The influence of the chameleon field potential on transition frequencies of gravitationally bound quantum states of ultra-cold neutrons

TL;DR

This paper investigates how the chameleon field potential affects the transition frequencies of gravitationally bound ultra-cold neutrons, providing analytical and numerical solutions to model these effects.

Contribution

It introduces approximate analytical solutions for the chameleon field potential influencing ultra-cold neutrons, enabling precise analysis of their quantum transition frequencies.

Findings

Analytical solutions for the chameleon field potential are consistent with numerical results.

The solutions facilitate quantitative analysis of chameleon field effects on neutron quantum states.

Potential contributions to modifications in transition frequencies are identified.

Abstract

We calculate the chameleon field potential for ultracold neutrons, bouncing on top of one or between two neutron mirrors in the gravitational field of the Earth. For the resulting non--linear equations of motion we give approximate analytical solutions and compare them with exact numerical ones for which we propose the analytical fit. The obtained solutions may be used for the quantitative analysis of contributions of a chameleon field to the transition frequencies of quantum states of ultra-cold neutrons bound in the gravitational field of the Earth.