  Carbon abundances in late-type stars are important in a variety of
astrophysical contexts. However C i lines, one of the main abundance
diagnostics, are sensitive to departures from local thermodynamic equilibrium
(LTE). We present a model atom for non-LTE analyses of C i lines, that uses a
new, physically-motivated recipe for the rates of neutral hydrogen impact
excitation. We analyse C i lines in the solar spectrum, employing a
three-dimensional (3D) hydrodynamic model solar atmosphere and 3D non-LTE
radiative transfer. We find negative non-LTE abundance corrections for C i
lines in the solar photosphere, in accordance with previous studies, reaching
up to around 0.1 dex in the disk-integrated flux. We also present the first
fully consistent 3D non-LTE solar carbon abundance determination: we infer log
$\epsilon_{\text{C}}$ = $8.44\pm0.02$, in good agreement with the current
standard value. Our models reproduce the observed solar centre-to-limb
variations of various C i lines, without any adjustments to the rates of
neutral hydrogen impact excitation, suggesting that the proposed recipe may be
a solution to the long-standing problem of how to reliably model inelastic
collisions with neutral hydrogen in late-type stellar atmospheres.
