Collective excitations of finite fermi systems in the region of a phase transition

Analytical solution of the two-level model with pair formations in the region of phase transition, which is valid at large particle numbers, is found. Assuming the universal character of certain properties of this solution, the scheme of constructing the collective Hamiltonian in the transition region is developed for many-level system on the basis of the generalized density matrix method. As an illustration, the phase transition in a system with monopole interaction is considered.