Nuclear single particle wave function and energies within model with pair correlations and fixed particle number

Minimization of the basic state energy calculated with the function representing a projection of the Bardin-Cooper-Shriffer function on a certain number of particles results into a system of equations for single-particle functions and amplitudes characterizing distribution of nucleon pairs along single-particle levels. One studies the conditions of steady-state when Hamiltonian does not bind the function of basic state with partial-hole and dual vibrational excitations. In approximation of invariability of single-particle basis and amplitudes of pair distribution one determined the energy of states of partial and hole types in odd atomic nuclei