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Nuclear Disintegration by Positron- K Electron Annihilation

1952; American Institute of Physics; Volume: 85; Issue: 3 Linguagem: Inglês

10.1103/physrev.85.447

1536-6065

R. D. Present, S. C. Chen,

Radiation Detection and Scintillator Technologies

A new process for the annihilation of fast positrons is discussed, in which a positron with insufficient energy to excite or disintegrate a nucleus by collision, annihilates a $K$ electron of an atom with subsequent excitation or disintegration of its nucleus. If the positron energy is close to threshold for the process, competition from two-quanta annihilation does not occur. The process is of first order and, apart from the occurrence of negative energy states, is the reverse of internal conversion. The cross section can be factored into a cross section for annihilation with emission of a photon converging on the nucleus times a probability for nuclear disintegration. In the electric dipole case, the latter is just the ratio of the photodisintegration cross section to the $P$-wave blackbody absorption cross section of the nucleus. The photo-disintegration cross section is taken from experiment.The annihilation cross section in light elements has been calculated in the Born approximation using the complete retarded interaction corresponding to converging spherical waves of electric dipole radiation (the nucleus acts as a sink for these waves, in addition to conserving momentum). For large incident energy of the positron ($\ensuremath{\gg}m{c}^{2}$) the difference between positive and negative energy states can be neglected approximately, and the cross section obtained by detailed balancing from the internal conversion coefficient. Insofar as accurate values of the latter are known in the proper energy range for high atomic numbers $Z$, the annihilation cross section for very fast positrons can be obtained to a good approximation for the same values of $Z$.Numerical estimates have been made for the disintegration of ${\mathrm{Be}}^{9}$ with emission of a neutron and also for the disintegration of ${\mathrm{U}}^{238}$ resulting in nuclear fission. The total annihilation-disintegration cross sections near the threshold in these two cases are \ensuremath{\sim}${10}^{\ensuremath{-}34}$ ${\mathrm{cm}}^{2}$ and \ensuremath{\sim}${10}^{\ensuremath{-}31}$ ${\mathrm{cm}}^{2}$, respectively. The total cross section for an annihilation---excitation of ${\mathrm{In}}^{115}$ into an activation level for the metastable state, resulting in the formation of a nuclear isomer, is found to be \ensuremath{\sim}${10}^{\ensuremath{-}26}$ ${\mathrm{cm}}^{2}$.