  Problems involving the capture of a moving entity by a trap occur in a
variety of physical situations, the moving entity being an electron, an
excitation, an atom, a molecule, a biological object such as a receptor
cluster, a cell, or even an animal such as a mouse carrying an epidemic.
Theoretical considerations have almost always assumed that the particle motion
is translationally invariant. We study here the case when that assumption is
relaxed, in that the particle is additionally subjected to a harmonic
potential. This tethering to a center modifies the reaction-diffusion
phenomenon. Using a Smoluchowski equation to describe the system, we carry out
a study which is explicit in 1 dimension but can be easily extended for
arbitrary dimensions. Interesting features emerge depending on the relative
location of the trap, the attractive center and the initial placement of the
diffusing particle.
