We have studied the decay pattern of the $J^{\pi }=1_{4742\mathrm{keV}}^{-}$ state of ${}^{88}\mathrm{Sr}$ to probe its quadrupole-octupole coupled two-phonon structure. In particular, a unique fingerprint to prove the two-phonon nature is the $E2$ decay strength of the $1_{4742\mathrm{keV}}^{-}\to 3_1^{-}$ transition into the one-octupole-phonon state. $\gamma$-ray spectroscopy was performed after the $\beta$ decay of ${}^{88}\mathrm{Rb}$ to obtain the necessary sensitivity for this weak-intensity decay branch. Sufficient amounts of ${}^{88}\mathrm{Rb}$ $(T_{1/2}=17.8 \min )$ were produced by neutron activation of natural Rb in the TRIGA Mark II reactor. The results show that the $B\left(E2\right)$ value of the $1_{4742\mathrm{keV}}^{-}\to 3_1^{-}$ transition is equal to the $B\left(E2\right)$ of the $2_1^{+}\to 0_1^{+}$ transition, directly demonstrating the quadrupole-octupole coupled two-phonon nature of the $1^{-}$ state. A comparison of the results with energy-density functional plus quasiparticle-phonon model calculations shows remarkable agreement, corroborating this assignment.

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• Nuclear structure & decays
• 59 ≤ A ≤ 89
• Nuclear data analysis & compilation