Quantum corrections and multioccupancy in a semi-classical gas

TL;DR

This paper explores how quantum corrections to a semi-classical gas relate to multioccupancy of quantum states, using a novel concept of pseudo-molecules formed through scattering processes.

Contribution

It introduces a physical approach linking quantum corrections to multioccupancy via pseudo-molecules in momentum space.

Findings

Quantum corrections expressed as a power series in eta.

Multioccupancy associated with pseudo-molecules formed by scattering.

Pseudo-molecules result from multiple scattering among non-interacting particles.

Abstract

The quantum corrections to the behavior of a semi-classical gas can be expressed as a power series of the ratio $eta$ between the cube of De Broglie's thermal wavelength and the specific volume. The connection between $eta$ and the multioccupancy of quantum states is the aim of the present work. By means of a chemical/physical approach it is possible to associate $eta$ to the concrete realization of multioccupancy in momentum space, through the formation of what we call "pseudo-molecules", i.e. multiplets of particles sharing momenta whose differences are negligeable in the continuous spctrum approximation. The pseudo-molecules result as casual consequences of multiple scattering processes among non interacting (scattering apart) particles.