Investigation of thermal properties of Hulth\'{e}n potential from statistical and superstatistical perspectives with various distributions

TL;DR

This paper explores the thermal properties of the Hulthén potential using statistical and superstatistical methods, demonstrating that Tsallis statistics provide better modeling results than traditional approaches across various distributions.

Contribution

It introduces a comparative analysis of statistical and superstatistical approaches, especially Tsallis statistics, for modeling the Hulthén potential's thermal properties with multiple distributions.

Findings

Tsallis statistics outperform ordinary statistics in modeling the Hulthén potential.

Uniform and 2-level distributions yield similar results due to universal relationships.

F distribution does not revert to ordinary statistics at q=1.

Abstract

The Hulth\'{e}n potential is a short-range potential that has been widely used in various fields of physics. In this paper, we investigate the distribution functions for the Hulth\'{e}n potential by using statistical and superstatistical methods. We first review the ordinary statistics and superstatistics methods. We then consider some distribution functions, such as uniform, 2-level, gamma, and log-normal and F distributions. Finally, we investigate the behavior of the Hulth\'{e}n potential for statistical and superstatistical methods and compare the results with each other. We use the Tsallis statistics of the superstatistical system. We conclude that the Tsallis behavior of different distribution functions for the Hulth\'{e}n potential exhibits better results than the statistical method. We examined the thermal properties of the Hulth\'{e}n potential for five different distributions: Uniform, 2-level, Gamma, Log-normal, and F. We plotted the Helmholtz free energy and the entropy as functions of temperature for various values of q. It shows that the two uniform and 2-level distributions have the same results due to the universal relationship and that the F distribution does not become ordinary statistics at q=1. It also reveals that the curves of the Helmholtz free energy and the entropy change their order and behavior as q increases and that some distributions disappear or coincide at certain values of q. One can discuss the physical implications of our results and their applications in nuclear and atomic physics in the future.