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• W2017103675 abstract "Arbitrarily complicated rearrangement collisions describable by the time-independent nonrelativestic Schrödinger equation are treated in a wholly time-independent framework, without explicit reference to transition probabilities. Introducing a generalized probability current operator for many-particle systems, the current flow at large distances can be computed in complete analogy with one-particle scattering. This procedure leads to the same formal expressions for reaction rates as are obtained from more conventional formulations; it is an immediate consequence of the asymptotic behavior of the Green's function that the matrix elements Ψf(−)∗ViΨi = ψf∗VfΨi(+) yield the scattering amplitude A(i → f), and that Ψf(−) is a solution with incoming scattered waves. Moreover the time-independent formulation avoids perplexities associated with the necessity for computing transition probabilities from projections on sets of nonorthogonal states. In the reaction a + b → c + d + e for instance it turns out automatically, without projecting the solutions on plane wave states, that coincidences are observed in counters placed at large distances τc, τd, τe only when τc, τd, τc are in the ratios of the classical velocities of c, d, e; here c, d, e are a rearranement of the particles contained in a, b.These procedures can be applied either in the laboratory or center-of-mass systems; eliminating the center-of-mass coordinates does not simplify the calculations for three-body breakup ab → cde. Reciprocity relations for two and three-body breakup are examined, and mathematical difficulties of this time-independent formulation are discussed." @default.
• W2017103675 created "2016-06-24" @default.
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• W2017103675 date "1958-09-01" @default.
• W2017103675 modified "2023-09-23" @default.
• W2017103675 title "Time-independent nonrelativistic collision theory" @default.
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• W2017103675 doi "https://doi.org/10.1016/0003-4916(58)90004-6" @default.
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