Calculation of screened Coulomb potential matrices and its application to He bound and resonant states

Abstract

We present two analytical methods, Taylor expansion and Gegenbauer expansion, to efficiently and accurately calculate the two-electron screened Coulomb potential matrix elements with Slater-type configuration-interaction basis functions. The former permits great advantages in fast computation of the potential matrices at small screening parameters and the latter allows accurate calculation of the matrices at all screening parameters. The bound and resonant states of a He atom embedded in the screening environment are calculated by employing the variational and complex-scaling methods, respectively, and the results are compared with other theoretical predictions. The expectation values of some physical quantities for He ground state are compared with the recent calculation of Ancarani and Rodriguez [Phys. Rev. A 89, 012507 (2014)] and extended to stronger screening environment. The energies and widths for the doubly excited resonant states are in good agreement with previous calculations, while the interelectronic angle $arccos\ensuremath{\langle}cos({\ensuremath{\theta}}_{12})\ensuremath{\rangle}$ show significant discrepancies with the Feshbach projection calculation of Ord\'o\~nez-Lasso et al. [Phys. Rev. A 88, 012702 (2013)]. The expectation values of $\ensuremath{\langle}{\mathbf{p}}_{\mathbf{1}}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{p}}_{\mathbf{2}}\ensuremath{\rangle}$ are also calculated for the resonant states investigated here. We conclude that the present methods in the framework of complex scaling enable us to get reliable energy, width, and other physical quantities of the resonant states in a variety of screening conditions.