Alan Burgess

Coulomb integrals: tables and sum rules

The tables of free-free integrals for attractive Coulomb fields, given by Burgess (see abstr. A55239 of 1970) have been corrected and extended. The source of inaccuracy is discussed, and a sum rule is derived which is of interest in connection with partial collision strengths, oscillator strengths and Gaunt factors.

High-energy Born collision strengths for optically forbidden transitions

Collision strengths for optically forbidden transitions in positive ions excited by electron impact tend to finite limits as the energy of the colliding electron becomes infinitely great. This statement applies to theoretical data obtained by means of approximations which ignore relativistic effects. The high-energy limiting values are given by the Born approximation, which Bethe showed can be reduced to a closed expression requiring integration over momentum transfer and the radial distance of the atomic orbital. In the appendix we describe an accurate numerical procedure for evaluating this double integral and also show how to perform the Racah algebra which arises when mixed configurations are used to describe the target. We make applications to several isoelectronic sequences taking configuration interaction into account.

Dielectronic recombination to form helium-like ions

The discrepancy between the results of Shore for helium-like ions, and the general formula for dielectronic recombination given by Burgess, is shown to be due to errors in the former. Further results on these ions are given.

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 → ∞, and hence, rate coefficients which have the correct high temperature behaviour (~C/T1/2 with the correct value of C). We provide a computer program for calculating these. An error in Fauchers derivation of the Born formula is also discussed.