Radoslaw Szmytkowski and Jürgen Hinze 1996 J. Phys. A: Math. Gen. 29 6125 doi:10.1088/0305-4470/29/18/037
Kapur - Peierls and Wigner R-matrix theories for the Dirac equation
Radoslaw Szmytkowski
and Jürgen Hinze
An R-matrix theory for the Dirac equation is shown to exist in spite of incompleteness of a relativistic R-matrix basis on the reaction surface, a phenomenon which does not occur in the non-relativistic case. The theory is constructed for the most general boundary conditions imposed on expansion basis functions. It is shown that the incompleteness of the expansion basis on the reaction surface results in a matrix correction appearing in the eigenfunction expansion of the R-matrix. The correction vanishes in the non-relativistic limit. The approach is applied to the relativistic generalizations of the Kapur - Peierls and Wigner resonance reaction theories.
- PACS
-
03.65.Pm Relativistic wave equations
03.65.Ta Foundations of quantum mechanics; measurement theory
- MSC
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81Uxx Scattering theory (See also 34A55, 34L25, 34L40, 35P25, 47A40)
- Subjects
- Dates
-
Issue 18 (21 September 1996)
Received 20 March 1996
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Kapur - Peierls and Wigner R-matrix theories for the Dirac equation
Radoslaw Szmytkowski and Jürgen Hinze 1996 J. Phys. A: Math. Gen. 29 6125
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