Electric monopole transition from the superdeformed band in $^{40}$Ca

The electric monopole ($E0$) transition strength $\rho^2$ for the transition connecting the third 0$^+$ level, a "superdeformed" band head, to the "spherical" 0$^+$ ground state in doubly magic $^{40}$Ca has been determined via $e^+e^-$ pair-conversion spectroscopy. The measured value, $\rho^2(E0; 0^+_3 \to 0^+_1)~=~2.3(5)\times10^{-3}$, is the smallest $\rho^2(E0; 0^+ \to 0^+)$ found in $A<50$ nuclei. In contrast, the $E0$ transition strength to the ground state observed from the second 0$^+$ state, a band head of "normal" deformation, is an order of magnitude larger, $\rho^2(E0; 0^+_2 \to 0^+_1)~=~25.9(16)\times~10^{-3}$, which shows significant mixing between these two states. Large-Scale Shell Model (LSSM) calculations were performed to understand the microscopic structure of the excited states, and the configuration mixing between them; experimental $\rho^2$ values in $^{40}$Ca and neighboring isotopes were well reproduced by the LSSM calculations. The unusually small $\rho^2(E0; 0^+_3 \to 0^+_1)$ value is due to destructive interference in the mixing of shape-coexisting structures, which are based on several different multiparticle-multihole excitations. This observation goes beyond the usual treatment of $E0$ strengths, where two-state shape mixing cannot result in destructive interference.