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On the vacuum-polarization Uehling potential for a Fermi charge distribution

Abstract

We present analytical formulas for the vacuum-polarization Uehling potential in the case where the finite size of the nucleus is modeled by a Fermi charge distribution. Using a Sommerfeld-type development, the potential is expressed in terms of multiple derivatives of a particular integral. The latter and its derivatives can be evaluated exactly in terms of Bickley-Naylor functions, whose connection to the Uehling potential was already pointed out in the pure Coulomb case, and of usual Bessel functions of the second kind. The cusp and asymptotic expressions for the Uehling potential with a Fermi charge distribution are also provided. Analytical results for the higher-order-contribution Källén-Sabry potential are given.

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  • 13 February 2020

    Some typographical errors remain after the publication of my paper ���On the vacuum-polarization Uehling potential for a Fermi charge distribution���, Eur. Phys. J. D 72, 61 (2018). In order to improve its clarity and accuracy, the corrections are itemized below:

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Correspondence to Jean-Christophe Pain.

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Pain, J. On the vacuum-polarization Uehling potential for a Fermi charge distribution. Eur. Phys. J. D 72, 61 (2018). https://doi.org/10.1140/epjd/e2018-80457-8

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Keywords

  • Atomic Physics