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We apply the cluster-folding (CF) model for $\vec{p}+^{6}$He scattering at200 MeV, where the potential between $\vec{p}$ and $^{4}$He is fitted to dataon $\vec{p}+^{4}$He scattering at 200 MeV. For $\vec{p}+^{6}$He scattering at200 MeV, the CF model reproduces measured differential cross section with nofree parameter, We then predict the analyzing power $A_y(q)$ with the CF model,where $q$ is the transfer momentum. Johnson, Al-Khalili and Tostevin constructa theory for one-neutron halo scattering, taking (1) the adiabaticapproximation and (2) neglecting the interaction between a valence neutron anda target, and yield a simple relationship between the elastic scattering of ahalo nucleus and of its core under certain conditions. We improve their theorywith (3) the eikonal approximation in order to determine $A_y(q)$ for $^{6}$Hefrom the data on $A_y(q)$ for $^{4}$He. The improved theory is accurate, whenapproximation (1)--(3) are good. Among the three approximations, approximation(2) is most essential. The CF model shows that approximation (2) is good in$0.9 < q < 2.4$ fm$^{-1}$. In the improved theory, the $A_y(q)$ for $^{6}$He isthe same as that for $^{4}$He. In $0.9 < q < 2.4$ fm$^{-1}$, we then predict$A_y(q)$ for $\vec{p}+^{6}$He scattering at 200 MeV from measured $A_y(q)$ for$\vec{p}+^{4}$He scattering at 200 MeV. We thus predict $A_y(q)$ with themodel-dependent and the model-independent prescription. The ratio ofdifferential cross sections measured for $^{6}$He to that for $^{4}$He isrelated to the wave function of $^{6}$He. We then determine the radius between$^{4}$He and the center-of-mass of valence two neutrons in $^{6}$He. The radiusis 5.77 fm.

Prediction of the analyzing power for $\vec{p}$+$^{6}$He elastic scattering at 200 MeV from $\vec{p}$+$^{4}$He elastic scattering at 200 MeV