The Escape Rate of a Molecule

TL;DR

This paper derives an explicit formula and estimates for the escape rate of molecules in celestial mechanics at high energies, linking it to measurable properties in scattering experiments.

Contribution

It provides the first explicit formula and computable estimates for the escape rate in the n-centre problem at high energies, connecting celestial mechanics with molecular scattering.

Findings

Explicit formula for escape rate at high energies

Computable estimates of the escape rate

Demonstrates the diameter of a molecule is measurable in scattering experiments

Abstract

We show existence and give an implicit formula for the escape rate of the n-centre problem of celestial mechanics for high energies. Furthermore we give precise computable estimates of this rate. This exponential decay rate plays an important role especially in semiclassical scattering theory of n-atomic molecules. Our result shows that the diameter of a molecule is measurable in a (classical) high-energy scattering experiment.