The lifetime of the $0_3^{+}$ state in ${}^{120}\mathrm{Sn}$ was measured for the first time by applying the fast-timing technique following thermal neutron capture. The mean lifetime of $\tau =50\left(7\right)$ ps leads to an $E0$ transition strength of ${10}^3\times {\rho }^2(E0;0_3^{+}\to 0_2^{+})=120\left(50\right)$, 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 ${}^{116}\mathrm{Sn}$ to ${}^{120}\mathrm{Sn}$.

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• Collective levels
• Electromagnetic transitions
• Lifetimes & widths
• Nuclear structure & decays
• Shape coexistence
• 90 ≤ A ≤ 149
• Neutron capture