CN excitation and electron densities in diffuse molecular clouds
  Utilising previous work by the authors on the spin-coupled rotational
cross-sections for electron-CN collisions, data for the associated rate
coefficients is presented. Data on rotational, fine-structure and
hyperfine-structure transition involving rotational levels up to $N$=20 are
computed for temperatures in the range 10 -- 1000~K. Rates are calculated by
combining Born-corrected R-matrix calculations with the infinite-order-sudden
(IOS) approximation. The dominant hyperfine transitions are those with $\Delta
N=\Delta j= \Delta F=1$. For dipole-allowed transitions, electron-impact rates
are shown to exceed those for excitation of CN by para-H$_2$($j=0$) by five
orders of magnitude. The role of electron collisions in the excitation of CN in
diffuse clouds, where local excitation competes with the cosmic microwave
background (CMB) photons, is considered. Radiative transfer calculations are
performed and the results compared to observations. These comparisons suggest
that electron density lies in the range $n(e)\sim 0.01-0.06$~cm$^{-3}$ for
typical physical conditions present in diffuse clouds.
