Energy-density-functional calculations including proton-neutron mixing

We present results of calculations based on the Skyrme energy density functional that include arbitrary mixing between protons and neutrons. In this framework, single-particle states are superpositions of proton and neutron components and the energy density functional is fully invariant with respect to three-dimensional rotations in the isospin space. The isospin of the system is controlled by means of the isocranking method, which carries the standard cranking approach over to isospin space. We show numerical results of the isocranking calculations performed for isobaric analog states in the $A=14$ and $A=40–56$ nuclei. We also present results obtained for high-isospin states in ${}^{48}$Cr, with constraints on the isospin implemented using the augmented Lagrange method.

Figure 1

Results obtained without the Coulomb interaction: (a) energies of the $T=0$, 2, and 4 states in $A=48$ isobars and (b) the s.p. Routhians of the $T=4$ states.

Figure 2

Same as in Fig. 1 but with the Coulomb interaction included. The inset shows the isocranking frequencies used for the $T\simeq 4$ calculation in the ${\lambda }_x-{\lambda }_z$ plane.

Figure 3

(a) Energies of the $T\simeq 4$ states in $A=40–56$ isobars with even $A/2$ as functions of $\langle {\widehat{T}}_z\rangle$. For $A=40$, 44, 48, 52, and 56, we used the values of $({\lambda }_{\mathrm{off}},{\lambda }^{\prime })=(-6.8,13.6)$, $(-7.4,12.4)$, $(-8.0,12.0)$, $(-8.4,11.6)$, and $(-8.8,12.4)$ MeV, respectively. (b) Excitation energies of ${}^{48}$Cr for $\langle {\widehat{T}}_x\rangle =0$, 2, 4, 6, and 8, calculated by using the augmented Lagrange method.

Figure 4

Energies of $T\simeq 1$ states in $A=14$ isobars in comparison with the experimental data [13].