Amplitude reconstruction inNNscattering at 6 GeV/c: Where do we stand and what measurements should be done?

We study the problem of amplitude reconstruction at a fixed $t (-t\sim 0.3$ ${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c}}^2$). The five amplitudes are reconstructed, up to an overall phase, by 9 observables $\sigma$, $P_0$, $C_{\mathrm{nn}}$, $K_{\mathrm{nn}}$, $D_{\mathrm{nn}}$, $C_{\mathrm{ss}}$, $C_{\mathrm{sl}}$, $C_{\mathrm{ll}}$, and $I\left(\mathrm{sn}0s\right)\mathrm{}$. This set includes all possible single-scattering measurements. The status of the amplitude reconstruction is discussed. To study both discrete ambiguities and the effects of the measurement errors, we employ a Monte Carlo method. We find that $D_{\mathrm{ls}}$ and $I\left(\mathrm{ns}0s\right)\mathrm{}$ remove the prominent ambiguities. In addition, given the current precision, $R$ and $I\left(\mathrm{ls}0n\right)\mathrm{}$ will significantly improve the amplitude determination.