  The problem of one pair of identical nucleons sitting in ${\cal N}$ single
particle levels of a potential well and interacting through the pairing force
is treated introducing even Grassmann variables. The eigenvectors are
analytically expressed solely in terms of these with coefficients fixed by the
eigenvalues and the single particle energies. When the latter are those of an
harmonic oscillator well an accurate expression is derived for both the
collective eigenvalue and for those trapped in between the single particle
levels, for any strength of the pairing interaction and for any number of
levels. Notably the trapped solutions are labelled through an index upon which
they depend parabolically.
