Second-order processes in physics is a research topic focusing attention from several fields worldwide including, for example, non-linear quantum electrodynamics with high-power lasers, neutrinoless double-$beta$ decay, and stimulated atomic two-photon transitions. For the electromagnetic nuclear interaction, the observation of the competitive double-$gamma$ decay from $^{137mathrm{m}}$Ba has opened up the nuclear structure field for detailed investigation of second-order processes through the manifestation of off-diagonal nuclear polarizability. Here we confirm this observation with an $8.7sigma$ significance, and an improved value on the double-photon versus single-photon branching ratio as $2.62times10^{-6}(30)$. Our results, however, contradict the conclusions from the original experiment, where the decay was interpreted to be dominated by a quadrupole-quadrupole component. Here, we find a substantial enhancement in the energy distribution consistent with a dominating octupole-dipole character and a rather small quadrupole-quadrupole element in the decay, hindered due to an evolution of the internal nuclear structure. The implied strongly hindered double-photon branching in $^{137mathrm{m}}$Ba opens up the possibility of the double-photon branching as a feasible tool for nuclear-structure studies on off-diagonal polarizability in nuclei where this hindrance is not present.
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