Abstract
We propose a method for the approximate computation of the Green function of a scalar massless field phi subjected to potential barriers of given size and shape in space-time. This technique is applied to the case of a 3D Gaussian ellipsoidlike barrier, placed on the axis between two pointlike sources of the field. Instead of the Green function we compute its temporal integral, that gives the static potential energy of the interaction of the two sources. Such interaction takes place in part by tunneling of the quanta of phi across the barrier. We evaluate numerically the correction to the potential in dependence on the barrier size and on the barrier-sources distance. (C) 1999 American Institute of Physics. [S0022-2488(99)04906-3].