Probability of a stellar encounter in a spherical cluster in the case where the velocity distribution function of the field stars is symmetric relative to the direction toward the cluster center

A pair encounter scheme is considered in coordinates tied to the direction toward the cluster center. It is assumed that the cluster is characterized by an anisotropic distribution of star velocities. Expressions for the encounter probability are obtained for specified energy changes and specified velocity directions relative to the initial direction of motion and to the cluster center direction.