Matrix diagonalization algorithm and its applicability to the nuclear shell model

An importance-sampling iterative algorithm for diagonalizing shell model Hamiltonian matrices is reviewed and implemented in a spin uncoupled basis. Shell model spaces of dimensions up to N≲109 are considered. The analysis shows that about 10% of the basis states are enough to bring the eigenvalues to convergence. This fraction of states, however, is insufficient to lead to convergence of the transition strengths, thereby limiting the applicability of the method to not too large spaces. In its domain of validity, the method yields a large number of eigensolutions and can be usefully adopted for rather complete studies of low-energy spectroscopy. This is done here for 132,134Xe isotopes. The calculation yields spectra and electromagnetic responses in fairly good agreement with the available experimental data and unveils the properties of the low-energy states of these isotopes, including their proton-neutron symmetry.