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- W2081566936 abstract "The zero-energy scattering in a particular partial wave by a potential V=${mathit{V}}_{mathit{s}}$+${mathit{V}}_{mathit{c}}$ that is a superposition of short range and attractive Coulomb components is characterized by the additional phase shift ${mathrm{ensuremath{delta}}}_{mathit{s}}$(0), due to ${mathit{V}}_{mathit{s}}$. It has been known for many years that ${mathrm{ensuremath{delta}}}_{mathit{s}}$(0)(modensuremath{pi})=ensuremath{mu}(ensuremath{infty})ensuremath{pi}, where ensuremath{mu}(n) is the quantum defect of the nth energy level. In analogy with Levinson's theorem for short-range potentials, one might expect that a more precise statement, based on an absolute definition of the phase shift, would be ${mathrm{ensuremath{delta}}}_{mathit{s}}$(0)=ensuremath{mu}(ensuremath{infty})ensuremath{pi}, with the value of the largest integer contained in ensuremath{mu}(ensuremath{infty}) representing the number of additional bound states due to ${mathit{V}}_{mathit{s}}$. A simple derivation of this relation is presented here, based on variational principles for the binding energies and phase shifts, and on the property (fundamental to quantum-defect theory) that appropriately normalized bound-state wave functions for nensuremath{rightarrow}ensuremath{infty} merge smoothly into the energy-normalized regular continuum solutions at the continuum threshold." @default.
- W2081566936 created "2016-06-24" @default.
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- W2081566936 date "1995-11-01" @default.
- W2081566936 modified "2023-09-24" @default.
- W2081566936 title "Levinson-Seaton theorem for potentials with an attractive Coulomb tail" @default.
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- W2081566936 doi "https://doi.org/10.1103/physreva.52.3824" @default.
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