Shape and structure of N=Z $^{64}$Ge; Electromagnetic transition rates from the application of the Recoil Distance Method to knock-out reactions.

Transition rate measurements are reported for the $2^+_1$ and $2^+_2$ states in the N=Z nucleus $^{64}$Ge. The measurement was done utilizing the Recoil Distance Method (RDM) and a unique combination of state of the art instruments at the National Superconducting Cyclotron Laboratory (NSCL). States of interest were populated via an intermediate energy single neutron knock-out reaction. RDM studies of knock-out and fragmentation reaction products hold the promise of reaching far from stability and providing lifetime information for intermediate-spin excited states in a wide range of exotic nuclei. The large-scale Shell Model calculations applying the recently developed GXPF1A interaction are in excellent agreement with the above results. Theoretical analysis suggests that $^{64}$Ge is a collective $\gamma$-soft anharmonic vibrator.