Properties of an $\alpha$ particle in a Bohrium $270$ Nucleus under the Generalized Symmetric Woods-Saxon Potential

TL;DR

This paper investigates the properties of an alpha particle within a Bohrium 270 nucleus using the Schrödinger equation and a generalized potential, analyzing thermodynamic and stability aspects with results close to experimental data.

Contribution

It introduces a detailed quantum and thermodynamic analysis of alpha particles in Bohrium 270 using the generalized symmetric Woods-Saxon potential, including quasi-bound states.

Findings

Calculated energy eigenvalues and wave functions.

Derived thermodynamic functions as a function of temperature.

Estimated kinetic energy close to experimental values.

Abstract

The energy eigenvalues and the wave functions of an $\alpha$ particle in a Bohrium $270$ nucleus were calculated by solving Schr\"odinger equation for Generalized Symmetric Woods-Saxon potential. Using the energy spectrum by excluding and including the quasi-bound eigenvalues, entropy, internal energy, Helmholtz energy, and specific heat, as functions of reduced temperature were calculated. Stability and emission characteristics are interpreted in terms of the wave and thermodynamic functions. The kinetic energy of a decayed $\alpha$ particle was calculated using the quasi-bound states, which is found close to the experimental value.