Stability of angular extrapolation methods for determining the deuteron asymptotic D-state to S-state ratio.

Abstract

We review the current status of the extraction of the deuteron $D$-state to $S$-state ratio, $\ensuremath{\eta}$, from measurements of the tensor polarized cross section, $\ensuremath{\sigma}{T}_{22}$, in elastic d + p scattering. We examine various extrapolation techniques for obtaining $\ensuremath{\eta}$ and conclude in several independent ways that such techniques suffer from large truncation errors. First we show that different methods for determining $\ensuremath{\eta}$ give rise to very different results. Second, we use a theoretical model which estimates $\ensuremath{\eta}$ to demonstrate the magnitude of the truncation error. Third, high-precision analyzing power data also generate large changes when compared with the results from earlier, less precise measurements. The original estimates of $\ensuremath{\eta}$ appeared to agree with theory; we show that such agreement was fortuitous, and was the result of the simultaneous neglect of large Coulomb penetrability corrections and large truncation errors. We conclude that the uncertainty in $\ensuremath{\eta}$ is considerably larger than was suggested by the errors quoted in the literature.