Numerical approach of some three-body problems

Abstract 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 Schrodinger 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.

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