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

Abstract

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.