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 ${}^{118}\mathrm{Sn}$. We thus present here the first measurement of the $0_3^{+}$ lifetime in ${}^{118}\mathrm{Sn}$ using the fast-timing technique following thermal-neutron capture. The observed enhancement in ${\rho }^2(E0;0_3^{+}\to 0_2^{+})$ of 150(30) milliunits provides compelling indications for multiple shape coexistence in ${}^{118}\mathrm{Sn}$. Additionally, three distinct shapes in ${}^{116,118,120}\mathrm{Sn}$ naturally emerged in theoretical calculations based on the quantum-number-projected generator coordinate method employing a relativistic energy density functional.

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