The Formation of Electron-Positron Pairs by Internal Conversion of $\gamma$-Radiation

The production of an electron and positron by the spherical $\gamma$-wave emitted from a nucleus has been considered on the basis of different approximation methods (Section II, III, IV), which yield simple closed formulae for the probability of the process. Regarding the nucleus as a Hertzian oscillator, both the dipole and quadripole radiation are treated. The approximate methods, which may be classified according to which of a certain set of parameters (the momenta of the particles, $\alpha Z$, and eventually the ratios of these) are to be considered small, form a consistent scheme (§6, where also the case of the plane $\gamma$-wave is discussed). A discussion of the qualitative features of the angular and energy distribution is given (§7 and §8) and a comparison is made with the rigorous treatment of the problem by Jäger and Hulme (§9). This shows that both the differential and total internal conversion coefficient may be computed with a fair degree of accuracy by the combined use of the Born and the Schrödinger approximation results.