The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are treated in the generalized seniority scheme, for generalized seniority v ≤ 3. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell model space.

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Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem.Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realistic interactions, in the generalized seniority scheme with one broken proton pair and one broken neutron pair. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shellmodel space. We demonstrate that, even for the Ti isotopes, significant benefit would be obtained in going beyond the approximation of one broken pair of each type, while the Cr isotopes require further broken pairs to provide even qualitative accuracy.

A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of one-body and two-body operators and basis state overlaps.

We address the removal of states with center-of-mass excitation from the SU(3) nocore shell model [SU(3)-NCSM] space, i.e., construction of the nonspurious subspace. A procedure is formulated based on solution of the null-space problem for the centerof-mass harmonic oscillator lowering operatorB (01) c.m. , operating at the level of SU(3) irreducible representations. Isolation of the center-of-mass free subspace for the SU(3)-NCSM provides the foundation for exact removal of center-of-mass dynamics in the proposed Sp(3, R) symplectic no-core shell model. We outline the construction process for the matrix representation ofB (01) c.m. , present the algorithm for obtaining the nonspurious space, and examine the dimensions obtained for center-of-mass free SU(3) subspaces in representative light nuclei.