Analytical $$\boldsymbol{\alpha}\boldsymbol{+}\boldsymbol{\alpha}$$ Potential for Energy Range between 6 and 280 MeV
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NUCLEI Theory
Analytical α + α Potential for Energy Range between 6 and 280 MeV Zakaria M. M. Mahmoud1), 2)* and Mahmoud A. Hassanien2) Received August 15, 2019; revised December 17, 2019; accepted December 17, 2019
Abstract—In this work we derive analytically a real α + α potential using the JLM effective nucleon– nucleon (NN) interaction. The aim is to obtain analytically self-energy dependent α + α effective interaction. We used two different overlapping local density approximations, (geometrical and arithmetic averages, respectively) in JLM parameterization. The derived real potentials in companion with phenomenological Wood–Saxon (WS) imaginary potential are tested in the analysis of the elastic scattering of α + α, over a wide range of energy and angular distribution. The analysis is performed in the framework of optical model for several sets of data measured at three different ranges of energies, 6.5–18, 40.8–47.3, and 100– 280 MeV. The predictions of the calculated potentials are satisfactory in reproduction of experimental data. We conclude that both analyticaly derived potentials provide successful description of the experimental data. DOI: 10.1134/S106377882003014X
1. INTRODUCTION In nuclear physics the nucleus–nucleus interaction is the main input in understanding many nuclear processes. So, derivation of this interaction from microscopic point of view makes these processes understandable and predictable [1]. Among nucleus– nucleus systems, the α + α is the simplest. The α-particle own several properties make the α + α system very interesting. It is small in size (rms radius = 1.45 fm [2]), has zero spin–isospin, large binding energy (28 MeV) and relatively high reaction threshold. These intrinsic properties of α-particle let people consider it as a rigid internal configuration. Thus, we could get unambiguous information about the direct part of the nucleon–nucleon interaction through the analysis of α + α scattering. Moreover, it is the most stable of all possible clusters used in the cluster model. Therefore, with an appropriate α + α interaction it is possible to calculate the αlike structure for the typical A = 4m alpha-cluster N = Z light nuclei (m is the number of alphas) [3]. For decades, the α + α interaction is subjected to many theoretical [4–8] and experimental [9, 10] studies. In these studies, the interaction was treated phenomenologically or microscopically with some adjustable parameters. These parameters mostly fit 1)
Physics Department, Faculty of Science, King Khalid University, Guraiger, Abha 62529, Saudi Arabia. 2) Physics Department, Faculty of Science, New Valley University, New Valley Governorate, Egypt. * E-mail: [email protected]
the experimental ground state energy and the decay width of the virtual 8 Be nucleus or the phase shifts of the α + α elastic scattering. For example, a simple WS [11, 12] and Gaussian [13] potentials, are able to reproduce the energy and the decay width of the virtual 8 Be nucleus in the ground state as well as the scattering phase shift of
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