Direct demonstration of the two-phonon structure of the $J^{\ddot{I}}€=1_{4742\mathrm{keV}}^{-}$ state of ${}^{88}$Sr

Abstract

We have studied the decay pattern of the $J^{\ddot{I}}€=1_{4742\mathrm{keV}}^{-}$ state of ${}^{88}$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. ${\hat{I}}^3$-ray spectroscopy was performed after the ${\hat{I}}^2$-decay of ${}^{88}$Rb to obtain the necessary sensitivity for this weak-intensity decay branch. Sufficient amounts of ${}^{88}$Rb (T${}_{1/2}$ = 17.8 min) were produced by neutron activation of natural Rb in the TR IGA Mark II reactor. The results show that the $B(E2)$ value of the $1_{4742\mathrm{keV}}^{-}\to 3_1^{-}$ transition is equal to the $B(E2)$ 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 rema rkable agreement, corroborating this assignment.