  We study a reaction-diffusion process that involves two species of atoms,
immobile and diffusing. We assume that initially only immobile atoms, uniformly
distributed throughout the entire space, are present. Diffusing atoms are
injected at the origin by a source which is turned on at time t=0. When a
diffusing atom collides with an immobile atom, the two atoms form an immobile
stable molecule. The region occupied by molecules is asymptotically spherical
with radius growing as t^{1/d} in d>=2 dimensions. We investigate the survival
probability that a diffusing atom has not become a part of a molecule during
the time interval t after its injection and the probability density of such a
particle. We show that asymptotically the survival probability (i) saturates in
one dimension, (ii) vanishes algebraically with time in two dimensions (with
exponent being a function of the dimensionless flux and determined as a zero of
a confluent hypergeometric function), and (iii) exhibits a stretched
exponential decay in three dimensions.
