Broken pairs in the interacting boson model: Projection of spurious states

Abstract

The interacting boson model is extended by the inclusion of selective noncollective fermion states through the successive breaking of the correlated S and D pairs (s and d bosons͒. High angular momentum states are generated in this way, and their structure described by the coupling between fermions in broken pairs and the boson core. The model space of bosons and broken pairs contains also unphysical states that are generated automatically when fermions couple to angular momenta J F ϭ0 and 2. A procedure is derived for the projection of spurious components from bases that contain one fermion pair. Spurious states are identified and an algorithm for their projection is constructed. The model is applied to the description of states in the spherical nucleus 116 Sn, and the weakly deformed nucleus 82 Sr. Calculated spectra and transition probabilities are compared with experimental data. It is found that projection of spurious states from the model space is essential for a description of excited states with low angular momenta above the yrast, while it is less important for high-spin states close to the yrast line.

Nuclear matrix elements for double-βdecay

“…A paper with those for 48 Ti is in preparation [109]. The quality of these, as well as of the unpublished results for 96 Zr is equal to that of the results obtained previously [95][96][97][98][99][100][101][102][103][104][105][106][107]. For the semimagic nuclei 116−124 Sn and 136 Xe, we have obtained the parameters by a fit to the energy of the low-lying states using the same procedure as in Ref.…”

“…For most nuclei, the Hamiltonian parameters are taken from the literature [95][96][97][98][99][100][101][102][103][104][105][106][107]. The values of the Hamiltonian parameters, as well as the references from which they were taken, are given in Table XXIII.…”

“…For the semimagic nuclei 116−124 Sn and 136 Xe, we have obtained the parameters by a fit to the energy of the low-lying states using the same procedure as in Ref. [103] for 116 Sn, while 48 Ca has been taken as doubly magic. This procedure is compatible with the generalized seniority (GS) scheme, which appears to be good for semi-magic nuclei, as extensively discussed in the 1980s for pairing plus quadrupole interactions, and as shown recently for realistic interactions [110].…”

Experimental and Theoretical Study of Quasi-Particle Alignment in 82Sr

“…Since the fraction of un-paired protons determines the variation of g factor with spin, the rapid rising of g factors at spins 6 + and 8 + can be interpreted by the increase of the unpaired proton alignment. Table 1 shows our calculated percentages of un-paired protons in the positive parity states in 82 Sr together with the percentages calculated by S. Cacciamani et al [11], in terms of the interacting boson model. Though the results given by S. Cacciamani et al show the breaking of the paired protons, the percentages of un-paired protons do not significantly change with spin.…”

Interacting boson model plus broken-pair description of high-spin dipole bands

“…If the fermions in the broken pair are different from the unpaired fermion, the fermion basis contains two protons and one neutron or vice versa. We have applied the model to the description of high-spin states in even-even and odd-even nuclei in the Hg [3][4][5], Sr-Zr [7][8][9][10] and Nd-Sm [11][12][13] regions. In several even-even nuclei high-spin bands have been observed, that could not be described by model calculations.…”