Investigations of electric monopole transitions in medium-mass to heavy nuclei: Beyond mean field calculations with the Gogny force

The five dimensional collective Hamiltonian (5DCH) implemented with Gogny force has been employed in systematic calculations of electric monopole $\left(E0\right)$ transitions in even-even nuclei with masses $30<A<310$. Significant improvements in the comparison between experimental data and calculations are achieved using (i) stronger collective masses than those inferred from the Inglis-Beliaev approximation and (ii) the $E0$ transition operator as defined by Church and Weneser [E. L. Church and J. Weneser, Phys. Rev. 103, 1035 (1956)]. Main emphasis has been placed on the square of the $E0$ transition strength, ${\rho }^2(E0;0_2^{+}\to 0_1^{+})$, for transitions between the first $0^{+}$ excited state and ground state levels. The dimensionless parameter $X(E0/E2)$ has also been considered in 5DCH calculations covering the rare earth and actinide regions where sparse data are available. Finally, the quasiparticle random-phase approximation (QRPA) implemented with Gogny force has been considered as a complementary model for the interpretation of ${\rho }^2(E0;0_i^{+}\to 0_1^{+})$, $i\ne 2$, data available for ${}_{166}\mathrm{Er}$ and ${}_{238}U$. The 5DCH model provides a reasonable description of collective $E0$ transitions, but fails otherwise. Specific shell effects are not considered in the present modeling. Global improvements in ${\rho }^2\left(E0\right)$ and $X(E0/E2)$ predictions would be achieved by implementing the energy density functional with quasiparticle components.