The quantum ultra-cold neutron gas trapped in the two-dimensional harmonic oscillator potential on the Earth's gravitational field

TL;DR

This paper investigates the properties of a quantum ultra-cold neutron gas confined in a two-dimensional harmonic oscillator potential under Earth's gravity, focusing on Fermi energy and density distribution.

Contribution

It introduces the analysis of Fermi energy and density distribution for the neutron gas in a harmonic oscillator potential, expanding on previous work with a square-well potential.

Findings

Fermi energy calculated for the harmonic oscillator trap

Density distribution profiles analyzed and compared

Dependence on the trapping potential shape confirmed

Abstract

In our previous paper, we have investigated the thermodynamics of the quantum ultra-cold neutron gas trapped in the two-dimensional square-well potential on the Earth's gravitational field. We have pointed out that they have strong dependence on the shape of the trapping potential. In the present paper, we estimate the Fermi energy and the density distribution of the Fermi gas with two-dimensional harmonic oscillator potential, instead of the square-well potential. Then we discuss them in terms of the Fermi energy and the density distribution as compared with both of cases.