Microscopic method for E0 transition matrix elements

Abstract

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 wavefunctions. 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 energy-density functional and might be used to provide new constraints for them.

E0 transition strength in stable Ni isotopes

“…The calculated ρ 2 (E0) for the remixed 0 + states was about a factor of two smaller than in experiment (comparable to the level of agreement achieved in the other nuclei studied in Ref. [52]). This observation highlights the sensitivity of E0 transition strengths to configuration mixing and to small components of the wavefunctions for the states involved in the transition.…”

“…The microscopic model of Brown et al [52] does not reproduce the new experimental results for 2 + → 2 + transitions, although this model is successful in reproducing E0 transition strengths in 0 + → 0 + cases. In 58 Ni, the calculated ρ 2 (E0) value for the 0 + 2 → 0 + 1 transition was much larger than the experimental value.…”

Identification of significant E0 strength in the 22+→21+ transitions of 58,60,62Ni

“…Ref. [32] considered the 0 + 2 → 0 + 1 and 0 + 3 → 0 + 1 transitions in 58 Ni. The calculated M (E0) for the 0 + 2 → 0 + 1 transitions was much larger than the experimental value.…”

“…The EDF part of the calculation used the Skx and s3 Skyrme parameter sets that were used in Ref. [32]. The calculated values of |M (E0)| are significantly smaller than experiment.…”

“…For example, for 58 Ni the wavefunctions are dominated by the two-neutron configurations outside of a 56 Ni closed core. The only possible two-neutron configurations for 2 + are [(1p 3/2 ) 2 ], [(0f 5/2 ) 2 ], [1p 1/2 , 0f 5/2 ], A non-zero matrix element comes from only mixed configurations (as in the example of the 1p 1/2 and 0g 9/2 orbitals in 90 Zr [32]). We also consider the jj44 model space which allows for neutrons in the (0f 5/2 , 1p 3/2 , 1p 1/2 , 0g 9/2 ) orbitals.…”