Nuclear energy density optimization: Large deformations

A new Skyrme-like energy density suitable for studies of strongly elongated nuclei was 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 ${}^{240}$Pu and neighboring nuclei.

Figure 1

Excitation energies of fission isomers considered in the unedf1 optimization as functions of the HO basis deformation.

Figure 2

Absolute values of the correlation matrix of Table  presented in a color-coded format.

Figure 3

Sensitivity of unedf1 to different types of data entering the ${\chi }^2$ function.

Figure 4

Overall change in $\mathbf{x}$ for the unedf1 when the datum $d_i$ is changed by an amount of $0.1w_i$ one by one. The four rightmost data points marked FI correspond to excitation energies of fission isomers. The results for unedf0 and unedf1ex of Sec. 3d2 are also shown.

Figure 5

Similar as in Fig. 3 but for the unedf1ex parameter set.

Figure 6

Surface-symmetry coefficient (15) (upper panels) and surface coefficient (lower panels) versus $A^{-1/3}$ for unedf0 (left) and unedf1 (right).

Figure 7

Binding energy residuals between unedf1 results and experiment for 555 even-even nuclei. Isotopic chains of a given element are connected by lines.

Figure 8

Two-neutron (top) and two-proton (bottom) separation energy residuals between unedf1 results and experiment.

Figure 9

Single-proton energies for ${}^{208}$Pb, calculated with unedf0 and unedf1 EDFs compared to the experimental values of Ref. [72].

Figure 10

Fission pathway for ${}^{240}$Pu along the mass quadrupole moment $Q_{20}$ calculated using hfodd with SkM${}^{*}$, unedf0, and unedf1 EDFs. The ground-state energies have been normalized to zero. $E_{II}$, $E_A$, and $E_B$ indicate, respectively, the experimental energy of fission isomer and the inner and outer barrier heights [80].

Figure 11

Comparison of unedf0 and unedf1 predictions for the energy $N$-neutron drops trapped in an HO potential with $\hslash \omega =5$ MeV and 10 MeV with the AFDMC ab initio results of Ref. [88].