Eur. Phys. J. B 31, 17-24 (2003)
https://doi.org/10.1140/epjb/e2003-00003-1

On the N-exciton normalization factor

¹ GPS, Université Denis Diderot and Université Pierre et Marie Curie, CNRS, Tour 23, 2 place Jussieu, 75251 Paris Cedex 05, France
² Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, 24 rue Lhomond, 75231 Paris Cedex 05, France
³ Laboratoire d'Optique Appliquée, ENSTA-École Polytechnique, CNRS, chemin de la Hunière, 91761 Palaiseau Cedex, France

Corresponding author: ^a combescot@gps.jussieu.fr

Received: 30 May 2002
Revised: 12 October 2002
Published online: 27 January 2003

Abstract

The N-ground-state-exciton normalization factor, namely , with the exact ground state exciton creation operator, differs from N! because the excitons are not perfect bosons. The quantity F_N turns out to be crucial for problems dealing with interacting excitons. Indeed, the excitons feel each other not only through the Coulomb interaction but also through Pauli exclusion between their components. A quite novel purely Pauli contribution exists in their many-body effects, which relies directly on F_N. Following procedures used in the commutation technique we recently introduced to treat interacting close-to-bosons, and in the BCS theory of superconductivity, we rederive important relations verified by the F_N's. We also give new explicit expressions of F_N valid for small but large, as F_N does not read in terms of η but , the exciton number N being possibly huge in macroscopic samples. Due to this superextensivity, F_N does not appear alone in physical quantities, but through ratios like . We end this work by giving the η expansion of these ratios, useful for all purely Pauli many-body effects.