Thermodynamic Properties of a Nucleon under the Generalized Symmetric Woods-Saxon Potential in Flourine 17 Isotope

TL;DR

This paper analytically investigates the thermodynamic properties of a nucleon in Fluorine 17 using a generalized Woods-Saxon potential, revealing confinement and tunneling behaviors and aligning with experimental fission data.

Contribution

It provides an exact analytical solution for the Schrödinger equation in this context and explores temperature-dependent thermodynamic quantities including energy, entropy, and free energy.

Findings

Nucleon is fully confined within the nucleus in bound states.

Tunneling probabilities are present for quasi-bound states.

Thermodynamic properties vary with temperature, indicating nuclear stability at high excitation temperatures.

Abstract

The exact analytical solution of the Schr\"odinger equation for a generalized symmetrical Woods-Saxon potential are examined for a nucleon in Fluorine 17 nucleus for bound and quasi-bound states in one dimension. The wave functions imply that the nucleon is completely confined within the nucleus, i.e., no decay probability for bound states, while tunneling probabilities arise for the quasi-bound state. We have calculated the temperature dependent Helmholtz free energies, the internal energies, the entropies and the specific heat capacities of the system. It is shown that, when the quasi-bound state is included, the internal energy and entropy increase, while the Helmholtz energy decreases at high temperatures. Very high excitation temperatures imply that the nucleus does not tend to release a nucleon. The calculated quasi bound state energy is in reasonable agreement with the experimental data on the cumulative fission energy issued by IAEA.