Multiple shape coexistence near Sn118: First 03+ lifetime measurement

The intruder bands in Sn isotopes, built on the 2p-2h excitation across the $Z = 50$ proton shell gap, are well-known examples of shape coexistence near the neutron mid-shell region. Spectroscopic signatures for shape coexistence include enhanced $E0$ transitions between the $0^+$ band heads. However, the underlying shape coexistence and mixing has been unclear because lifetime information for the excited $0^+$ states was incomplete in $^{118}$Sn. We thus present here the first measurement of the $0^+_3$ lifetime in $^{118}$Sn using the fast-timing technique following thermal-neutron capture. The observed enhancement in $\rho^2(E0; 0^+_3 \rightarrow 0^+_2)$ of 150(30) milliunits provides compelling indications for multiple shape coexistence in $^{118}$Sn. Additionally, three distinct shapes in $^{116,118,120}$Sn naturally emerged in theoretical calculations based on the quantum-number-projected generator coordinate method employing a relativistic energy density functional.