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An approximate method for calculating the proβaβility 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 descriβed in the framework of the Thomas -Fermi statistical model. This approximation makes it easy the calculation of the average proβaβilities of various processes involving all the electrons of the atom. The total proβaβility of single-photon annihilation is calculated using an approximate analytical expression for the atomic electrons’ density. A good agreement βetween the proβaβilities calculated in the proposed approach and the estimates oβtained in the framework of quantum mechanics was oβtained. [ABSTRACT FROM AUTHOR]

The role of the nuclear charge screening and correctness of Born approximation for electron which is leaving atom in the process of atomic ionization at annihilation of positron with another electron of daughter's atom at β+-decay is studied. Processes of the different atomic shells ionization at annihilation of positron, emitted at β+-decay, with Kelectron of daughter's atom are considered. It is shown that the screening effect is important only for shell with n = 4. While corrections to the Born approximation plays the essential role for all shells. It is shown that the most probable process is related with emission of other K-electron. [ABSTRACT FROM AUTHOR]

The process of atomic shell ionization during annihilation of positron, emitted at β+-decay, with K-electron of daughter's atom is considered. The role of nuclear Coulomb field at calculation of the probability of this process is investigated. It is shown that the correct account of the influence of this factor on the states of electron and positron changes the probability of atomic ionization appreciably. The ratio of the probabilities of processes of atomic ionization and usual β+- decay is notably changed. [ABSTRACT FROM AUTHOR]