Abstract:

Electron scattering Coulomb form factors for the single-particle quadrupole transitions in the
p-shell 10B nucleus have been studied. Core polarization effects are included through a
microscopic theory that includes excitations from the core orbits up to higher orbits with (2 hbar omega)
excitations. The modified surface delta interaction is employed as a residual interaction. The
effect of core polarization is found essential in both the transition strengths and momentum
transfer dependence of form factors, and gives remarkably good agreement with the measured
data with no adjustable parameters.

1. Introduction

Comparisons between calculated and measured longitudinal electron scattering form factors have long been used as stringent tests of models of nuclear structure [1, 2]. Shell model within a restricted model space succeeded in describing static properties of nuclei when effective charges are used. The Coulomb form factors have been discussed for the stable sd-shell nuclei using sd-shell wave functions with phenomenological effective charges [3]. For p-shell nuclei, the Cohen–Kurath (CK) [4] model explains the low-energy properties of p-shell nuclei well. However, at higher-momentum transfer, it fails to describe the form factors. Radhi et al [5–9] have successfully proved that the inclusion of core polarization (CP) effects in the p-shell and sd-shell is essential to improve the calculations of the form factors. Restricted 1p-shell models were found to provide
good predictions for the 10B natural parity level spectrum and transverse form factors [10]. However, they were less successful for C2 form factors and give just 45% of the total observed C2 transition strength. Expanding the shell-model space to include (2 hbar omega) configurations in describing the form factors of 10B, Cichocki et al [10] found that only a 10% improvement was realized. The purpose of this work is to study the C2 form factors for 10B by including higher-energy configurations as a first-order CP through a microscopic
theory, which combines shell model wave functions and highly excited states.Single-particle wave functions are used as a zeroth contribution and the effect of CP is included as a first-order perturbation theory with the modified surface delta interaction (MSDI) [11] as a residual interaction and a (2 hbar omega) for the energy denominator. The single-particle wave functions are those of the harmonic-oscillator (HO) potential
with size parameter b chosen to reproduce the measured root-mean-square (rms) charge radii of these nuclei.

2. Theory

The CP effect on the form factors is based on a microscopic theory, which combines shell model wave functions and configurations with higher energy as first-order perturbations; these are called CP effects. The reduced matrix elements of the electron scattering operator T3 are expressed as the sum of the product of the elements of the one-body density matrix (OBDM). where  and  label single-particle states (isospin is included)
for the model space. For p-shell nuclei, the orbits 1p3/2 and 1p1/2 define the model space. The states |0i i and 0f are described by the model space wave functions.Greek symbols are used to denote quantum numbers in the
coordinate space and isospace.

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This paper is accepted for publication at 16 April, 2012 and Published online at 9 May, 2012 by Physica Scripta, by the IOP Science on behalf of the Royal Swedish Academy, Phys. Scr. 85 (2012) 065201.
http://dx.doi.org/10.1088/0031-8949/85/06/065201