Competition between pairing and deformation in finite Fermi systems

The problem of the possible deformation of finite Fermi systems with particle numbers of ≤10⁴ is studied within the Bardeen-Cooper-Schrieffer model. It is shown that for slight deformations of a spherical system consisting of one valence l shell (l ≫ 1), the results of the quasi-particle theory and the exact Richard- son theory virtually coincide. Analysis of the equilibrium deformation of a cluster shows that the system does not keep its spherical form even at a low number of valence particles.