A Variational Approach to Nuclear Reactions

The formalism of Wigner and Eisenbud for nuclear reactions is carried out by means of a variation principle. A variation principle of the Hulthén type is derived for the $R$ matrix and applied to trial wave functions written in terms of the resonance functions, $X_{\lambda }$, of the Wigner-Eisenbud formalism. As a result, a finite level formula for the $R$ matrix is directly obtained.