Coupled-State Calculations of Proton-Hydrogen Scattering in the Sturmian Representation

Proton-hydrogen scattering has been solved in the Sturmian representation. The Sturmian functions of Rotenberg form an infinite, discrete, and complete basis set without a continuum. Comparison has been made with the following proton-hydrogen scattering experiments: transfer and excitation cross sections to the $2s$ and $2p$ states, the total exchange cross section, and the notable experiments of Helbig and Everhart on the total transfer probability at 3°. Particularly excellent agreement is found with the last. This work is a direct extension of previous calculations for the proton-hydrogen scattering problem developed by the authors in which the expansion basis functions were discrete, traveling hydrogenic states. The present work demonstrates the role of the hydrogenic continuum.