Neutron and gamma width correlations in neutron capture reactions: A comparative study

Three different procedures are generally adopted in the analysis of correlation observed between neutron and $\gamma$ widths in neutron capture experiments. We present a quantitative comparison of the three methods, the valence model, optical model, and shell model with an "exact" calculation including core excitation effects. The ${}_{}{}^{28}{}_{}{}^{}\mathrm{Sn}(n, \gamma )$ reaction is taken as an example which demonstrates that the approximation used for the single particle amplitudes and the omission of core excitation effects are possible sources of error in conventional calculations. Among the conventional procedures we conclude that because of possible external region contributions and its lack of sensitivity to the potential used, the optical model formulation of Lane and Mughabgab represent the most useful alternative.