  We devise a theory of adsorption of low-energy atoms on suspended graphene
membranes maintained at 10 K based on a model of atom-acoustic phonon
interactions. Our primary technique includes a non-perturbative method which
treats the dynamics of the multiple phonons in an exact manner within the
purview of the Independent Boson Model. We present a study on the effects of
the phonons assisting the renormalization as well as decay of the incident atom
propagator and discuss results for the many-body adsorption rates for atomic
hydrogen on graphene micromembranes. Additionally, we report similarities of
this model with other branches of quantum field theories that include
long-range interactions like quantum electrodynamics (QED) and perturbative
gravity.
