Exotic atoms in two dimensions

We study the behavior of energy levels in two dimensions for exotic atoms, i.e., when a long-range attractive potential is supplemented by a short-range interaction, and compare the results with these of the one- and three-dimensional cases. The energy shifts are well reproduced by a scattering leng...

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Bibliographic Details
Published inarXiv.org
Main Authors Combescure Monique, Fayard, Claude, Khare Avinash, Jean-Marc, Richard
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.05.2011
Subjects
Energy levels
Scattering
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Summary:We study the behavior of energy levels in two dimensions for exotic atoms, i.e., when a long-range attractive potential is supplemented by a short-range interaction, and compare the results with these of the one- and three-dimensional cases. The energy shifts are well reproduced by a scattering length formula \( \delta{E}= A_0^2/\ln (a/R)\), where \(a\) is the scattering length in the short-range potential, \(A_0^2/(2\,\pi)\) the square of the wave function at the origin in the external potential, and \(R\) is related to the derivative with respect to the energy of the solution that is regular at large distances.
ISSN:2331-8422