Effect of Nuclear Charge on Internally Produced Pairs
Abstract
The effect of nuclear charge on internally converted pairs is investigated using the relativistic SommerfeldMaue solutions of the iterated Dirac equation. The orthonormal properties of these wave functions are studied and timedependent perturbation theory is adapted to allow for their nonorthogonality. The integrals involved are studied using the Fourier transforms of the wave functions. The matrix elements are obtained in terms of one fundamental integral, evaluated by using an integral representation of Butler. The procedure is very simple and promises generalizations. The matrix elements are shown to be complex only through n=/+iZ(137v_{+/}), where v_{+/} is the velocity of the positron or the negatron and Z is the nuclear charge. The following conclusions are drawn. Firstly, the first Born approximation results when multiplied by the wellknown Sommerfeld factors of the negatron and positron are accurate to a term proportional to n^{2}. For 5percent resolutions, Z<~20, the kinetic energy must be more than 100 kev. Secondly, this result is valid for all electric and magnetic multipole transitions. Finally, this result is shown to apply to all transitions taking place between unbound states and to hold for higher order perturbation terms.
 Publication:

Physical Review
 Pub Date:
 November 1954
 DOI:
 10.1103/PhysRev.96.1066
 Bibcode:
 1954PhRv...96.1066H