Evidence for shape coexistence in ${}^{120}$Sn from the first $0_3^{+}$ lifetime measurement

The lifetime of the $0_3^{+}$ state in ${}^{120}$Sn was measured for the first time applying the fast-timing technique following thermal neutron capture. The mean lifetime of $\tau =50(7)$~ps leads to a $E0$ transition strength of ${10}^3\times {\rho }^2(E0;0_3^{+}\to 0_2^{+})=120(50)$, suggesting shape coexistence and a high degree of mixing between the $0_2^{+}$ and $0_3^{+}$ states. With the newly measured lifetime, the $B(E2;0_3^{+}\to 2_1^{+})$ value is 0.50(7)~W.u., which reveals that the ${\rho }^2(E0;0_3^{+}\to 0_1^{+})$ increases by a factor of $\approx 3.4$ from ${}^{116}$Sn to ${}^{120}$Sn.