Ab Initio Derivation of Model Energy Density Functionals

I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.

Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals

We calculate properties of the ground and excited states of nuclei in the nobelium region for proton and neutron numbers of 92 <= Z <= 104 and 144 <= N <= 156, respectively. We use three different energy-density-functional (EDF) approaches, based on covariant, Skyrme, and Gogny functionals, each within two different parameter sets. A comparative analysis of the results obtained for odd-even mass staggerings, quasiparticle spectra, and moments of inertia allows us to identify single-particle and shell effects that are characteristic to these different models and to illustrate possible systematic uncertainties related to using the EDF modelling

Pairing-induced speedup of nuclear spontaneous fission

Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes. To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of $^{264}$Fm and $^{240}$Pu using the state-of-the-art self-consistent framework. We employ the superfluid nuclear density functional theory with the Skyrme energy density functional SkM$^*$ and a density-dependent pairing interaction. Along with shape variables, proton and neutron pairing correlations are taken as collective coordinates. The collective inertia tensor is calculated within the nonperturbative cranking approximation. The fission paths are obtained by using the least action principle in a four-dimensional collective space of shape and pairing coordinates. Pairing correlations are enhanced along the minimum-action fission path. For the symmetric fission of $^{264}$Fm, where the effect of triaxiality on the fission barrier is large, the geometry of fission pathway in the space of shape degrees of freedom is weakly impacted by pairing. This is not the case for $^{240}$Pu where pairing fluctuations restore the axial symmetry of the dynamic fission trajectory. The minimum-action fission path is strongly impacted by nucleonic pairing. In some cases, the dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. Consequently, in the dynamical description of nuclear fission, particle-particle correlations should be considered on the same footing as those associated with shape degrees of freedom.

Spectroscopic properties of nuclear Skyrme energy density functionals

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.

Nonlocal energy density functionals for low-energy nuclear structure

We introduce a finite-range pseudopotential built as an expansion in derivatives up to next-to-next-to-next-to-leading order (N$^3$LO) and we calculate the corresponding nonlocal energy density functional (EDF). The coupling constants of the nonlocal EDF, for both finite nuclei and infinite nuclear matter, are expressed through the parameters of the pseudopotential. All central, spin-orbit, and tensor terms of the pseudopotential are derived both in the spherical-tensor and Cartesian representation. At next-to-leading order (NLO), we also derive relations between the nonlocal EDF expressed in the spherical-tensor and Cartesian formalism. Finally, a simplified version of the finite-range pseudopotential is considered, which generates the EDF identical to that generated by a local potential.

Rotational properties of nuclei around $^{254}$No investigated using a spectroscopic-quality Skyrme energy density functional

Nuclei in the $Zapprox100$ mass region represent the heaviest systems where detailed spectroscopic information is experimentally available. Although microscopic-macroscopic and self-consistent models have achieved great success in describing the data in this mass region, a fully satisfying precise theoretical description is still missing. By using fine-tuned parametrizations of the energy density functionals, the present work aims at an improved description of the single-particle properties and rotational bands in the nobelium region. Such locally optimized parameterizations may have better properties when extrapolating towards the superheavy region. Skyrme-Hartree-Fock-Bogolyubov and Lipkin-Nogami methods were used to calculate the quasiparticle energies and rotational bands of nuclei in the nobelium region. Starting from the most recent Skyrme parametrization, UNEDF1, the spin-orbit coupling constants and pairing strengths have been tuned, so as to achieve a better agreement with the excitation spectra and odd-even mass differences in $^{251}$Cf and $^{249}$Bk. The quasiparticle properties of $^{251}$Cf and $^{249}$Bk were very well reproduced. At the same time, crucial deformed neutron and proton shell gaps open up at $N=152$ and $Z=100$, respectively. Rotational bands in Fm, No, and Rf isotopes, where experimental data are available, were also fairly well described. To help future improvements towards a more precise description, small deficiencies of the approach were carefully identified. In the $Zapprox100$ mass region, larger spin-orbit strengths than those from global adjustments lead to improved agreement with data. Puzzling effects of particle-number restoration on the calculated moment of inertia, at odds with the experimental behaviour, require further scrutiny.

Isospin mixing within the symmetry restored density functional theory and beyond

We present results of systematic calculations of the isospin-symmetry-breaking corrections to the superallowed I=$0+,T=1 --> I=0+,T=1 beta-decays, based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT). We discuss theoretical uncertainties of the formalism related to the basis truncation, parametrization of the underlying energy density functional, and ambiguities related to determination of Slater determinants in odd-odd nuclei. A generalization of the double-projected DFT model towards a no core shell-model-like configuration-mixing approach is formulated and implemented. We also discuss new opportunities in charge-symmetry- and charge-independence-breaking studies offered by the newly developed DFT formalism involving proton-neutron mixing in the particle-hole channel.

Polarization corrections to single-particle energies studied within the energy-density-functional and QRPA approaches

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.

Isospin mixing within the multi-reference nuclear density functional theory and beyond - selected aspects

The results of systematic calculations of isospin-symmetry-breaking corrections to superallowed beta-decays based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT) are reviewed with an emphasis on theoretical uncertainties of the model. Extensions of the formalism towards no core shell model approach with basis cutoff scheme dictated by the self-consistent particle-hole DFT solutions will be also discussed.

Deformations and quasiparticle spectra of nuclei in the nobelium region

We have performed self-consistent Skyrme Hartree-Fock-Bogolyubov calculations for nuclei close to $^{254}$No. Self-consistent deformations, including $beta_{2,4,6,8}$ as functions of the rotational frequency, were determined for even-even nuclei $^{246,248,250}$Fm, $^{252,254}$No, and $^{256}$Rf. The quasiparticle spectra for N=151 isotones and Z=99 isotopes were calculated and compared with experimental data and the results of Woods-Saxon calculations. We found that our calculations give high-order deformations similar to those obtained for the Woods-Saxon potential, and that the experimental quasiparticle energies are reasonably well reproduced.