Probability distributions of atomic scattering lengths

TL;DR

This paper derives the probability distributions of atomic scattering lengths' real and imaginary parts within a two-channel model, revealing that inelastic scattering rates can be lower than previously estimated, with the real part following a Cauchy distribution.

Contribution

It extends the understanding of atomic scattering lengths by deriving their probability distributions in a two-channel model, highlighting the behavior of inelastic scattering.

Findings

Real part of scattering length is Cauchy-distributed.

Imaginary part of scattering length peaks near zero.

Inelastic scattering rates may be smaller than naive estimates.

Abstract

The probability distribution of the real and imaginary parts of atomic scattering lengths $a$ are derived, in a two-channel model that allows for inelastic scattering to occur. While the real part of $a$ remains Cauchy-distributed, as predicted for single channel scattering in the classic work of Gribakin and Flambaum, the imaginary part of $a$ is seen to be strongly peaked near zero. Two-body inelastic scattering rates may therefore be smaller in general than a naive estimate would suggest.