ABSTRACT
In the process of dielectronic recombination (dr), radiative capture of an electron by a positive ion occurs via compound resonance states of the electron + ion system (states with two or more electrons excited). These states can decay by autoionisation, with probability A, or by radiative stabilisation, with probability R. in general, these are competing processes: one may have A > R or A < R.
It is assumed that wavefunctions have been obtained for the electron + ion system, allowing for resonances but neglecting interactions with the radiation field. The interactions are then handled using the general formulation of the problem given by Davies and Seaton. A scattering matrix 𝓖 is calculated allowing for radiative channels. It has submatrices 𝓖ee, which describes electron-electron scattering allowing for radiative decays, and 𝓖pe, which describes photon emission following electron capture. Using the unitarity of 𝓖, the total dr rate can be expressed in terms of 𝓖ee.
The first case to be considered is that for which the electron + ion wavefunction can be described in terms of a set of open channels and a set of square integrable functions (‘bound channels’)· Formulae are obtained, of Breit-Wigner type, which are similar to but more general than those given in a number of previous papers.
The main new results are for resonances in Rydberg series converging to excited states of the recombining ion. The energies of the resonances are E n = –½z 2/(n – μ)2 relative to the excited-ion state (z is the ion’s charge, n an integer, μ a quantum defect and atomic units are used) and the resonance separations are δE n = (E n – E n– 1) = z 2/(n – μ)3. The radiative transition occurs in the ion with probability R independent of n. For smaller values of n one has A n ≫ R but A n is proportional to δE n and, as n increases, eventually becomes smaller than R. For very large n the separations δE n become small compared with the radiative width and all resonance structure is wiped out.
Formulae derived from ab initio theory are compared with those deduced previously using intuitive arguments. There are some differences between our formulae and those used by Burgess but little difference in calculated total dr rates for plasma conditions.
