Shape coexistence revealed in the $$N=Z$$N=Z isotope $$^{72}$$72 Kr through inelastic scattering

The $$N=Z=36$$ nucleus $$^{72}$$Kr has been studied by inelastic scattering at intermediate energies. Two targets, $$^{9}$$Be and $$^{197}$$Au, were used to extract the nuclear deformation length, $$\delta _\text {N}$$, and the reduced E2 transition probability, B(E2). The previously unknown non-yrast $$2^+$$ and $$4^+$$ states as well as a new candidate for the octupole $$3^-$$ state have been observed in the scattering on the Be target and placed in the level scheme based on $$\gamma -\gamma $$ coincidences. The second $$2^+$$ state was also observed in the scattering on the Au target and the $$B(E2;\;2^+_2 \rightarrow 0^+_1)$$ value could be determined for the first time. Analyzing the results in terms of a two-band mixing model shows clear evidence for a oblate-prolate shape coexistence and can be explained by a shape change from an oblate ground state to prolate deformed yrast band from the first $$2^+$$ state. This interpretation is corroborated by beyond mean field calculations using the Gogny D1S interaction.