On the N-exciton normalization factor
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The N-ground-state-exciton normalization factor, namely 〈v| B0NB0dagN| v〉 = N!FN, with B0dag the exact ground state exciton creation operator, differs from N! because the excitons are not perfect bosons. The quantity FN 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 FN. 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 FN's. We also give new explicit expressions of FN valid for η = Nax3/\(\) small but N2ax3/\(\) large, as FN does not read in terms of η but Nη, the exciton number N being possibly huge in macroscopic samples. Due to this superextensivity, FN does not appear alone in physical quantities, but through ratios like FN + p/FN. We end this work by giving the η expansion of these ratios, useful for all purely Pauli many-body effects.
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