Shapes of neutron - rich A ≈ 190 odd - odd nuclei

Following from the prediction by Hilton and Mang [1] of “giant backbending” in 180Hf, caused by a collective oblate rotational band crossing the prolate ground-state band, there has been further theoretical investigation of this phenomenon [2–5]. The calculated shape change is understood to be induced by the effects of rotation alignment. It is related to the prediction of a ground-state shape transition from prolate to oblate with increasing neutron number [5–8] in the same mass region. An important consideration is the reinforcing effect of the protons and neutrons, both of which have their Fermi levels high in their respective shells. Thus high-K couplings for prolate shapes compete with low-K couplings for oblate shapes. It is the rotation alignment of the latter that, unusually, enables collective oblate rotation (γ = −60◦ in the Lund convention) to become yrast, i.e., to have the lowest excitation energy at a given angular momentum. Nevertheless, the experimental situation remains inconclusive [4,5,9]. The present work gives further theoretical insight by studying odd-odd nuclei in the neutron-rich A ≈ 190 region. The initial supposition was that, since the proton and neutron shape-driving effects reinforce one another, it may be sufficient to have a single nucleon of each type in order to manifest the prolate-oblate shape coexistence. This is indeed found from the calculations, as shown below, and may lead to improved experimental opportunities to test the predictions. Total Routhian surface (TRS) calculations have been performed for odd-odd N = 115 and 117 isotopes of tantalum (Z = 73), rhenium (Z = 75), and iridium (Z = 77), complementing our earlier study of even-even nuclides [5]. The single-particle energies are obtained from the deformed Woods-Saxon potential [10], with the Lipkin-Nogami (LN) treatment of pairing [11]. This avoids the spurious pairing phase transition encountered in the simpler BCS approach. The pairing strength, G, is determined by the average-gap method [12]. The total energy of a configuration consists of a macroscopic part which is obtained from the standard liquid-drop model [13] and a microscopic part resulting from the Strutinsky shell correction [14], δEshell = ELN − ẼStrut. Calculations are performed in the lattice of quadrupole (β2, γ ) deformations with hexadecapole (β4) variation. For a given