Multipole wavefunctions for photoelectrons in crystals. IV. The irregular functions and the matching to an impurity

Extension of the method of partial waves to scattering by an impurity center in a crystal requires the construction of energy eigenfunctions of the unperturbed crystal that are irregular at the center. These irregular solutions of a nonseparable problem are constructed by utilizing the expansion of the Green's function into the regular solutions symmetry-adapted about the impurity center, which have been obtained earlier. The wavefunction within an impurity can thus be continued throughout the surrounding crystal by matching it at the impurity boundary to a superposition of regular and irregular solutions. This procedure is compared to the current EXAFS treatment of photoabsorption