Eur. Phys. J. D 63, 369-373 (2011)
https://doi.org/10.1140/epjd/e2011-20174-4

Regular Article

Spectral singularities and zero energy bound states

¹ National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch, 7602 Matieland, South Africa
² Department de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
³ Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

^a e-mail: dieter@physics.sun.ac.za

Received: 23 March 2011
Published online: 23 June 2011

Abstract

Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled.