Main effects of the Earth's rotation on the stationary states of ultra-cold neutrons

TL;DR

This paper investigates how Earth's rotation affects the energy levels of ultra-cold neutrons, finding that relativistic corrections are negligible but the main rotational effect causes a proportional energy shift.

Contribution

It provides a detailed analysis of Earth's rotation effects on UCN energy levels, highlighting the negligible relativistic corrections and quantifying the main angular-momentum induced energy shift.

Findings

Relativistic corrections are negligible for UCN in Earth's gravity.

Main rotational effect causes a proportional energy shift.

Energy levels are affected by Earth's rotation through angular momentum.

Abstract

The relativistic corrections in the Hamiltonian for a particle in a uniformly rotating frame are discussed. They are shown to be negligible in the case of ultra-cold neutrons (UCN) in the Earth's gravity. The effect, on the energy levels of UCN, of the main term due to the Earth's rotation, i.e. the angular-momentum term, is calculated. The energy shift is found proportional to the energy level itself.