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We present a statistical approximate solution of the bound, non-hierarchicalthree-body problem, and extend it to a general analysis of encounters betweenhard binary systems and single stars. Any such encounter terminates when one ofthe three stars is ejected to infinity, leaving behind a remnant binary; theproblem of binary-single star-scattering consists of finding the probabilitydistribution of the orbital parameters of the remnant binary, as a function ofthe total energy and the total angular momentum. Here, we model the encounteras a series of close, non-hierarchical, triple approaches, interspersed withhierarchical phases, in which the system consists of an inner binary and a starthat orbits it -- this turns the evolution of the entire encounter to a randomwalk between consecutive hierarchical phases. We use the solution of the bound,non-hierarchical three-body problem to find the walker's transitionprobabilities, which we generalise to situations in which tidal interactionsare important. Besides tides, any dissipative process may be incorporated intothe random walk model, as it is completely general. Our approximate solutioncan reproduce the results of the extensive body of past numerical simulations,and can account for different environments and different dissipative effects.Therefore, this model can effectively replace the need for direct few-bodyintegrations for the study of binary-single encounters in any environment.Furthermore, it allows for a simply inclusion of dissipative forces typicallynot accounted for in full N-body integration schemes.

An Analytical, Statistical Approximate Solution for Dissipative and non-Dissipative Binary-Single Stellar Encounters