Calculation of doubly excited states of helium with a finite discrete spectrum

Doubly excited states in helium are calculated with many-body perturbation theory to all orders in the electron-electron interaction. A finite and numerical basis set, rotated out into the complex plane, is used. Results, for energies and widths, are presented for states with electrons in the n=2 and n=3 states. The possiblity of an accuracy of a few parts in ${10}^6$ is demonstrated. The method is equally applicable to the study of doubly excited states of many-electron systems and the extension to the corresponding relativistic procedure is straightforward.