  During reionization, intergalactic ionization fronts (I-fronts) are sources
of Ly$\alpha$ line radiation produced by collisional excitation of hydrogen
atoms within the fronts. In principle, detecting this emission could provide
direct evidence for a reionizing intergalactic medium (IGM). In this paper, we
use a suite of high-resolution one-dimensional radiative transfer simulations
run on cosmological density fields to quantify the parameter space of I-front
Ly$\alpha$ emission. We find that the Ly$\alpha$ production efficiency -- the
ratio of emitted Ly$\alpha$ flux to incident ionizing flux driving the front --
depends mainly on the I-front speed and the spectral index of the ionizing
radiation. IGM density fluctuations on scales smaller than the typical I-front
width produce scatter in the efficiency, but they do not significantly boost
its mean value. The Ly$\alpha$ flux emitted by an I-front is largest if 3
conditions are met simultaneously: (1) the incident ionizing flux is large; (2)
the incident spectrum is hard, consisting of more energetic photons; (3) the
I-front is traveling through a cosmological over-density, which causes it to
propagate more slowly. We present a convenient parameterization of the
efficiency in terms of I-front speed and incident spectral index. We make these
results publicly available as an interpolation table and we provide a simple
fitting function for a representative ionizing background spectrum. Our results
can be applied as a sub-grid model for I-front Ly$\alpha$ emissions in
reionization simulations with spatial and/or temporal resolutions too coarse to
resolve I-front structure. In a companion paper, we use our results to explore
the possibility of directly imaging Ly$\alpha$ emission around neutral islands
during the last phases of reionization.
