Radoslaw Szmytkowski and Jürgen Hinze 1996 J. Phys. B: At. Mol. Opt. Phys. 29 761 doi:10.1088/0953-4075/29/4/018
Radoslaw Szmytkowski and Jürgen Hinze
Show affiliationsThe convergence of the non-relativistic and relativistic fixed-boundary-condition R-matrix expansions at the reaction volume boundary is discussed. It is shown that in the non-relativistic case the expansion of the wavefunction converges to this function at the boundary. In the relativistic case, however, the expansion does not generally converge to the wavefunction at the reaction surface because the set of relativistic basis functions spanning the interior of the reaction volume is incomplete on the surface. With one exception, this fact has not been recognized before and has been a source of errors in previous presentations of the relativistic R-matrix method. We present a corrected derivation of the R-matrix theory for the Dirac equation and generalize it to the multi-channel case. We also explain why, in spite of being based on an incorrect theory, the results of electron - atom and electron - ion scattering calculations performed so far within the framework of the relativistic R-matrix method were not afflicted by these errors.
31.30.J- Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
82.20.-w Chemical kinetics and dynamics
34.80.-i Electron and positron scattering
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces
Issue 4 (28 February 1996)
Received 14 August 1995, in final form 23 November 1995
An Erratum for this article has been published in 1996 J. Phys. B: At. Mol. Opt. Phys. 29 3800
Radoslaw Szmytkowski and Jürgen Hinze 1996 J. Phys. B: At. Mol. Opt. Phys. 29 761
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