Search for a Zero-Phonon Gamma-Ray Transition inPd108andBa134

The nuclear quadrupole vibrational model allows one-phonon transitions but forbids both two-phonon and zero-phonon transitions. Whereas there exists a large amount of experimental information on the degree of forbiddenness of two-phonon transitions, there is little meaningful information on zero-phonon transitions. We have looked for the zero-phonon transition between the first $4^{+}$ state and the second $2^{+}$ state (between members of the two-phonon triplet) in the vibrational-type nuclei ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$ and ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$. We were not able to detect the zero-phonon $\gamma$ rays. The limits set on the intensities of these transitions lead to notable degrees of forbiddenness. For ${}_{}{}^{108}{}_{}{}^{}\mathrm{Pd}$ and ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}$, respectively the ratio $\frac{{B\left(E2\mathrm{}\right)\mathrm{}}_{4\to 2}}{{B\left(E2\mathrm{}\right)\mathrm{}}_{4\to 2^{\prime }}}$ is greater than 80 and 360 (limits based on two standard deviations). For these nuclei the forbiddenness of a zero-phonon transition is at least as large as the forbiddenness of a two-phonon transition.