On proton excitation of forbidden lines in positive ions

The semi-classical impact parameter approximations used by Bahcall and Wolf and by Bely and Faucher, for proton excitation of electric quadrupole transitions in positive ions, both fail at high energies, giving cross sections which do not fall off correctly as constant/E. This is in contrast with the pioneering example of Seaton for Fe+13 and of Reid and Schwarz for S+3, both of whom achieve the correct functional form, but do not ensure the correct constant of proportionality. By combining the Born and semi-classical approximations one can obtain cross sections which have the full correct behaviour as E ->infinity , and hence, rate coefficients which have the correct high temperature behaviour (similar to C/T (1/2) with the correct value of C). We provide a computer program for calculating these. An error in Faucher's derivation of the Born formula is also discussed.