Augmented random phase approximation

An infinite set of ladder diagrams are summed to yield an augmented random phase approximation (ARPA) to the Bethe−Salpeter amplitude equation. The final equation is of the easily solved form of the RPA amplitude eigenvalue equation but with a more complete (augmented) vertex which is the product of a matrix and an inverse matrix. The diagonal ARPA vertex is obtained by taking only the diagonal terms of the inverse matrix, making inversion necessary. The diagonal ARPA should include the most important hole−hole and particle−particle terms which are left out of the RPA. The final ARPA equation is derived two ways, by direct diagram summation and from the integral equation for the ladder vertex.