Proceedings of the DAE Symp. on Nucl. Phys. 63 (2018) 334

RMF model based Investigation of Two Neutron Separation Energies for Middle Weight Nuclides near Drip Lines Smriti Thakur,∗ Virender Thakur,† and Shashi K Dhiman‡ Department of Physics, Himachal Pradesh University, Summer-Hill, Shimla-171005, INDIA

Introduction separable pairing interaction parameter, G = 3 The production of more and more new iso- 728 MeVfm and pairing width, a = 0.644 fm topes has revived the interest in nuclear struc- in the p-p channel. The Lagrangian density ture models in recent years. Understanding for mesons exchange approximation is given the structure of the atomic nucleus is one of as [1], the central challenges in nuclear physics. The ∑ µ 1 µ 1 2 2 study of nuclei lying far from the line of β- L = ψi(iγµ∂ − m)ψi + ∂µσ∂ σ − m σ 2 2 σ stability play an important role in our under- i standing of nuclear physics. Far away from 1 1 1 1 − Ω Ωµν + m2 ω ωµ − R⃗ R⃗ µν + m2⃗ρ .⃗ρ µ stability line, the limits of nuclear existence 2 µν 2 ω µ 4 µν 2 ρ µ are reached, where one or more nucleons are 1 − F F µν − g ψψσ − g ψγµψω − g ψ⃗τγµψ.⃗ρ no longer bound. Near nuclear driplines, the 4 µν σ ω µ ρ µ physics is very interesting and has fascinated µ −eψγ ψAµ. (1) the researchers to work on it. The purpose of present work to investigate theoretically the And the total Lagrangian density for point- two neutron separation energy (S2n) which re- coupling models is [2], flects the magicity of Shell Structure in the iso- 1 topic chains of Germanium, Selenium, Stron- L = ψ(iγ.∂ − m)ψ − αS(ρ)(ψψ)(ψψ) tium and Krypton. Our results are compli- 2 mented by the close agreement with the recent 1 µ 1 µ − αV (ρ)(ψγ ψ)(ψγµψ) − αTV (ρ)(ψ⃗τγ ψ)(ψ⃗τγµψ) available experimental data [4]. 2 2 1 1 − τ − δ (∂ ψψ)(∂ν ψψ) − eψγ.A 3 ψ. (2) Theoretical Framework 2 S ν 2 We have employed relativistic self- The Hamiltonian densities can be calculated consistent mean field models to construct from Eqs.(1,2) and hence the nuclear energy the Nuclear Density Functionals from La- density functional for DD-ME2, DD-PC1 re- grangian densities based on mesons exchange spectively. and point coupling models. The pairing correlations of nucleons are considered by Results and Discussions the relativistic Hartree-Bogoliubov functional The two neutron separation energy is de- based on quasi-particle operators of Bogoli- fined as the energy required to remove two ubov transformations. The nuclear energy neutrons from a nucleus. The two neutron density functionals are constructed by using separation energy is calculated using the for- meson coupling model with DD-ME2 pa- mula, rameterizations [1] and point coupling model with DD-PC1 parameterizations [2] with a S2n(Z,N) = [B(Z,N) − B(Z,N − 2)], (3)

where S2n(Z,N) defines the two neutron sepa- ration energy for the nuclei with atomic num- ∗Electronic address: [email protected] ber Z and neutron number N. We have theo- † Electronic address: [email protected] retically calculated S2n(Z,N) results for even- ‡Electronic address: [email protected] even isotopes of Ge, Se, Kr and Sr with the

Available online at www.sympnp.org/proceedings Proceedings of the DAE Symp. on Nucl. Phys. 63 (2018) 335

35 abrupt decrease in S2n(Z,N) values in Figs.(1 DDME,Ge DDME,Se DDPC,Ge DDPC,Se and 2) indicate that the energy necessary to 30 Expt.,Ge Expt.,Se

25

20 30 DDME,Kr DDME,Sr (MeV)

2n DDPC,Kr DDPC,Sr S 15 Expt.,Kr Expt.,Sr 25 10

5 20 (MeV) 2n 0 S 30 40 50 60 40 50 60 Neutron Number N Neutron Number N 15

FIG. 1: (color online) Variation in experimen- 10 tal and theoretical two neutron separation energy (S2n) in MeV plotted as a function of neutron 40 50 60 40 50 60 number N, for the exotic nuclei of Germanium and Neutron Number N Neutron Number N Selenium. Experimental Data is taken from [4] FIG. 2: (color online) Variation in experimen- tal and theoretical two neutron separation energy help of binding energies B(Z,N) and B(Z,N-2), (S2n) in MeV plotted as a function of neutron and then compared these theoretical results number N, for the exotic nuclei of Krypton and Strontium. Experimental data is taken from [4] with the experimental data [4]. In the Fig.(1), we compared the theoretical and experimen- tal results for two neutron separation energy S2n(Z,N) as a function of neutron number N remove two neutrons from (Z, N + 2) nucleus for the isotopes of Germanium left panel and is much smaller than the energy required to re- Selenium right panel. In left panel of Fig.(1), move two neutrons from (Z, N) nucleus, where we observed a significant drop in S2n(Z,N) val- N are the number of neutrons at nuclear magic 60 72 82 numbers. Our theoretical results confirm the ues at 32Ge, 32Ge of about 5 MeV and 32Ge of about 10 MeV illustrating the N = 28, 40 presence of N = 28, 40 and 50 sub-shell gap in and 50 shell effect respectively in isotopes of Ge isotopes. Also the confirmation of N = 40 Germanium. In right panel of Fig.(1) for the and 50 sub-shell gap in Se, Kr and Sr nuclei. isotopes of Selenium, we observed three such 74 84 declines at 34Se of about 5 MeV and 34Se of about 10 MeV to representing N = 40 and N References = 50 shell gaps. In Fig. (2), we present the [1] G. A. Lalazissis, T. Nikˇsi´c,D. Vretenar results for S2n(Z,N) for isotopes of Krypton and P. Ring, Phys. Rev. C 71 024312 in left panel and Strontium in right panel. In (2005). left panel of Fig.(2), we observed an abrupt [2] T. Nikˇsi´c,D. Vretenar and P. Ring, Phys. 76 Rev. C 78 034318 (2008). decrease in S2n(Z,N) at 36Kr of about 5 MeV 82 [3] T. Nikˇzi´c,P. Ring, D. Vretenar, Y. Tian and 36Kr of about 10 MeV illustrating the N = 40 and N = 50 shell effect respectively in and Z. Y. Ma, Phys. Rev. C 81 054318 isotopes of Krypton. However in case of Stron- (2010). tium also N = 40 and 50 shell structure effects [4] W.J. Huang, G. Audi, Meng Wang, F.G. 74 Kondev, S. Naimi and Xing Xu, Chinese are observed at 38Sr (of about 5 MeV) and 84 Physics C 41 030002 (2017). 38Sr (of about 10 MeV) respectively. These

Available online at www.sympnp.org/proceedings