Electron-impact excitation of diatomic hydride cations II: OH$^+$ and
  SH$^+$
  R-matrix calculations combined with the adiabatic-nuclei-rotation and
Coulomb-Born approximations are used to compute electron-impact rotational rate
coefficients for two open-shell diatomic cations of astrophysical interest: the
hydoxyl and sulphanyl ions, OH$^+$ and SH$^+$. Hyperfine resolved rate
coefficients are deduced using the infinite-order-sudden approximation. The
propensity rule $\Delta F=\Delta j=\Delta N=\pm 1$ is observed, as is expected
for cations with a large dipole moment. A model for OH$^+$ excitation in the
Orion Bar photon-dominated region (PDR) is presented which nicely reproduces
Herschel observations for an electron fraction $x_e=10^{-4}$ and an OH$^+$
column density of $3\times 10^{13}$~cm$^{-2}$. Electron impact electronic
excitation cross sections and rate coefficients for the ions are also
presented.
