Contribution of high energy configurations to longitudinal and transverse form factors in p- and sd-shell nuclei
F A Majeed1* and L A Najim2
1Department of Physics, College of Education for Pure Sciences, University of Babylon, PO Box 4, Hilla, Babylon, Iraq
2Department of Physics, College of Science, University of Mosul, Mosul, Iraq

Received: 24 August 2014 / Accepted: 03 November 2014 / Published online: 20 November 2014

Abstract: Longitudinal and transverse electron scattering form factors for some selected positive and negative parity states of stable odd-A nuclei (7Li, 13C and 17O) in the p- and sd-shells are investigated by considering the higher energy configurations outside the p- and sd-shells. The higher energy configurations, referred to as core polarization effects, are considered by means of a microscopic theory that includes excitations from the core 1s-1p, 2s-1d orbits to the higher allowed orbits with 4hx excitations. The calculations are performed in the p- and sd-shell model spaces by employing Cohen-Kurath, Reehal and Wildenthal interactions respectively, while the core polarization effects are calculated with the modified surface delta interaction as residual interaction. The predicted form factors are compared with the available experimental data and it is shown that the inclusion of the higher excited configurations is very essential in the calculations of the form factors and the reduced transition probabilities to obtain reasonable description of the data with no adjustable parameters.
Keywords: Longitudinal and transverse form factors; Shell model ; Calculated first-order core polarization effects
PACS Nos.: 25.30.Dh; 21.60.Cs; 27.20.?n

1. Introduction

The fundamental goal of nuclear structure theory is to understand the properties of complex nuclei in terms of the
nucleon–nucleon (N–N) interaction [1]. The conventional multi-particle shell model with configuration mixing has
proved to be of great practical value in the interpretation of a large number of experimental data such as static properties, but it is not satisfactory to describe the inelastic electron scattering data. In fact, one needs to include the effects of higher configurations outside the p- and sd-shell model space, called core-polarization (CP) effects. The concept of the CP effects has been introduced in order to account for the participation of configurations from outside of the model space in the transition. The CP effects have been calculated by using microscopic models to study the Coulomb form factors for transition between single-particle (or- hole) states
with LS closed shell [2]. The Coulomb form factors for E4 transition in sd-shell nuclei have been investigated by Sagawa et al. [3] taking into account core polarization effects using self consistent Hartree-Fock ? random phase
approximation calculations, which improve their calculations significantly and agree well with the experimental form factors.Amicroscopic model has recently been used [4, 5] in order to study the CP effects on the longitudinal form factors of p- and fp-shell nuclei. For p-shell nuclei, Cohen and Kurath [6] model explains well the low-energy properties of pshell nuclei. However, at higher-momentum transfer, it fails to describe the form factors. Cichocki et al. [7] have expanded the shell-model space to include 2hbar omega configurations in describing the form factors of 10B and have found only a 10 %improvement in the calculations of form factors.
The effect of CP is considered by Sato et al. [8] to describe the form factors of 12C and 13C. The first-order CP effects have been considered by Sato et al. [9] with the p-shell model space and it significantly improves their work in comparison with the experimental data. The work of Radhi et al. [10–14]