New results in the external Milne problem in cylindrical symmetry. Part 1. One-group approximation

The asymptotic flux and the extrapolation distance are calculated in the one-group cylindrical Milne problem (''black'' cylinder of radius R immersed in an infinite homogeneous medium characterized by C<1). The methods are based both on the reseults of Case's elementary solutions approach in a plane geometry and on the classical perturbational and variational procedures. For large and small R the extrapolation distance is given in the form of asymptotic expansions. For intermediate values of R a version of the variational method is developed. For two examples (c=0.95 and c=0.90) numerical results are presented. The convergence of the methods and the comparison in the regions where both may be applied indicate that sufficient accuracy is achieved. (author)