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
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.
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2011