  We derive the expansion of the irregular physical solution over the spherical
solutions at negative energies, which is necessary for obtaining the $S$ matrix
of the process. The relation of this expansion to the theory developed by
Giannakees et al., Phys. Rev. A 94, 013419 (2016), is analyzed. In particular,
we show that the expansion of the irregular solution missing in Giannakees et
al.'s theory can be derived from one of their main postulates. The expansion
thus obtained turns out to be numerically equivalent to our expansion up to
high angular momenta. Analytical expressions for the key matrix of both
expansions are derived.
