Analytic solution of the Coulomb–Volkov problem

Derive an analytic solution to the Coulomb–Volkov problem for scattering states that simultaneously account for the Coulomb interaction and the external-field-driven Volkov dynamics.

Background

The proposed surface-flux framework requires analytically tractable fragment or scattering wavefunctions in the exterior domain. Volkov waves provide such an approximation when long-range Coulomb interactions are neglected, but including the Coulomb interaction leads to the Coulomb–Volkov problem. The paper notes that no analytic solution is currently known. Approximate treatments, such as the eikonal Volkov approximation, are available but may be unsuitable for numerical surface-flux calculations because they are only approximately orthogonal. Finding exact Coulomb–Volkov waves numerically would require solving an auxiliary single-ionization problem for every momentum of interest and would undermine the computational efficiency of the tSURFF approach, particularly as the number of ionized electrons increases.