Index of refraction of gases for matter waves: effect of the motion of the gas particles on the calculation of the index

TL;DR

This paper examines different formulas relating the index of refraction of gases for matter waves, highlighting inconsistencies and proposing a correction aligned with standard scattering theory, with implications for neutron physics.

Contribution

The paper clarifies the correct formula for the index of refraction of gases for matter waves, resolving inconsistencies in previous formulas and aligning with scattering cross-section definitions.

Findings

The formula by C.C. aligns with standard scattering theory.

Previous formulas are inconsistent with the total scattering cross-section.

The index of refraction depends on well-known physical quantities and gas density.

Abstract

Two different formulae relating the index of refraction $n$ of gases for atom waves to the scattering amplitude have been published. We show here that these two formulae are not consistent with the definition of the total scattering cross-section while the formula developed by one of us (C.C.) in her thesis is in agreement with this standard knowledge. We discuss this result, in particular in the neutron case for which such an index was first introduced. We finally evaluate the index of refraction as a function of well known quantities and we discuss the order of magnitude of the ratio of $(n-1)/n_t$, where $n_t$ is the gas density.