Background: Electron scattering provides a powerful tool to determine charge distributions and transition densities of nuclei. This tool will soon be available for short-lived neutron-rich nuclei.
Purpose: Beyond-mean-field methods have been successfully applied to the study of excitation spectra of nuclei in the whole nuclear chart. These methods permit determination of energies and transition probabilities starting from an effective in-medium nucleon-nucleon interaction but without other phenomenological ingredients. Such a method has recently been extended to calculate the charge density of nuclei deformed at the mean-field level of approximation [J. M. Yao et al., Phys. Rev. C 86, 014310 (2012)]. The aim of this work is to further extend the method to the determination of transition densities between low-lying excited states.
Method: The starting point of our method is a set of Hartree-Fock-Bogoliubov wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density functional. Correlations beyond the mean field are introduced by projecting mean-field wave functions on angular momentum and particle number and by mixing the symmetry-restored wave functions.
Results: We give in this paper detailed formulas derived for the calculation of densities and form factors. These formulas are rather easy to obtain when both initial and final states are 0(+) states but are far from being trivial when one of the states has a finite J value. Illustrative applications to Mg-24 and to the even-mass Ni58-68 have permitted an analysis of the main features of our method, in particular the effect of deformation on densities and form factors. An illustrative calculation of both elastic and inelastic scattering form factors is presented.
Conclusions: We present a very general framework to calculate densities of and transition densities between low-lying states that can be applied to any nucleus. Achieving better agreement with the experimental data will require improving the energy density functionals that are currently used and also introducing quasiparticle excitations in the mean-field wave functions.