Shape coexistence and band mixing in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Sn</mml:mi><mml:mprescripts/><mml:none/><mml:mn>116</mml:mn></mml:mmultiscripts></mml:math>: Insights from density functional the

We employ the Bohr model and nuclear density functional theory to investigate the nuclear structure of the $^{116}\mathrm{Sn}$ isotope. Given that vibrational and rotational states are prevalent in midshell nuclei near $Z=50$ with shape coexistence, we applied the $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ vibrations of an axially symmetric rotor Hamiltonian to study band mixing. We estimated the mixing of the lowest vibrational and rotational ${0}^{+}$ and ${2}^{+}$ states and compared these results with predictions from other models. Our findings indicate that the $\ensuremath{\gamma}$ bands are significantly more deformed than the $\ensuremath{\beta}$ bands in $^{116}\mathrm{Sn}$.