A recent high-resolution $alpha$, $X$-ray, and $gamma$-ray coincidence-spectroscopy experiment offered first glimpse of excitation schemes of isotopes along $alpha$-decay chains of $Z=115$. To understand these observations and to make predictions abo
ut shell structure of superheavy nuclei below $^{288}115$, we employ two complementary mean-field models: self-consistent Skyrme Energy Density Functional approach and the macroscopic-microscopic Nilsson model. We discuss the spectroscopic information carried by the new data. In particular, candidates for the experimentally observed $E1$ transitions in $^{276}$Mt are proposed. We find that the presence and nature of low-energy $E1$ transitions in well-deformed nuclei around $Z=110, N=168$ strongly depends on the strength of the spin-orbit coupling; hence, it provides an excellent constraint on theoretical models of superheavy nuclei. To clarify competing theoretical scenarios, an experimental search for $E1$ transitions in odd-$A$ systems $^{275,277}$Mt, $^{275}$Hs, and $^{277}$Ds is strongly recommended.
Background: Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of
why the tin nuclei appear to be significantly softer than 208Pb. Purpose: We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semi-magic nuclei. Methods: We employ self-consistently the Quasiparticle Random Phase Approximation on top of spherical Hartree-Fock-Bogolyubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing. Results: We found that the difference between centroids of Giant Monopole Resonances measured in lead and tin (about 1 MeV) always turns out to be overestimated by about 100%. We also found that the volume incompressibility, obtained by adjusting the liquid-drop expression to microscopic results, is significantly larger than the infinite-matter incompressibility. Conclusions: The zero-range and separable pairing forces cannot induce modifications of monopole strength functions in tin to match experimental data.
Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclea
r many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required, as a step preliminary to the adjustment of the coupling constants. Purpose: Determine to which extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, to study the relations between the validity of the continuity equation and invariance of the functional under gauge transformations. Methods: Derive conditions for the validity of the continuity equation in the framework of time-dependent density functional theory. The conditions apply separately to the four spin-isospin channels of the one-body density matrix. Results: We obtained four sets of constraints on the coupling constants of the N3LO energy density functional that guarantee the validity of the continuity equation in all spin-isospin channels. In particular, for the scalar-isoscalar channel, the constraints are the same as those resulting from imposing the standard U(1) local-gauge-invariance conditions. Conclusions: Validity of the continuity equation in the four spin-isospin channels is equivalent to the local-gauge invariance of the energy density functional. For vector and isovector channels, such validity requires the invariance of the functional under local rotations in the spin and isospin spaces.
Four previously known rotational bands in 76Rb have been extended to moderate spins using the Gammasphere and Microball gamma ray and charged particle detector arrays and the 40Ca(40Ca,3pn) reaction at a beam energy of 165 MeV. The properties of two
of the negative-parity bands can only readily be interpreted in terms of the highly successful Cranked Nilsson-Strutinsky model calculations if they have the same configuration in terms of the number of g9/2 particles, but they result from different nuclear shapes (one near-oblate and the other near-prolate). These data appear to constitute a unique example of shape co-existing structures at medium spins.
