Internal Conversion Angular Correlations

Abstract

It is shown that the angular correlation between a conversion electron and any other radiation emitted in a double nuclear cascade can be obtained immediately if the corresponding correlation with a $\gamma$-ray replacing the conversion electron is known. This latter is known for all cases of practical interest. Specifically, if the correlation function for $\gamma$-rays and a radiation $x$ is expanded in Legendre polynomials, the correlation function with a conversion electron replacing the $\gamma$-ray is obtained by multiplying the coefficients of each polynomial $P_{\nu }$ by a parameter $b_{\nu }$. The case of conversion-conversion correlation, in all practical cases, is obtained from the $\gamma -\gamma$ correlation by inserting two factors $b_{\nu }$, one for each conversion electron. The coefficients $b_{\nu }$ are calculated relativistically and numerical results are presented for $K$-shell conversion for 12 values of $Z$ in the range $10<~Z<~96$ and transition energies from $0.3 m{c}^2$ to $5.0 m{c}^2$ for ten multipoles (5 electric and 5 magnetic). It is pointed out that the present results apply in $\gamma$-electron correlation if the $\gamma$ is a mixed multipole but the case in which the conversion transition is mixed is not computed. The angular distribution functions for electrons in a coulomb field undergoing any type of transition are obtained in terms of the relevant matrix elements by the use of the Green function for the Dirac electron in a coulomb field. It is also shown that the angular distribution function is obtained from matrix elements based on, not the scattered wave, but on the time-space reversed scattered wave.