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

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.