Anisotropic radiative emission effects on deduced resonant-transfer-excitation cross sections

The radiation emitted by an ion collisionally excited by an electron beam is anisotropic. We discuss two schemes, one for use with LS-coupling cross sections and one for intermediate coupling, whereby theoretical resonant-transfer-excitation cross sections can be modified to take account of this anisotropy when making comparisons with experimental results deduced from observations of radiation at a particular beam angle. We have carried out such calculations for a number of ions initially in an S state, viz. F⁶⁺, Caq+ (q=16--19), and Nbq+ (q=29--31). In all cases, neglecting hyperfine structure, the allowance for anisotropic radiative emission at right angles to the beam axis was found to result in only a small increase (10--15 %) in the cross section over results that assumed isotropy. Allowance for hyperfine structure reduced even this anisotropy by 20% for ¹⁹F⁶⁺ (I=1/2) and by 80% for ⁹³Nb (I=9/2) ions; results for ⁴⁰Ca (I=0) ions remain unchanged.