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

• Main Author: S. N. Fedotkin
• Format: Article
• Language: English
• Published: Institute for Nuclear Research, National Academy of Sciences of Ukraine 2020-03-01
• Series: Âderna Fìzika ta Energetika
• Subjects: annihilation; β+-decay; atomic shell; k-electron; thomas - fermi approximation.
• Online Access: http://jnpae.kinr.kiev.ua/21.1/html/21.1.0005.html

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.