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 $\ensuremath{\gamma}$-ray replacing the conversion electron is known. This latter is known for all cases of practical interest. Specifically, if the correlation function for $\ensuremath{\gamma}$-rays and a radiation $x$ is expanded in Legendre polynomials, the correlation function with a conversion electron replacing the $\ensuremath{\gamma}$-ray is obtained by multiplying the coefficients of each polynomial ${P}_{\ensuremath{\nu}}$ by a parameter ${b}_{\ensuremath{\nu}}$. The case of conversion-conversion correlation, in all practical cases, is obtained from the $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ correlation by inserting two factors ${b}_{\ensuremath{\nu}}$, one for each conversion electron. The coefficients ${b}_{\ensuremath{\nu}}$ 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 $\ensuremath{\gamma}$-electron correlation if the $\ensuremath{\gamma}$ 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.