Theoretical study of electron-impact excitation of H(1s) into the states using a two-dimensionalR-matrix propagator

Abstract

Electron-impact excitation of the ground state of hydrogen into the states is studied by propagating the R-matrix in the two radial dimensions. Integral cross sections and resonance parameters are presented for collision energies from 0.75 Ryd (the n = 2 threshold) up to 0.96 Ryd (the n = 5 threshold). Below the n = 3 threshold, there is very good agreement with results from other methods and with experimental data. Between the n = 3 and n = 4 thresholds, integral cross sections are in better agreement with those of a coupled pseudostate method than with those of the J-matrix method, while resonance parameters are in good agreement with those of a 15-state R-matrix calculation.

AnR-matrix with pseudostates approach to the electron-impact excitation of H I for diagnostic applications in fusion plasmas

“…Apart from Aggarwal et al (1991), these calculations have focused on transitions between the ground state and terms up to the n = 3 shell. An exception is Dunseath et al (1999) who have employed a novel two-dimensional R-matrix propagator technique to study resonance widths in a small energy band below 0.96 Ryd. However, in general, excitation data involving the n = 3, 4, 5 and 6 shells are sparse in energy or incomplete in transitions.…”

Shape resonances in electron-hydrogen scattering

“…In our previous work (Dunseath et al 1999), by fitting the eigenphase sum we found the 1 P o shape resonance at 0.751 34 Ryd with a width of 1.55 × 10 −3 Ryd. By fitting the lifetime, we now find the resonance at 0.751 22 Ryd, lying between the two experimental values, with a width of 1.41×10 −3 Ryd, which is slightly narrower than that deduced from the measurements.…”

“…Details of our method of propagating the R-matrix in two dimensions together with the parameters used in the calculation have been given in a previous paper (Dunseath et al 1999). Briefly, the R-matrix (the inverse of the logarithmic derivative matrix) is propagated in two dimensions in steps of 10 a 0 out to a distance of 100 a 0 , beyond which a one-dimensional propagation method (Light and Walker 1976) is used to obtain the R-matrix at some large distance r asy .…”

“…As we have already noted, this is the case just above threshold: the rapidly decreasing phase can greatly distort or even destroy any resonance structure, rendering it extremely difficult to ascertain whether a resonance is actually there or not. In the case of the 1 P o shape resonance just above the n = 2 threshold, a satisfactory fit can be made by adding a term proportional to (E − E th ) −1 (where E th is the threshold energy) to the background phase (Callaway 1982, Dunseath et al 1999. Above higher thresholds, however, this still does not allow a reliable fit to be made.…”

“…In a recent paper (Dunseath et al 1999) we used the method of R-matrix propagation in two dimensions (Dunseath et al 1996) to study electron-hydrogen scattering at collision energies up to 0.96 Ryd (the n = 5 threshold). In particular, we presented an extensive set of energies and widths for the series of Feshbach resonances converging to the n = 3, 4 and 5 thresholds.…”