Nuclear Systematics in the Interacting Boson (IBA) Model

Abstract

Within the framework of the interacting boson approximation, simple analytical formulae are presented for analysing the mass dependence of particle transfer, inelastic scattering and electromagnetic decay from experimental data in nuclear physics. It is shown that the identical boson model provides a useful tool to correlate the results of these experiments and that the extension to equivalent proton and neutron bosons leads to some new and interesting results in the Pt-Hg mass region, namely the possibility of phase transitions and symmetry breaking.

Gyromagnetic ratios of excited states in186W

“…Tests of this were provided by the experimentally exposed g-factor systematics of the 2[, 2) ~, and 4+ states in lss'19~ [3][4][5]; it was shown [4,5] that the first-order M1 operator in IBM-2 (in which admixtures of the Majorana states were incorporated) implied mass variations of the gfactors of these levels which were totally inconsistent with the empirical results. Thus, neither of the above findings for E2 or M1 observables in the Os nuclides appear to support, justify, or demand admixtures of maximal F-spin symmetric and Majorana states; without such coupling, the predictions in IBM-2 differ little from those in IBM-1 [8][9][10][11] to first-order in the boson operators.…”

“…(2)] incorporating F-spin admixtures implied mass variations of the gfactors totally inconsistent with experiment [4,5], again calling into question the necessity of the admixtures of Majorana states in this mass region. Decoupling of these non-maximally symmetric states has the effect that to first-order in the boson operators, predictions of IBM-2 differ little from those of IBM-1 [8][9][10][11] for the lowest states. In these circumstances, equation (2) [as is the case for the first-order M1 IBM-1 operator] predicts constant inter-level gfactors for all states of the same F-spin in a given nucleus (including those of the ground-state-,/%, and v-bands), and, additionally allows for only a trivial mass dependence of the gyromagnetic ratios of corresponding levels [4,5,8].…”

“…The two IBM formulations, nevertheless, differ with respect to predictions of M1 observables [B(M1) rates and g-factors]. In IBM-l, the presence of M1 transitions and/or any disparities in the gyromagnetic ratios of the lower eigenstates enter only via the M1 operator taken to second order [1][2][3], while in IBM-2, M1 transitions and g-factor variations can be accommodated in its first-order M1 operatorbut only through admixtures of F-spin symmetric and Majorana states [4][5][6][7][8].…”

“…In the case of M1 quantities, the first-order IBM-1 operator does not admit of M1 transitions and/or any departures from strict constancy of the gyromagnetic ratios of the lowest eigenstates of a given nucleus. In IBM-2, however, admixtures of maximal F-spin symmetric and Majorana states are directly manifest through the first-order M1 operator [4][5][6][7][8] to allow for M1 transitions, departures from constancy of the level g-factors within a nucleus, and mass variations of the gyromagnetic ratios of corresponding levels. Tests of this were provided by the experimentally exposed g-factor systematics of the 2[, 2) ~, and 4+ states in lss'19~ [3][4][5]; it was shown [4,5] that the first-order M1 operator in IBM-2 (in which admixtures of the Majorana states were incorporated) implied mass variations of the gfactors of these levels which were totally inconsistent with the empirical results.…”

Measurements ofg(41+,22+)in70,72<

“…A different approach, provided by the interacting boson model [28,29], can be considered. Sambataro [30], using the formulation of Morrison [31], expressed the g factor of the 2 + 1 state in terms of the number of valence proton bosons, N π , valence neutron bosons, N ν , and the effective g factors of proton and neutron bosons, g π and g ν , respectively…”