  Using variational mean-field theory, many-body dissipative effects on the
threshold law for quantum sticking and reflection of neutral and charged
particles are examined. For the case of an ohmic bosonic bath, we study the
effects of the infrared divergence on the probability of sticking and obtain a
non-perturbative expression for the sticking rate. We find that for weak
dissipative coupling $\alpha$, the low energy threshold laws for quantum
sticking are modified by an infrared singularity in the bath. The sticking
probability for a neutral particle with incident energy $E\to 0$ behaves
asymptotically as ${\it s}\sim E^{(1+\alpha)/2(1-\alpha)}$; for a charged
particle, we obtain ${\it s}\sim E^{\alpha/2(1-\alpha)}$. Thus, "quantum
mirrors" --surfaces that become perfectly reflective to particles with incident
energies asymptotically approaching zero-- can also exist for charged
particles.
