Validity of the SD-pair truncation of the shell model - art. no. 014316

The validity of the SD-pair truncation of the shell model is tested in a si ngle j shell and in many j shells within the framework of the nucleon pair shell model. It is found that the SD-pair truncation is a good approximatio n of the shell model in the single-j case when the Hamiltonian consists of (monopole and quadrupole) pairing plus quadrupole-quadrupole-type interacti on. The SD-pair truncation deteriorates if the quadrupole-quadrupole intera ction is artificially large compared with the monopole pairing interaction. For multi-j shells, schematic calculations in the degenerate sd, pf, and s dg shells are performed for the extreme case of a pure quadrupole-quadrupol e interaction. There is a large difference between the binding energies id the SD-pair-truncated subspace and those calculated in the full shell model space as in the case of a single-j shell. However, it is found that the ba sic properties of the band structure remain intact, and that the difference in energy levels, i.e., moments of inertia, can be easily absorbed by adju sting interaction strengths without changing the transition rates.