## 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

Zbl 0141.23202
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