We address the question of how to improve the agreement between theoretical nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly magic nuclei, the SPEs can be deduced from spectroscopic properties of odd nuclei that have one
more, or one less neutron or proton. Theoretically, bare SPEs, before being confronted with experiment, must be corrected for the effects of the particle-vibration-coupling (PVC). In the present work, we determine the PVC corrections in a fully self-consistent way. Then, we adjust the SPEs, with PVC corrections included, to empirical data. In this way, the agreement with experiment, on average, improves; nevertheless, large discrepancies still remain. We conclude that the main source of disagreement is still in the underlying mean fields, and not in including or neglecting the PVC corrections.
Background: Models based on using perturbative polarization corrections and mean-field blocking approximation give conflicting results for masses of odd nuclei. Purpose: Systematically investigate the polarization and mean-field models, implemented
within self-consistent approaches that use identical interactions and model spaces, so as to find reasons for the conflicts between them. Methods: For density-dependent interactions and with pairing correlations included, we derive and study links between the mean-field and polarization results obtained for energies of odd nuclei. We also identify and discuss differences between the polarization-correction and full particle-vibration-coupling (PVC) models. Numerical calculations are performed for the mean-field ground-state properties of deformed odd nuclei and then compared to the polarization corrections determined by using the approach that conserves spherical symmetry. Results: We have identified and numerically evaluated self-interaction (SI) energies that are at the origin of different results obtained within the mean-field and polarization-correction approaches. Conclusions: Mean-field energies of odd nuclei are polluted by the SI energies, and this makes them different from those obtained by using polarization-correction methods. A comparison of both approaches allows for the identification and determination of the SI terms, which then can be calculated and removed from the mean-field results, giving the self-interaction-free energies. The simplest deformed mean-field approach that does not break parity symmetry is unable to reproduce full PVC effects.
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.
