region. J. Blomqvist, in Proceedings of the 4th International Conference on Nuclei far from Stability, Denmark, 1981 (CERN, Geneva, 1981), p. 536. W.T. Chou and E.K. Warburton, Phys. Rev. C 45, 1720 (1992). Sukhendusekhar Sarkar, M. Saha Sarkar, Phys. Rev. C 64 (2001) 014312 and references therein. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Procedure SINGLE PARTICLE ENERGIES (SPES) modified the CW5082 interaction. The valence space consists of five proton orbitals, [1g7/2 , 2d5/2 , 2d3/2, 3s1/2 and 1h11/2 ] with energies [0.(-9.6629), 0.9624, 2.4396, 2.6972, 2.7915] respectively, and [1h9/2, 2f7/2 , 2f5/2 , 3p3/2 , 3p1/2 and 1i 13/2] for neutrons with energies in MeV, [1.5609, 0.0 (-2.4553), 2.0046, 0.8537, 1.6557, 2.6950], respectively with 132Sn as the inert core. CHANGE IN TWO BODY MATRIX ELEMENTS (TBMES) In SMN change the neutron-neutron and proton-neutron tbmes keeping the proton-proton tbmes the same as those in CW5082. In SMPN change the neutron-neutron, proton-neutron AND proton-proton tbmes . 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Changes in two body matrix elements (tbmes) Neutron-neutron tbmes The six neutron-neutron diagonal tbmes with I = 0+ were multiplied by a factor of 0.48. This factor is obtained by reproducing the binding energy of 134Sn (-6.365 MeV). All the binding energies in MeV are with respect to 132Sn. Three excited states in 134Sn, predominantly from the neutron (2f7/2 )2, at energies 725.6, 1073.4, and 1247.4 keV are used to modify the < (2f7/2 )2 |V| (2f7/2 )2 > {2+,4+,6+ tbmes for neutrons. < (1h9/2 2f7/2 ) |V| (1h9/2 2f7/2 ) > {8+ changed to reproduce the energy of 8^+ level at 2508.9keV. neutron – proton tbmes Similarly, using binding energy (-12.952 MeV) and 1-, 2-, 3-, 4-, 7-, 8-, 10+, 9+, 10-, 11- and 12- excited levels at energies 13.0, 330.7, 383.5, 554.8, 283.0, 1073, 2434, 2126, 4094, 4425 and 4517 keV respectively, of 134Sb, we have modified 12 dominant proton-neutron tbmes. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Evolution of collectivity in neutron -rich Sn isotopes Level spectra of 135-138 Sn are unknown. The production rate very very low – difficult to produce more neutron rich isotopes Astrophysical Scenario – important - with respect to the r-process, 136Sn is a waiting-point nucleus for moderate neutron densities Theoretical suggestions and experimental hints that beyond the 132Sn core the Z=50 shell gap quickly disappears and nuclear deformation shows up around N =87. Already around N=84-85 a mild collectivity is recognised in the spectra of 137Te, 137I the spectra of 138Te and 139I show good vibrational characteristics. Thus it is of interest to see whether deformation develops in the close-to-dripline Sn isotopes. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Both give similar agreement: comparatively better with SMPN; R4=E4/E2 indicate vibrational spectrum Z=52, N=86 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

NEW FEATURE IN THE SEMI-MAGIC neutron –rich isotopes Depressed 2+ 24 May 2010, Italy Z=50, N=88 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS

Effective Single Particle Energy (ESPE) The ESPE is defined as bare single particle energy (spe) added with the monopole part of the diagonal two body matrix elements (TBME). The bare spe is originated from the interaction of a valence nucleon with the doubly closed core. The monopole interaction contribution is the (2J +1) weighted average of the diagonal TBME, which arises from the interaction of a valence nucleon with the other valence nucleons. Where stands for the (diagonal) matrix element of a state where two nucleons are coupled to an angular momentum J and an isospin T. If neutrons occupy j and one looks into the orbit j( j) as a proton orbit, the shift of the single-particle energy of j is given by where nn (j) is (the expectation value of) the number of neutrons in the orbit j. 24 May 2010, Italy 10th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS