Coupling of collective quadrupole and monopole pairing vibrations in the Ge nuclei

The coupling of the solutions to the random phase approximation pairing vibration and the collective quadrupole oscillation, obtained from a boson expansion approach, is used to describe simultaneously many properties of the even-even isotopes of Ge. Low lying energies, $E0\mathrm{}$ and $E2\mathrm{}$ transitions, two nucleon transfer amplitudes, and quadrupole moments are calculated and fairly good agreement is obtained compared to experiment. In particular the behavior of the ${\mathrm{O}}_2^{+}$ state energy as a function of mass is accurately described including the prediction of its being the lowest energy excited state of ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$. The shape of the nucleus is concluded to be in a transitional region between prolate and oblate.