Near-threshold quantization and scattering lengths

Harald Friedrich and Patrick Raab
Phys. Rev. A 77, 012703 – Published 7 January 2008

Abstract

We formulate the quantization rule nthn=F(En) for bound-state energies En in a deep potential well with a long-range attractive tail for an extended range of near-threshold energies. This makes it possible to accurately read off the scattering length a from the energy of a high-lying (not necessarily the highest-lying) bound state via a=a¯+btan[πF(En)]. For a potential tail proportional to 1rα, α>3, the constants a¯ and b are known and an explicit and universally valid expression for the function F(E) is given analytically.

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  • Received 10 July 2007

DOI:https://doi.org/10.1103/PhysRevA.77.012703

©2008 American Physical Society

Authors & Affiliations

Harald Friedrich and Patrick Raab

  • Physik Department, Technische Universität München, 85747 Garching, Germany

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Vol. 77, Iss. 1 — January 2008

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