Nuclear Structure of 104,106,108Sn Isotopes Using the NuShell Computer Code
Khalid S. Jassim
Department of Physics, College of Education for Pure Science,
University of Babylon, PO Box 4, Hillah-Babylon, Iraq
Abstract:
Shell model calculations for 104;106;108Sn are preformed using the NuShell code for windows with an effective interaction based on the CD-Bonn nucleon-nucleon interaction. The level schemes are compared with the available experimental data up to 3.98, 11.319, and 4.256 MeV in 104Sn, 106Sn, and 108Sn, respectively. Very good agreement was obtained for each of the nuclei, especially for 106Sn. The electron scattering form factor, transition probabilities B (E2; 0+ ? 2+1), and charge density distribution have been found using a shell model
calculation.
PACS numbers: 21.60Cs, 27.60.+j, 21.10.Ft, 25.30.Dh
DOI: 10.6122/CJP.51.441
I. INTRODUCTION
The region of light Sn isotopes between the N = 50 and 82 shell closures provide the longest chain of semi-magic nuclei accessible to nuclear structure studies. Both in the neutron valence space of a full major shell and with emphasis on excitations of the Z = 50 core Sn isotopes, it has been intensively investigated from both experimental and theoretical perspectives. The main goal has been to study the excitation mechanisms around
the exotic isotope 100Sn, the heaviest symmetric double magic nucleus recently produced in nuclear fragmentation reactions [1, 2]. The perturbative many-body method used to calculate such an effective interaction, appropriate for nuclear structure calculations at low and intermediate energies, starts with the free nucleon-nucleon interaction. CD-Bonn and Nijmegen1 two-body effective nucleon-nucleon interactions are used to calculate the
effective NN interactions in the desired model space. The effect of the repulsive core of the NN potential at close range, which is unsuitable for a perturbative treatment, is taken into account in the effective interaction. One can then derive expressions for the effective interactions and transition operators via the many-body G-matrix method [3]. The simplest approach in analysing the spectra of light Sn isotopes is to consider 100Sn as an inert core and to treat only the neutron degrees of freedom, using the single-particle orbits of the N = 50–82 shell as a model space, i.e., the orbits 1g7=2, 2d5=2, 2d3=2, 3s1=2,and 1h11=2. Extensive shell model calculations have been performed along this line [4]; using the Lanczos iteration method states for as many as 12 extra-core neutrons have been calculated. Similar studies have also been done in heavy Sn isotopes [5] and in the N = 82 isotones [6], where systems with up to 14 valence particles have been studied. The structure of neutron-rich nuclei with a few nucleons beyond 132Sn [7] have been investigated by means of large-scale shell-model calculations. The results show evidence of hexadecupole correlation in addition to octupole correlation in this mass region.
On the one hand, the results still deviate significantly from theoretical predictions and, on the other hand, the results indicate a decreasing trend of the energy levels with increasing number of valence particles outside of the 100Sn core. Experimentally, the nuclear properties of 100Sn are only indirectly known [7, 8], although its existence has already been confirmed [9–11]. Properties of the 2+ states around 132Sn have been also studied by
Terasaki et al. [6] in a separable quadrupole-plus-pairing model.
A large-scale shell model calculation was carried out in the Sn100pn model space with the Sn100pn interaction. This interaction was obtained from a realistic interaction developed by Brown et al. [6] starting with a G matrix derived from the CD-Bonn nucleonnucleon interaction. There are three parts in this interaction, which are the proton-proton (Sn100pp), neutron-neutron (Sn100nn), and proton-neutron (Sn100pn) interactions, along with the coulomb interaction (Sn100co) between the protons. In this work, I am interested in the Sn isotopes only, the neutron-neutron part, i.e., only Sn100nn was relevant for my calculation. The calculations have been performed using doubly magic 100Sn as the core and the valance neutrons (4, 6, and 8) distributed over the single particle-orbits 1s1=2, 2d5=2,2d3=2, 2g7=2, and 1h11=2. The neutron single-particle energies are ?8:7167 MeV, ?10:6089 MeV, ?8:6944 MeV, ?10:2893 MeV, and ?8:8152 MeV for the 3s1=2, 2d5=2, 2d3=2, 1g7=2,and 1h11=2 orbitals, respectively [6]. The energy level results and transition probabilities are compared with the experimental levels, as shown in Figures 1, 2, and 3.