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Clarification of the relationship between bound and scattering states in quantum mechanics: Application to 12C + alpha

J. -M. Sparenberg
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Abstract

Using phase-equivalent supersymmetric partner potentials, a general result from the inverse problem in quantum scattering theory is illustrated, i.e., that bound-state properties cannot be extracted from the phase shifts of a single partial wave, as a matter of principle. In particular, recent R-matrix analyses of the 12C + alpha system, extracting the asymptotic normalization constant of the 2+ subthreshold state, C12, from the l=2 elastic-scattering phase shifts and bound-state energy, are shown to be unreliable. In contrast, this important constant in nuclear astrophysics can be deduced from the simultaneous analysis of the l=0, 2, 4, 6 partial waves in a simplified potential model. A new supersymmetric inversion potential and existing models give C12=144500+-8500 fm-1/2.

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J. -M. Sparenberg. 2004-03-25. Clarification of the relationship between bound and scattering states in quantum mechanics: Application to 12C + alpha. https://doi.org/10.1103/physrevc.69.034601

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