  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
$^{137\mathrm{m}}$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
$8.7\sigma$ significance, and an improved value on the double-photon versus
single-photon branching ratio as $2.62\times10^{-6}(30)$. 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
$^{137\mathrm{m}}$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.
