Double-step truncation procedure for large-scale shell-model calculations

We present a procedure that is helpful to reduce the computational complexity of large-scale shell-model calculations, by preserving as much as possible the role of the rejected degrees of freedom in an effective approach. Our truncation is driven first by the analysis of the effective single-particle energies of the original large-scale shell-model Hamiltonian, in order to locate the relevant degrees of freedom to describe a class of isotopes or isotones, namely the single-particle orbitals that will constitute a new truncated model space. The second step is to perform a unitary transformation of the original Hamiltonian from its model space into the truncated one. This transformation generates a new shell-model Hamiltonian, defined in a smaller model space, that retains effectively the role of the excluded single-particle orbitals. As an application of this procedure, we have chosen a realistic shell-model Hamiltonian defined in a large model space, set up by seven proton and five neutron single-particle orbitals outside Sr-88. We study the dependence of shell-model results upon different truncations of the original model space for the Zr, Mo, Ru, Pd, Cd, and Sn isotopic chains, showing the reliability of this truncation procedure.