Shape coexistence and evolution in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Sr</mml:mi><mml:mprescripts/><mml:none/><mml:mn>98</mml:mn></mml:mmultiscripts></mml:math>

Shape coexistence between the strongly deformed ground state and the weakly deformed ${0}_{2}^{+}$ state in $^{98}\mathrm{Sr}$ has been a major topic of interest due to the energy difference of 215 keV, which is the smallest in all even-even nuclei. The electric monopole transition strength ${\ensuremath{\rho}}^{2}(E0)$ is an important quantity that can relate the deformation difference and the shape mixing between the two ${0}^{+}$ states, which are admixtures of the vibrational (S) and the rotational (D) states in a simple mixing model. In a $\ensuremath{\beta}$-decay spectroscopy experiment, the experimental ${\ensuremath{\rho}}^{2}(E0)$ was measured. A value of 0.053(5) is consistent with the previous measurement and was combined with known electric quadrupole transition strengths $B(E2)$ in calculations of a two-state mixing model. Based on a systematic study on neighboring Kr, Zr, and Mo isotopes, the mixing of the ${0}^{+}$ and ${2}^{+}$ states in $^{98}\mathrm{Sr}$ was determined to be 8.6% and 1.3%, respectively, corresponding to deformation parameters ${\ensuremath{\beta}}_{\text{D}}=0.38(1)$ and ${\ensuremath{\beta}}_{\text{S}}=\ensuremath{-}0.23(2)$. These parameters reproduce experimental transition strengths well except for the ${4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+}$ transition, which suggests a smaller D-band deformation for $J\ensuremath{\ge}4$.