No-Core Shell Model Calculations for 6,8He, 8,10,12B

Fouad A. Majeed*, Sarah S. Ahmed
Department of Physics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq
*Corresponding author: fouadalajeeli@yahoo.com
Received May 01, 2015; Revised May 13, 2015; Accepted May 25, 2015
Abstract:

The excitation energies of 6,8He and 8,10,12B isotopes in the p-shell region have been calculated by using large-basis no-core (i.e. considering all nucleons active with partial restrictions imposed on some nucleons). The shell model calculations have been performed using spsdpf model space with wbt effective residual interaction fitted for the p-shell nuclei. Three set of restrictions have been imposed named (0+1)?w ,(0+2)?w ,(0+3)?w in our calculations have been used. The comparison of our theoretical work with the recent available experimental data shows that the restriction (0+3)????? gives best results for Helium isotopes while (0+1)?w is in better agreement with the experiment for Boron isotopes. Keywords: excitation energies, no-core shell model, light nuclei Cite This Article: Fouad A. Majeed, and Sarah S. Ahmed, “No-Core Shell Model Calculations for 6,8He, 8,10,12B.”
International Journal of Physics, vol. 3, no. 4 (2015): 155-158. doi: 10.12691/ijp-3-4-3. 1.

Introduction

The understanding of the nuclear structure is one of the central challenges in nuclear physics. By choosing the proper effective interaction and the model space can lead to predict a wide range of observables by the nuclear shell model systematically and correctly [1]. Wide range of standard effective interaction has been studied such as the Cohen-Kurath interaction for light nuclei [2]. This effective interaction forms an essential input to all shell-model studies. Equipped with modern sophisticated effective interactions, the shell model has successfully described many properties of nuclei [3]. Large-scale shell model calculations have been successfully conducted to investigate the low-lying energy levels, binding energies and the reduced transition probabilities for even-even 52,54,56Cr and 54-66Fe isotopes by employing gxpf1, gxpf1a, fpd6 and kb3g effective interactions by Majeed and Ejam [4,5] where their results are in good global agreement with the experimental data. Barrett, et al., [6] discussed the standard formulation and the transnational invariant of the no-core shell-model approach. They presented their results for three and four nucleon systems interacting by the nucleon-nucleon (NN) potentials or other CD-Bonn in spaces of model included up to 18 ?? and 50 ?? HO excitations. They apply their ab initio no-core shell model approach to the lightest nuclei, 3H, 3He, 4He. Ab initio no-core shell model (NCSM) calculations have been performed by Vary et al., [7] where they started with an intrinsic Hamiltonian for all nucleons in the nucleus. They have used a realistic two-nucleon and tri-nucleon interactions recently developed from effective field theory and chiral perturbation theory. They derived a finite basis-space dependent Hermitical effective Hamiltonian. The resulting finite Hamiltonian matrix Problem is solved by diagonalization on parallel computers. Applications range from light nuclei to multi quark systems and, recently, to quantum field theory including systems with bosons.
The aim of the present work is to study excitation energies for light isotopes 6,8 He and 8,10,12 B by means of large-scale shell model calculations by employing model space spsdpf with wbt effective interaction using the recent shell model code Nushellx@msu [7], then compare these theoretical attempts with the most recent experimental data. 2.

Shell Model
The basic assumption of the nuclear shell model is that to a first approximation each nucleon moves independently in a potential that represents the average interaction with the other nucleons in a nucleus. This independent motion can be understood qualitatively from a combination of the weakness of the long-range nuclear attraction and the Pauli Exclusion Principle [9].In a non-relativistic approximation, nuclear properties are described by the Schr?dinger equation for A nucleons [9] ()()ˆ1,2,,41,2,,HEA??…=… (1)
where H ??contains nucleon kinetic energy operators and interactions between nucleons of a two-body and, eventually, of three-body character, i.e. ()()21,,2AiijHWijWijm<=??=??++?????????? (2)
?(1,2,3,…, A) is an A-body wave function, while i denotes all relevant coordinates ri??????? ,sj????? ,ti????? of a given particle(i=1,2, … ,A).Although the three-body forces are proved to be important, in the present work we will consider only the two-body interaction .