Pairing Hamiltonian for one pair of identical nucleons bound in a potential well - art. no. 011302

The problem of one pair of identical nucleons sitting in N single particle levels of a potential well and interacting through the pairing force is tre ated introducing even Grassmann variables. The eigenvectors are analyticall y expressed solely in terms of these with coefficients fixed by the eigenva lues and the single particle energies. When the latter are those of a harmo nic oscillator well an accurate expression is derived for both the collecti ve eigenvalue and for those trapped in between the single particle levels, for any strength of the pairing interaction and any number of levels. Notab ly the trapped solutions are labeled through an index upon which they depen d parabolically.