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This is possible due to the exponential factor in $\phi^{\rm rec}_{\rm em}$ .

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... continuum

Within a small energy-distance $\xi$ below the ionization potential these in principle can be treated as a continuation of the photoionization cross-section (e.g. see Appendix II in Beigman et al. 1968).

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... spectrum

Here and below we neglect the difference in the electron and photon temperature, which is smaller than $\Delta T/T\sim 10^{-6}{-}10^{-4}$ at most times during recombination.

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