Density expansion of the energy of N close-to-boson excitons

Abstract

Pauli exclusion between the carriers of $N$ excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the hamiltonian expectation value in the $N$-ground-state-exciton state.Coulomb interaction enters this quantity at first order only by construction ; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in $(N{a}_x^3/\mathcal{V}{)}^n$ with $n\ge 2$ >. An \emph{exact} procedure to get these density dependent terms is given.

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