Expansions for the scattering wave function and radiative capture inR-matrix theory

We derive several expressions for the scattering wave functions in the frame of $R$-matrix theory. Particular attention is paid to the one-channel situation and to the one-level plus constant background approximation. These results are then applied to the radiative capture process. In particular, we investigate the possible appearance, and the physical interpretation, of asymmetric resonance peaks and of zeros in the capture cross section. The contributions of the external and internal regions are both included. Finally, we show that the resonance parameters of the one-level plus constant background Breit-Wigner approximation are stable against variation of the boundary parameters, the values of which therefore remain largely arbitrary. Correspondingly, the validity of this approximation does not depend critically upon the choice of the boundary parameters.