Nuclear Physics and Atomic Energy

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Nuclear Physics and Atomic Energy

  ISSN: 1818-331X (Print), 2074-0565 (Online)
  Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine
  Languages: Ukrainian, English, Russian
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Nucl. Phys. At. Energy 2020, volume 21, issue 1, pages 5-12.
Section: Nuclear Physics.
Received: 06.11.2019; Accepted: 19.03.2020; Published online: 14.05.2020.
PDF Full text (ru)
https://doi.org/10.15407/jnpae2020.01.005

Averaged overall atomic electrons probability of positrons annihilation at β+-decay

S. N. Fedotkin*

Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine

*Corresponding author. E-mail address: sfedot@kinr.kiev.ua

Abstract: An approximate method for calculating the probability of single-photon annihilation of a positron with an atomic electron at the β+-decay averaged over all electrons of the daughter atom is proposed. The electrons are described in the framework of the Thomas - Fermi statistical model. This approximation makes it easy the calculation of the average probabilities of various processes involving all the electrons of the atom. The total probability of single-photon annihilation is calculated using an approximate analytical expression for the atomic electrons’ density. A good agreement between the probabilities calculated in the proposed approach and the estimates obtained in the framework of quantum mechanics was obtained.

Keywords: annihilation, β+-decay, atomic shell, K-electron, Thomas - Fermi approximation.

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