Numerical approach of some three-body problems

On taking the two-proton decay in nuclear physics as a sample case we formulate a numerical method for three-body problems which are mathematically described by systems of coupled 2d Schrödinger equations in polar coordinates r,ϕ. With some minimal adaptations the method becomes applicable on other cases. The specific feature of the procedure consists in a shuttle propagation along r: two quantities are propagated, the log-derivative matrix and the solution itself, with a backwards propagation of the former, followed by a forwards propagation of the latter. The results show remarkable stability. Numerical illustrations from a simple test model are reported and we also explain how the data obtained in this way can be exploited to obtain useful physical information.