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

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 Schrödinger 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.

12 pages, 2 Tables, 4 Figures

References in corpus (8)

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• A note on the Woods-Saxon potential
• Parameterization of the Woods-Saxon Potential for Shell-Model Calculations
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• Corrected Analytical Solution of the Generalized Woods-Saxon Potential for Arbitrary $\ell$ States
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Cited by in corpus (6)

• Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential
• An Investigation of the Bound State Solutions of the Klein-Gordon Equation for the Generalized Woods-Saxon Potential in Spin Symmetry and Pseudo-spin Symmetry Limits
• A statistical mechanical analysis on the bound state solution of an energy-dependent deformed Hulthén potential energy
• Surface Interaction Effects to a Klein-Gordon Particle Embedded in a Woods-Saxon Potential Well in terms of Thermodynamic Functions
• A Comparative Interpretation of the Thermodynamic Functions of a Relativistic Bound State problem proposed with an Attractive or a Repulsive Surface Effect
• On the Role of Differentiation Parameter in a Bound State Solution of the Klein-Gordon Equation