Comparative effect of an addition of a surface term to the Woods-Saxon potential on the thermodynamics of a nucleon

TL;DR

This paper compares the effects of adding a surface term to the Woods-Saxon potential on a nucleon's thermodynamic properties, revealing spectrum shifts and their impact on energy, entropy, and heat capacity.

Contribution

It introduces a generalized potential with a surface term and analyzes its influence on nucleon spectra and thermodynamics, providing a more realistic model.

Findings

The surface term causes an upward shift in the spectrum.

The internal energy and specific heat increase due to the spectrum shift.

Entropy decreases because of fewer available states.

Abstract

In this study, we reveal the difference between Woods-Saxon (WS) and Generalized Symmetric Woods-Saxon (GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr\"odinger eq. for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem, an $\alpha$ particle confined in Bohrium-$270$ nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy, specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.