Derivations of universal exact complex absorption potentials by the generalized complex coordinate method

On the basis of the Moiseyev–Hirschfelder generalization of the complex coordinate method, a universal energy-independent complex absorbing potential (CAP), is derived. It is proven that the universal CAP consists of flux and diffusion-type operators. When a smooth exterior scaling is used, the CAP gets non-zero values in the region where the interaction potential vanishes. An illustrative numerical example is given where narrow and broad, isolated and overlapping resonances were all calculated with more than nine digits of accuracy.