A unitary correlation operator method

The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n–body operators is discussed. The one– and two–body–irreducible parts are worked out explicitly and the contribution of three–body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A = 48 are calculated with a spin–isospin–dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy– and mass–number–independent correlated two–body Hamiltonian reproduces all ”exact” many–body calculations surprisingly well. PACS: 21.60.-n; 21.30.Fe; 21.45.+v; 13.75.C