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We derive the ground-state energy of $N$ composite bosons made of fermionpairs using the recently developed composite boson many-body formalism. Weconcentrate on the $N$-pair energy linear in density. We show that thescattering relevant for scattering length contains not only direct and exchangeinteraction scatterings but also the dimensionless "Pauli scattering" forfermion exchange in the absence of fermion-fermion interaction. Numericalresolution of the resulting "ladder" integral equation for fermions interactingthrough long-range Coulomb forces --- which act as effective repulsion betweenexcitons made of same-spin electrons and same-spin holes --- shows that theprefactor of the $N$-exciton energy linear in density is substantiallydecreased from its Born approximation value, $13\pi/3$, by a factor$\simeq0.38$ for equal electron and hole effective masses. Interestingly, thisfactor goes to zero when the hole mass goes to infinity, making thetriplet-exciton gas unstable in this limit.

Coboson many-body approach to the $N$-exciton ground-state energy