Microscopic method for $E0$ transition matrix elements

We present a microscopic model for electric monopole ($E0$) transition matrix elements by combining a configuration interaction model for orbital occupations with an energy-density functional model for the single-particle potential and radial wave functions. The configuration interaction model is used to constrain the orbital occupations for the diagonal and off-diagonal matrix elements. These are used in an energy-density functional calculation to obtain a self-consistent transition density. This density contains the valence contribution, as well as the polarization of the protons by the valence protons and neutrons. We show connections between $E0$ matrix elements and isomer and isotope shifts of the charge radius. The spin-orbit correction to the charge density is important in some cases. This model accounts for a large part of the data over a wide region of the nuclear chart. It also accounts for the shape of the observed electron scattering form factors. The results depend on the Skyrme parameters used for the energy-density functional and might be used to provide new constraints for them.

Figure 1

Calculated proton transition densities for ${}^{90}\mathrm{Zr}$ obtained with the $\mathit{Skx}$ energy-density functional. Contributions are shown for the three terms in Eq. (17).

Figure 2

Calculated form factors for ${}^{26}\mathrm{Mg}$. The dashed lines are for the valence space contribution only. The solid lines take into account the valence space and the core polarization.