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Register a new userSymmetry restoration for odd-mass nuclei with a Skyrme energy density functional
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In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parameterization of the Skyrme energy functional and a volume-type pairing interaction are used.
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We perform a systematic study of the impact of the J^2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations, which covers a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants, with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of charge radii. Our main conclusion is that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.
[Background] Giant resonance (GR) is a typical collective mode of vibration. The deformation splitting of the isovector (IV) giant dipole resonance is well established. However, the splitting of GRs with other multipolarities is not well understood. [Purpose] I explore the IV monopole and quadrupole excitations and attempt to obtain the generic features of IV giant resonances in deformed nuclei by investigating the neutral and charge-exchange channels simultaneously. [Method] I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states. [Results] I find the concentration of the monopole strengths in the energy region of the isobaric analog or Gamow-Teller resonance irrespective of nuclear deformation, and the appearance of a high-energy giant resonance composed of the particle-hole configurations of $2hbar omega_0$ excitation. Splitting of the distribution of the strength occurs in the giant monopole and quadrupole resonances due to deformation. The lower $K$ states of quadrupole resonances appear lower in energy and possess the enhanced strengths in the prolate configuration, and vice versa in the oblate configuration, while the energy ordering depending on $K$ is not clear for the $J=1$ and $J=2$ spin-quadrupole resonances. [Conclusions] The deformation splitting occurs generously in the giant monopole and quadrupole resonances. The $K$-dependence of the quadrupole transition strengths is largely understood by the anisotropy of density distribution.
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.
The effective Skyrme energy density functionals are widely used in the study of nuclear structure, nuclear reaction and neutron star, but they are less established from the heavy ion collision data. In this work, we find 22 effective Skyrme parameter sets, when incorporated in use the transport model, ImQMD, to describe the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u. We use these sets to calculate the neutron skin of $^{208}$Pb based on the restricted density variation method, and obtain the neutron skin of $^{208}$Pb in the range of $delta R_{np}=0.18pm0.04$ fm.
We use the finite amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute beta-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.
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