Based on the Hartree-Fock-Bogoliubov solutions in large deformed coordinate spaces, the finite amplitude method for quasiparticle random phase approximation (FAM-QRPA) has been implemented, providing a suitable approach to probe collective excitation
s of weakly-bound nuclei embedded in the continuum. The monopole excitation modes in Magnesium isotopes up to the neutron drip line have been studied with the FAM-QRPA framework on both the coordinate-space and harmonic oscillator basis methods. Enhanced soft monopole strengths and collectivity as a result of weak-binding effects have been unambiguously demonstrated.
The parameters of the UNEDF2 nuclear energy density functional (EDF) model were obtained in an optimization to experimental data consisting of nuclear binding energies, proton radii, odd-even mass staggering data, fission-isomer excitation energies,
and single particle energies. In addition to parameter optimization, sensitivity analysis was done to obtain parameter uncertainties and correlations. The resulting UNEDF2 is an all-around EDF. However, the sensitivity analysis also demonstrated that the limits of current Skyrme-like EDFs have been reached and that novel approaches are called for.
First calculations for deformed nuclei with the Fayans functional are carried out for the uranium and lead isotopic chains. The ground state deformations and deformation energies are compared to Skyrme-Hartree-Fock-Bogolyubov results of HFB-17 and HF
B-27 functionals. For the uranium isotopic chain, the Fayans functional predictions are rather similar properties compared to HFB-17 and HFB-27. However, there is a disagreement for the lead isotopic chain. Both of the Skyrme HFB functionals predict rather strong deformations for the light Pb isotopes which does not agree with the experimental data on charge radii and magnetic moments of the odd Pb isotopes. On the other hand, the Fayans functional predicts a spherical ground state for all of the lead isotopes, in accordance with the data and the known in literature results obtained with the Gogny D1S force and SLy6 functional as well. The deformation energy curves are calculated and compared to four Skyrme functionals, SLy4, Sly6, SkM* and UNEDF1, for $^{238}$U nucleus and several lead deficient Pb isotopes. In the first case, the Fayans functional result is rather close to SkM* and UNEDF1 which, in particularly the latter one, describe the first and second barriers in $^{238}$U rather well. For the light lead isotopes, the Fayans deformation energy curves are qualitatively close to those of the SLy6 functional.
A new Skyrme-like energy density suitable for studies of strongly elongated nuclei has been determined in the framework of the Hartree-Fock-Bogoliubov theory using the recently developed model-based, derivative-free optimization algorithm POUNDerS. A
sensitivity analysis at the optimal solution has revealed the importance of states at large deformations in driving the parameterization of the functional. The good agreement with experimental data on masses and separation energies, achieved with the previous parameterization UNEDF0, is largely preserved. In addition, the new energy density UNEDF1 gives a much improved description of the fission barriers in 240Pu and neighboring nuclei.
