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Neutron Separation Energies of Ca, Sn and Pb Isotopes Using Different Proceedings of the DAE-BRNS Symp. on Nucl. Phys. 60 (2015) 130 Neutron separation energies of Ca, Sn and Pb isotopes using different mass models R. N. Panda1,∗ S. K. Patra2,† and S. A. Abbas3‡ 1Department of Physics, ITER, Siksha O Anusandhan University, Bhubaneswar-751 030, India 2Institute of Physics, Sachivalaya Marg, Bhubaneswar-751 005, India and 3Jafar Sadiq Research Institute, New Sir Syed Nagar, Aligarh - 202 002, India Introduction 40 35 RMF EXPT Many microscopic theories have been de- Ca INM voted for calculating nuclear masses, bind- 30 ing energies, nucleon separation energies and 25 other global properties. Nucleon separation 20 MeV 2n energy plays an important role in predicting S 15 new shell closures in the proton and neutron drip line nuclei. The one and two nucleon 10 separation energies are fundamental proper- 5 ties of the atomic nucleus. The systematic 0 study of proton and neutron separation ener- 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 N gies are essential to investigate nuclear struc- ture toward drip lines [1]. In literature it is FIG. 1: Two neutron separation energy for 20Ca understood that the energy spend in remov- as a function of N for fixed Z using different mass ing two fermions from a system of identical models and experimental result. fermions shows system stability [2]. If the pairing dominates in fermion-fermion inter- action, then energy required to separate two iment. The INM model of atomic nuclei was fermions for even number of particles will be prepared in 1999 [5] using known mass data of much higher than odd number. These charac- Audi-Wapstra published in 1993 [6]. During teristics can be observed from the study of two the last few decades, RMF theory is very suc- neutron separation energy S2n. It is known cessful in describing many nuclear phenomena that in neutron-rich nuclei, odd magic num- for both stable and unstable nuclei. RMF the- bers disappear and new ones appear. It is ory can reproduce the accurate nuclear satura- also very useful to plot S2n and study the tion properties in nuclear matter and account kinks as evidence for magicity [3]. In this automatically the spin orbit interaction. The work we present an investigation of S2n which use of RMF formalism for finite nuclei as well is quite a sensitive quantity to test any micro- as the infinite nuclear matter are well docu- scopic model [4]. Two popular models are Rel- mented and details can be found in [7]. ativistic Mean Field (RMF) and Infinite Nu- Two neutron separation energy is the re- clear Matter (INM) model. The objective of quired energy to remove two neutrons from a the present study is to undertake a system- nucleus with Z protons and N neutrons. It is atic analysis of two neutron separation energy calculated by using the expression: using these models in comparison with exper- S2n = BE(N,Z) − BE(N − 2,Z) (1) It is a big challenge for nuclear many body ∗Electronic address: [email protected] theories to explain shell closure, new magic- †Electronic address: [email protected] ity in terms of proton and neutron separation ‡Electronic address: [email protected] energies [3]. To discuss the usefulness of dif- Available online at www.sympnp.org/proceedings Proceedings of the DAE-BRNS Symp. on Nucl. Phys. 60 (2015) 131 shell closures if the proton spherical subshell closures will not influence the two neutron sep- 40 aration energies. RMF 35 EXP INM Summary and Conclusion 30 Sn In this work, the results of self-consistent 25 RMF calculations for two neutron separation MeV 20 2n energies have been performed for Ca, Sn and S 15 Pb isotopes using RMF theory for NL3 param- eter set. Our calculations using RMF theory 10 and predictions of INM model are in excellent 5 agreement with the experimental results [8] for 0 55 60 65 70 75 80 85 S2n. The two neutron separation energies and N their variation with proton and neutron num- FIG. 2: Same as figure 1 but for 50Sn. ber disclose nuclear structure information and it gives a check for various nuclear structure models. In this regard a further study like S2p, 24 S1p, S1n are in progress. RMF EXP Pb INM 20 References 16 [1] C. A. Radha, V. Ramasubramanian and MeV 2n 12 E. J. J. Samuel, Elect. J. of Theo. Phys. S 8, 327 (2011). 8 [2] S. Anghel, G. C. Danil, and N. C. Zamfir, 54 4 Rom. Journ. Phys. , 301 (2009). [3] A. Abbas, Mod. Phys. Lett. A 20, 2553 0 100 105 110 115 120 125 130 (2005). N [4] S. Zhang, Jie Meng and S. Zhou, Science 82 46 FIG. 3: Same as figure 1 but for Pb. in China(Series G) , 632 (2003). [5] R. C. Nayak and L. Satpathy, At. Data and Nucl. Data Tables 72, 213 (1999). ferent models we plot S2n as a function of N [6] G. Audi and A. H. Wapstra, Nucl. Phys. for a particular Z using different isotopes of A 565, 1 (1993). Ca, Sn and Pb. We shall find here that these [7] S. K. Patra and C. R. Praharaj, Phys. new plots give useful information regarding Rev. C 44, 2552 (1991); Y. K. Gambhir, P. the advantage of different models. The evolu- Ring, and A. Thimet, Ann. Phys. (N.Y.) tion of nuclear collectivity is observed in terms 198, 132 (1990). of smooth variation of S2n as a function of N [8] G. Audi, O. Bersillon, J. Blachot and A. or Z. It also shows the position of neutron sub- H. Wapstra, Nucl. Phys. A 729, 3 (2003). Available online at www.sympnp.org/proceedings.
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