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A renormalisation-group treatment of two-body scattering

Michael C. Birse·Judith A. McGovern·Keith G. Richardson
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Abstract

A Wilsonian renormalisation group is used to study nonrelativistic two-body scattering by a short-ranged potential. We identify two fixed points: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the linearised renormalisation group are used to assign a systematic power-counting to terms in the potential near each of these fixed points. The expansion around the nontrivial fixed point is shown to be equivalent to the effective-range expansion.

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Michael C. Birse, Judith A. McGovern, Keith G. Richardson. 1999-11-15. A renormalisation-group treatment of two-body scattering. https://doi.org/10.1063/1.1303016

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