On the change of density of states in two-body interactions

TL;DR

This paper derives a relation connecting the change in density of states in two-body scattering to the potential shape, revealing that DDOS is negative for repulsive potentials more repulsive than 1/r^2, differing from Levinson's theorem.

Contribution

It introduces a new relation linking DDOS to potential shape, providing insights into global properties of scattering states for specific potentials.

Findings

DDOS is negative at all energies for certain repulsive potentials

The relation offers a way to infer global DDOS properties from potential shape

The behavior differs from predictions of Levinson's theorem

Abstract

We derive a general relation in two-body scattering theory that more directly relates the change of density of states (DDOS) due to interaction to the shape of the potential. The relation allows us to infer certain global properties of the DDOS from the global properties of the potential. In particular, we show that DDOS is negative at all energies and for all partial waves, for potentials that are more repulsive than $+1/r^2$ everywhere. This behavior represents a different class of global properties of DDOS from that described by the Levinson's theorem.