On the N-exciton normalization factor

摘要

The N-ground-state-exciton normalization factor, namely = N!F_N, with B_0~+ 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 η = Na_x~3/V small but N~2a_x~3/V large, as F_N does not read in terms of η but N_η, 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 F_(N+p)/F_N. We end this work by giving the η expansion of these ratios, useful for all purely Pauli many-body effects.