  A continuum model for low-energy physisorption on a membrane under tension is
proposed and studied with variational mean-field theory. A discontinuous change
in the energy-dependent sticking coefficient is predicted under certain
conditions. This singularity is a result of the bosonic orthogonality
catastrophe of the vibrational states of the membrane. The energy-dependent
sticking coefficient is predicted to have exponential scaling in 1/E above the
singularity. The application of this model to the quantum sticking of cold
hydrogen to suspended graphene is discussed. The model predicts that a beam of
atomic hydrogen can be completely reflected by suspended graphene at ultralow
energies.
