Statistics of a random coil chain in the presence of a point (two-dimensional case) or line (three-dimensional case) obstacle

Exact expressions are given for the distribution function of the end-to-end vector of a random coil chain under the restriction that the chain makes a definite number of turns around a fixed point (two-dimensional case) or a fixed straight line (three-dimensional case). The ring-closure probability and the mean square end-to-end distance are also calculated. The final results are given in graphs.