  Quantitative understanding of the interstellar medium requires knowledge of
its physical conditions. Low frequency carbon radio recombination lines (CRRLs)
trace cold interstellar gas, and can be used to determine its physical
conditions (e.g., electron temperature and density). In this work we present
spatially resolved observations of the low frequency ($\leq390$ MHz) CRRLs
centered around C$268\alpha$, C$357\alpha$, C$494\alpha$ and C$539\alpha$
towards Cassiopeia A on scales of $\leq1.2$ pc. We compare the spatial
distribution of CRRLs with other ISM tracers. This comparison reveals a spatial
offset between the peak of the CRRLs and other tracers, which is very
characteristic for photodissociation regions and that we take as evidence for
CRRLs being preferentially detected from the surfaces of molecular clouds.
Using the CRRLs we constrain the gas electron temperature and density. These
constraints on the gas conditions suggest variations of less than a factor of
two in pressure over $\sim1$ pc scales, and an average hydrogen density of
$200$-$470$ cm$^{-3}$. From the electron temperature and density maps we also
constrain the ionized carbon emission measure, column density and path length.
Based on these, the hydrogen column density is larger than $10^{22}$ cm$^{-2}$,
with a peak of $\sim4\times10^{22}$ cm$^{-2}$ towards the South of Cassiopeia
A. Towards the southern peak the line of sight length is $\sim40$ pc over a
$\sim2$ pc wide structure, which implies that the gas is a thin surface layer
on a large (molecular) cloud that is only partially intersected by Cassiopeia
A. These observations highlight the utility of CRRLs as tracers of low density
extended HI and CO-dark gas halo's around molecular clouds.
