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Complex scaled spectrum completeness for coupled channels

Abstract : The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case of inelastic scattering with many channels, the existence of such a resolution under complex scaling is still debated. Taking advantage of results obtained earlier for the two channel case, this paper proposes a representation in which the convergence of a resolution of the identity can be more easily tested. The representation is valid for any finite number of coupled channels for inelastic scattering without rearrangement.
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B.G. Giraud, K. Kato, A. Ohnishi. Complex scaled spectrum completeness for coupled channels. Journal of Physics A: Mathematical and General (1975 - 2006), IOP Publishing, 2005, 37, pp.48-60. ⟨10.1088/0305-4470/37/48/004⟩. ⟨cea-02889418⟩

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