Odd nuclei and quasiparticle excitations within the Barcelona Catania Paris Madrid energy density functional

An extension of the Barcelona Catania Paris Madrid (BCPM) energy density functional is proposed to deal with odd-mass systems as well as multiquasiparticle excitations. The extension is based on the assumption that the equal filling approximation (EFA) is a valid alternative to the traditional full blocking procedure of the Hartree-Fock-Bogoliubov method. The assumption is supported by the excellent agreement between full blocking and EFA calculations obtained with different parametrizations of the Gogny interaction. The EFA augmented BCPM functional is used to compute low energy excitation spectra of selected nuclei in different regions of the nuclear chart, and high-$K$ isomers in ${}^{178}\mathrm{Hf}$. We show that BCPM predictions are in good agreement with Gogny D1M results and experimental data.

Figure 1

The lowest energy excitation spectra for several rutherfordium isotopes computed with the Gogny D1M force, using full blocking and the EFA method. Each state is represented by a symbol according to its parity and the method employed for its calculation. Symbols are placed along the horizontal axis according to the value of $2K$. Filled (empty) black circles represent full blocking results with positive (negative) parity. States with octupole deformation and no definite parity are depicted with a black $\times$ symbol. Filled (empty) red squares are used for positive (negative) states obtained with EFA. States with octupole deformation and no definite parity are depicted with a red $+$ symbol. All symbols are slightly displaced along the horizontal axis to improve legibility.

Figure 2

A comparison of results obtained for Rf isotopes with full blocking and the Gogny force with D1S and D1M parametrizations. For an interpretation of the plot, see caption of Fig. 1. In the present case, black circles (red squares) represent D1S (D1M) calculations.

Figure 3

A comparison of full blocking and EFA results for selected Pu, Dy, and La isotopes. For an interpretation of the plot, see caption of Fig. 1.

Figure 4

The lowest energy spectrum obtained for ${}^{253–259}\mathrm{Rf}$ with the BCPM functional and the D1M Gogny force. For an interpretation of the plot, see caption of Fig. 1. In the present case, black circles (red squares) represent BCPM (D1M) calculations. Experimental ground state $J$ values are marked with a gray bar. The height of the bar represents the energy window for the comparison with theoretical results (see text for details).

Figure 5

The lowest energy spectrum obtained for ${}^{239–245}\mathrm{Pu}$ with the BCPM functional and the D1M Gogny force. For an interpretation of the plot, see caption of Fig. 1. In the present case, black circles (red squares) represent BCPM (D1M) calculations. Experimental ground state $J$ values are marked with a gray bar. The height of the bar represents the energy window for the comparison with theoretical results (see text for details).

Figure 6

The lowest energy spectrum obtained for ${}^{155–161}\mathrm{Dy}$ with the BCPM functional and the D1M Gogny force. For an interpretation of the plot, see caption of Fig. 1. In the present case, black circles (red squares) represent BCPM (D1M) calculations. Experimental ground state $J$ values are marked with a gray bar. The height of the bar represents the energy window for the comparison with theoretical results (see text for details).

Figure 7

The lowest energy spectrum obtained for ${}^{135–141}\mathrm{La}$ with the BCPM functional and the D1M Gogny force using the EFA. For an interpretation of the plot, see caption of Fig. 1. In the present case, black circles (red squares) represent BCPM (D1M) calculations. Experimental ground state $J$ values are marked with a gray bar. The height of the bar represents the energy window for the comparison with theoretical results (see text for details).

Figure 8

The lowest energy spectrum obtained for ${}^{75,77}\mathrm{Kr}$ with the BCPM functional (a) and the D1M Gogny force (b) using the EFA. For an interpretation of the plot, see caption of Fig. 1. In the present case, black circles (red squares) represent BCPM (D1M) calculations. Experimental ground state $J$ values are marked with a gray bar. The height of the bar represents the energy window for the comparison with theoretical results (see text for details).

Figure 9

High-$K$ states in ${}^{178}\mathrm{Hf}$ obtained with the EFA using BCPM, Gogny D1S and Gogny D1M are compared with experimental data. The Gogny excitation energies have been compressed by a factor 0.75 to account for the effective mass.