  A study is reported of the quantum scattering resonances of dissociating
molecules using a semiclassical approach based on periodic-orbit theory. The
dynamics takes place on a potential energy surface with an energy barrier
separating two channels of dissociation. Above the barrier, the unstable
symmetric-stretch periodic orbit may undergo a supercritical pitchfork
bifurcation, leading to a classically chaotic regime. Signatures of the
bifurcation appear in the spectrum of resonances, which have a shorter lifetime
than classically expected. A method is proposed to evaluate semiclassically the
energy and lifetime of the quantum resonances in this intermediate regime.
