  Several classic problems for particles diffusing outside an arbitrary
configuration of non-overlapping partially reactive spherical traps in three
dimensions are revisited. For this purpose, we describe the generalized method
of separation of variables for solving boundary value problems of the
associated modified Helmholtz equation. In particular, we derive a
semi-analytical solution for the Green function that is the key ingredient to
determine various diffusion-reaction characteristics such as the survival
probability, the first-passage time distribution, and the reaction rate. We
also present modifications of the method to determine numerically or
asymptotically the eigenvalues and eigenfunctions of the Laplace operator and
of the Dirichlet-to-Neumann operator in such perforated domains. Some potential
applications in chemical physics and biophysics are discussed, including
diffusion-controlled reactions for mortal particles.
