Abstract

In this paper, we model the nuclear potential using Woods-Saxon and Yukawa interaction as the mean field in which each nucleon experiences a central force due to rest of the nucleons. The single particle energy states are obtained by solving the time independent Schrodinger wave equation using matrix diagonalization method with infinite spherical well wave-functions as the basis. The best fit model parameters are obtained by using variational Monte-Carlo algorithm wherein the relative mean-squared error, christened as chi-squared value, is minimized. The universal parameters obtained using Woods-Saxon potential are found to be matched with literature reported data resulting a chi-square value of 0.066 for neutron states and 0.069 for proton states whereas the chi-square value comes out to be 1.98 and 1.57 for neutron and proton states respectively by considering Yukawa potential. To further assess the performance of both the interaction potentials, the model parameters have been optimized for three different groups, light nuclei up to 16O - 56Ni, heavy nuclei 100Sn - 208Pb and all nuclei 16O - 208Pb. It is observed that Yukawa model performed reasonably well for light nuclei but did not give satisfactory results for the other two groups while Woods-Saxon potential gives satisfactory results for all magic nuclei across the periodic table.

Highlights

  • IntroductionThe interaction is modeled as harmonic oscillator, a central mean field potential experienced by each nucleon due to rest of the nucleons

  • One of the successful models for explaining the sudden increase in binding energy, at N or Z = 2, 8, 20, 50, 82 and 126 called as magic numbers, is the nuclear shell model [1]

  • We model the nuclear potential using Woods-Saxon and Yukawa interaction as the mean field in which each nucleon experiences a central force due to rest of the nucleons

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Summary

Introduction

The interaction is modeled as harmonic oscillator, a central mean field potential experienced by each nucleon due to rest of the nucleons. The actual shell closures were obtained only after including the spin-orbit interaction that is introduced as proportional to derivative of the mean field potential, whose experimental evidence has been found later [2]. There are other potential which have been suggested such as square well, cosh geometry [3] given by VN (r) = −V0 + cosh R a r a. R a where V0 is the depth of the well, R is radius of the nucleus and a is the diffuse parameter, but the most successful Woods-Saxon potential [4] for explaining shell closures is given as VWS V0 exp r − a R where V0

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