Microscopic origin of reflection-asymmetric nuclear shapes

Abstract

Background: The presence of nuclear ground states with stable reflection-asymmetric shapes is supported by rich experimental evidence. Theoretical surveys of odd-multipolarity deformations predict the existence of pear-shaped isotopes in several fairly localized regions of the nuclear landscape in the vicinity of near-lying single-particle shells with ∆ = ∆j = 3. Purpose:We analyze the role of isoscalar, isovector, neutron-proton, neutron-neutron, and proton-proton multipole interaction energies in inducing the onset of reflection-asymmetric ground-state deformations. Methods:The calculations are performed in the framework of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory using two Skyrme energy density functionals and density-dependent pairing force.Results: We show that reflection-asymmetric ground-state shapes of atomic nuclei are driven by the oddmultipolarity neutron-proton (or isoscalar) part of the nuclear interaction energy. This result is consistent with the particle-vibration picture, in which the main driver of octupole instability is the isoscalar octupole-octupole interaction giving rise to large E3 polarizability. Conclusions:The necessary condition for the appearance of localized regions of pear-shaped nuclei in the nuclear landscape is the presence of parity doublets involving ∆ = ∆j = 3 proton or neutron single-particle shells. This condition alone is, however, not sufficient to determine whether pear shapes actually appear, and -if so -what the corresponding reflection-asymmetric deformation energies are. The predicted small reflection-asymmetric deformation energies result from dramatic cancellations between even-and odd-multipolarity components of the nuclear binding energy.

Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: II. Time-reversal symmetry breaking

“…The complete effect can be several times larger than just the contribution of the time-odd terms, but it remains on the level of about a hundred keV. Compared to the rms deviation of the model on the total masses, σ(M ) = 0.668 MeV, it seems unlikely the pa- 15 We note in passing that EFA calculations producing larger binding energies than complete calculations with blocking is not a violation of the variational principle. The EFA deals with statistical mixtures of Bogoliubov states [39], while complete blocking calculations deal with pure Bogoliubov states that break timereversal.…”

“…3, that the EFA produces larger binding energies such that the difference plotted in Fig. 4 is positive across the entire isotopic chain 15 . The time-odd terms show only a modest amount of variation with neutron number and remain small everywhere.…”

“…Allowing for reflection-asymmetric shapes is not a priority for a description of masses, as in a mean-field approach octupole correlations are known to impact nuclear ground states for only a very limited number of nuclei in a few isolated regions of the nuclear chart [14,15]. The situation is very different for odd-mass and oddodd nuclei which constitute roughly three quarters of the chart of nuclei and whose ground states all have finite angular momentum, and hence break time-reversal symmetry.…”

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: II. Time-reversal symmetry breaking

“…A study employing a Gogny-type EDF found almost no effect on pairing gaps when including time-odd terms [110]. 16…”

“…Allowing for reflection-asymmetric shapes is not a priority for a description of masses, as in a mean-field approach octupole correlations are known to impact nuclear ground states for only a very limited number of nuclei in a few isolated regions of the nuclear chart [15,16]. The situation is very different for odd-mass and odd-odd nuclei which constitute roughly three quarters of the chart of nuclei and whose ground states all have finite angular momentum, and hence break time-reversal symmetry.…”