A Dispersive Optical Model Analysis of the Neutrons Scattering by Titanium Element Nucleus and Its Natural Isotopes

Haiddar Al-Mustafa,Anees Belal

doi:10.11648/j.ns.20200501.11

Abstract

In this paper, a dispersive optical model analysis of the neutrons scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100 MeV and for constant input values of the parameters of this mean field and the varied input values of Hatree-Fock approximation parameters of the nonlocal potential. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted (total, total reaction, elastic) cross sections within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), elastic differential cross section and polarization for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV showed the excellent agreement with available experimental data and better than these resulted from global parameterization of the optical model potential, and thus more reliable for calculation the cross sections of unknown interactions of elements nuclei and their isotopes such neutrons scattering by titanium element nucleus and its natural isotopes.

Highlights

The nuclear optical model potential is of the fundamental importance concepts in the nuclear physics
The present paper aims at presenting the dispersive optical model analysis (DOMA) of the neutrons scattering by titanium element nucleus and its natural isotopes and comparing the results with these resulted from global parametrization of the optical model potential and averrable experimental data within energy range (1-100) MeV and with calculation step of the previous range whose magnitude 1 MeV, according to evaluated fitting methodology
The methodology of a dispersive optical model analysis is similar to the proton scattering that is showed in references [7, 8], but because of; unavailable experimental data of the cross sections of the neutrons scattering by titanium element nucleus and its natural isotopes except only one value of the total cross section for the energy value (14.2 MeV), in addition to the variations of the total cross section value at this value of the energy for each isotope from the titanium isotopes, we have depended on the follow fitting methodology: i

Summary

Introduction

The nuclear optical model potential is of the fundamental importance concepts in the nuclear physics. It describes the motion of one nucleon, bound or unbound, in the mean field of all the other nucleons comprising the nucleus. The field due to the sum of all the individual nucleon-nucleon interactions is represented by a simple one-body potential. The application of the concept of the nuclear mean field is for understanding the properties of bound single-particle states and for elastic scattering of unbound nucleons [1,2,3]. The phenomenological optical model potential for nucleon-nucleus scattering, , is defined as [2,3,4,5,6]:

Methods

Results

Conclusion