  The coherent propagation of elastic waves in a solid filled with a random
distribution of pinned dislocation segments is studied to all orders in
perturbation theory. It is shown that, within the independent scattering
approximation, the perturbation series that generates the mass operator is a
geometric series that can thus be formally summed. A divergent quantity is
shown to be renormalizable to zero at low frequencies. At higher frequencies
said quantity can be expressed in terms of a cut-off with dimensions of length,
related to the dislocation length, and physical quantities can be computed in
terms of two parameters, to be determined by experiment. The approach used in
this problem is compared and contrasted with the scattering of de Broglie waves
by delta-function potentials as described by the Schr\"odinger equation.
