  The oscillation continuum in laser-induced fluorescence spectra of bound-free
$c^3\Sigma^+ \to a^3\Sigma^+$ and (4)$^1\Sigma^+ \to X^1\Sigma^+$ transitions
of the KCs molecule were recorded by Fourier-transform spectrometer and
modelled under the adiabatic approximation. The required interatomic potentials
for ground $a^3\Sigma^+$ and $X^1\Sigma^+$ states were reconstructed in an
analytical Chebishev-polynomial-expansion form in the framework of the
regularization direct-potential-fit procedure based on the simultaneous
consideration of experimental line positions from [R. Ferber et al, Phys. Rev.
A, \textbf{80}, 062501 (2009)] and the present \emph{ab initio} calculation of
short-range repulsive potential data. It was proved that the repulsive part
over dissociation limit of the derived $a^3\Sigma^+$ potential reproduces the
experiment better than the potentials reported in literature. It is also shown
that all empirical and semi-empirical potentials available for the
$X^1\Sigma^+$ state reproduce the bound-free (4)$^1\Sigma^+ \to X^1\Sigma^+$
spectrum with equal quality in the range of observations.
