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Nonlocal potentials and complex angular momentum theory. (English) Zbl 1218.81099

When two composite particles collide, the fermionic character of the components emerges and the antisymmetrization of the system generates repulsive exchange-forces followed by echoes due to Pauli’s exclusion principle. The notion of echo was introduced in parallel with the notion of resonance by K. W. McVoy [Ann. Phys. 43, 91–125 (1965)]. Despite of this parallel, the status of the echoes has remained obscure in terms of the analytic properties in energy of the scattering functions while the pole-resonance conceptual correspondence was successfully achieved by various authors, e.g., V. de Alfaro and T. Regge [Potential scattering. Amsterdam: North-Holland Publishing Comp. (1965; Zbl 0141.23202)].
In this paper, the authors study singularities of the partial scattering amplitude \(T\) for appropriate classes of nonlocal potentials, both in the complex momentum \(k\)-plane and in the complex angular momentum \(\lambda\)-plane. Their results extend Regge’s formalism to the case of nonlocal potentials and provide a framework for analyzing both resonances and echoes in terms of the polar singularities of \(T\) in the upper or lower half plane of \(\lambda\).

MSC:

81U05 \(2\)-body potential quantum scattering theory
35B34 Resonance in context of PDEs

Citations:

Zbl 0141.23202
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References:

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