title: Energy of N Cooper pairs by analytically solving the Richardson-Gaudin equations for conventional superconductors.
abstract: This Letter provides the solution to a yet unsolved basic problem of solid state physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50 yr old math problem by analytically solving Richardson-Gaudin equations which give the exact energy of these N pairs via N parameters coupled through N nonlinear equations. Our result fully supports the standard BCS result obtained for a pair number equal to half the number of states feeling the potential. More importantly, it shows that the interaction part of the N-pair energy depends on N as N(N-1) only from N=1 to the dense regime, a result which evidences that Cooper pairs interact via Pauli blocking only.
authors.affiliation: Institut de Recherche Mathématiques de Rennes, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France.
authors.forename: Michel
authors.initials: M
authors.lastname: Crouzeix
authors.forename: Monique
authors.initials: M
authors.lastname: Combescot