R-matrix approach with proper boundary conditions for dissipative and nondissipative collision processes

We develop an R-matrix approach to treating collision processes which explicitly takes into account, by means of a simple energy-dependent analytic function, the out-of-phase oscillations of the incident and scattered standing waves in the interior region. Thereby we avoid the use of the Bloch operator. In place of the Bloch operator the incident wave provides the source term in an inhomogeneous equation for the scattered wave. We take those subchannels not treated exactly into account via the optical potential, which is generally non-Hermitian due to dissipation at the boundary. The optical potential is constructed on a real analytic basis using a resolvent that satisfies outgoing-wave boundary conditions. The use of an analytic basis together with the direct determination of the K matrix, rather than the R matrix, at the boundary (this is done by matching the interior wave function to the nearly exact analytic solution beyond the boundary) makes the method particularly well suited to the treatment of ultracold collisions. We have tested our method by applying it to one-photon single-ionization of He(1s(2)) accompanied by excitation to He+(2s) or He+(2p) for photon energies above the complete breakup threshold, where the optical potential is non-Hermitian. Excellent agreement with experiment is obtained for the cross sections for photoionization to both He+ (n = 1) and to He+ (n = 2). The 2s-to-2p branching ratio is strongly influenced by both the optical potential and, at photon energies less than a few tens of eV above the breakup threshold, the nonadiabatic dipole mixing of the 2s and 2p states.