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The paper is devoted to the effects of superconducting pairing in smallmetallic grains. It turns out that at strong superconducting coupling and inthe limit of large Thouless conductance one can explicitly determine the lowenergy spectrum of the problem. We start with the strong coupling limit anddevelop a systematic expansion in powers of the inverse coupling constant forthe many-particle spectrum of the system. The strong coupling expansion isbased on the formal exact solution of the Richardson model and converges forrealistic values of the coupling constant. We use this expansion to study thelow energy excitations of the system, in particular energy and spin gaps in themany-body spectrum.Comment: 16 pages, 3 figure

Strong-coupling expansion for the pairing Hamiltonian for small superconducting metallic grains