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The problem of one pair of identical nucleons sitting in ${\cal N}$ singleparticle levels of a potential well and interacting through the pairing forceis treated introducing even Grassmann variables. The eigenvectors areanalytically expressed solely in terms of these with coefficients fixed by theeigenvalues and the single particle energies. When the latter are those of anharmonic oscillator well an accurate expression is derived for both thecollective eigenvalue and for those trapped in between the single particlelevels, for any strength of the pairing interaction and for any number oflevels. Notably the trapped solutions are labelled through an index upon whichthey depend parabolically.Comment: 5 pages, 1 postscript figur

Pairing Hamiltonian for one pair of identical nucleons bound in a potential well