Stability of angular extrapolation methods for determining the deuteron asymptoticD-state toS-state ratio

We review the current status of the extraction of the deuteron $D$-state to $S$-state ratio, $\eta$, from measurements of the tensor polarized cross section, $\sigma T_{22}$, in elastic d + p scattering. We examine various extrapolation techniques for obtaining $\eta$ and conclude in several independent ways that such techniques suffer from large truncation errors. First we show that different methods for determining $\eta$ give rise to very different results. Second, we use a theoretical model which estimates $\eta$ 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 $\eta$ 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 $\eta$ is considerably larger than was suggested by the errors quoted in the literature.