Electron Pair Production inπ−+dCapture

Abstract

The internal conversion coefficient $\rho \mathrm{}\left(p\right)=\frac{\left(\frac{d{W}_{2e}}{\mathrm{dp}}\right)}{\left(\frac{d{W}_{\gamma }}{\mathrm{dp}}\right)}$ relating the ${\pi }^{-}+d$ capture processes yielding $2n+e^{+}+e^{-}$ and $2n+\gamma$ is calculated as a function of the $n-n$ relative momentum $p$. It is found to be a slowly varying function of $p$, insensitive to the strength of the $n-n$ force. The spectrum of the electron pair energies (or of the momentum $p$) therefore depends sensitively on the $n-n$ scattering length, just as Watson and Stuart found to be the case for the photon spectrum. Thus, observation of the pair production process is an alternative method of measuring the $n-n$ scattering length.