  We apply the cluster-folding (CF) model for $\vec{p}+^{6}$He scattering at
200 MeV, where the potential between $\vec{p}$ and $^{4}$He is fitted to data
on $\vec{p}+^{4}$He scattering at 200 MeV. For $\vec{p}+^{6}$He scattering at
200 MeV, the CF model reproduces measured differential cross section with no
free 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 construct
a theory for one-neutron halo scattering, taking (1) the adiabatic
approximation and (2) neglecting the interaction between a valence neutron and
a target, and yield a simple relationship between the elastic scattering of a
halo nucleus and of its core under certain conditions. We improve their theory
with (3) the eikonal approximation in order to determine $A_y(q)$ for $^{6}$He
from the data on $A_y(q)$ for $^{4}$He. The improved theory is accurate, when
approximation (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 is
the 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 the
model-dependent and the model-independent prescription. The ratio of
differential cross sections measured for $^{6}$He to that for $^{4}$He is
related 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 radius
is 5.77 fm.
