Observation of mutually enhanced collectivity in self-conjugate<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mrow/><mml:mn mathvariant="bold">38</mml:mn><mml:mn mathvariant="bold">76</mml:mn></mml:msubsup></mml:math>Sr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn mathvariant="bold">38</mml:mn></mml:msub></mml:math>

The lifetimes of the first 2${}^{+}$ states in the neutron-deficient ${}^{76,78}$Sr isotopes were measured using a unique combination of the $\ensuremath{\gamma}$-ray line-shape method and two-step nucleon exchange reactions at intermediate energies. The transition rates for the 2${}^{+}$ states were determined to be $B(\mathrm{E}2;{2}^{+}\ensuremath{\rightarrow}{0}^{+})=2220(270)$ ${e}^{2}$fm${}^{4}$ for ${}^{76}$Sr and 1800(250) ${e}^{2}$fm${}^{4}$ for ${}^{78}$Sr, corresponding to large deformation of ${\ensuremath{\beta}}_{2}$ $=$ 0.45(3) for ${}^{76}$Sr and 0.40(3) for ${}^{78}$Sr. The present data provide experimental evidence for mutually enhanced collectivity that occurs at $N$ $=$ $Z$ $=$ 38. The systematic behavior of the excitation energies and $B(\mathrm{E}2)$ values indicates a signature of shape coexistence in ${}^{76}$Sr, characterizing ${}^{76}$Sr as one of most deformed nuclei with an unusually reduced $E$(4${}^{+}$)$/E$(2${}^{+}$) ratio.