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

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 with n > 2. Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na-x(3) /V)(n) with n greater than or equal to 2. An exact procedure to get these density dependent terms is given.