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

Background: Johnson, Al-Khalili, and Tostevin constructed a theory for one-neutron halo-nucleus scattering, taking (1) the adiabatic approximation and (2) neglecting the interaction between a valence neutron and a target, and yielding a simple relationship between the elastic scattering of a halo nucleus and of its core. The core-target scattering is calculated with the reduced mass between a halo nucleus and a target, and hence is not measured with the experiment.

Purpose: Our first aim is to apply their theory for $\vec{p}+{}^6\mathrm{He}$ elastic scattering as two-neutron halo-nucleus scattering and improve the theory with (3) the eikonal approximation. Our second aim is to investigate how good the improved theory is.

Methods: An improved valence-target-cutting (VTC) theory and cluster-folding (CF) model.

Results: The improved VTC theory shows a new relation between two differential cross sections measured for $\vec{p}+{}^{4,6}\mathrm{He}$ scattering. Using the relation, we show that the analyzing power $A_y\left(q\right)$ for ${}^6\mathrm{He}$ is the same as for ${}^4\mathrm{He}$. In the improved theory, the ratio of measured differential cross section for ${}^4\mathrm{He}$ to that for ${}^6\mathrm{He}$ determines a radius $r_{\alpha -2n}$ between ${}^4\mathrm{He}$ and the center of mass of two valence neutrons; the value is $r_{\alpha -2n}=3.54$ fm. Among the approximations (1)–(3), the approximation (2) is essential. In order to investigate the approximation (2), we apply the CF model for $\vec{p}+{}^6\mathrm{He}$ scattering at 200 MeV, where the potential between $\vec{p}$ and ${}^4\mathrm{He}$ is fitted to data on $\vec{p}+{}^4\mathrm{He}$ scattering at 200 MeV. For $\vec{p}+{}^6\mathrm{He}$ scattering at 200 MeV, the CF model reproduces the measured differential cross section with no free parameter. The CF model shows that the approximation (2) is good in $0.9\lesssim q\lesssim 2.4{\mathrm{fm}}^{-1}$, where $\hslash q$ is the transfer momentum. Using the improved theory, in $0.9\lesssim q\lesssim 2.4{\mathrm{fm}}^{-1}$, we predict $A_y\left(q\right)$ for ${}^6\mathrm{He}$ from measured $A_y\left(q\right)$ for ${}^4\mathrm{He}$.

Conclusions: The improved VTC theory shows shows that $A_y\left(q\right)$ for ${}^6\mathrm{He}$ is the same as for ${}^4\mathrm{He}$.

Figure 1

Two sets of coordinates in four-body model.

Figure 2

$Q$ dependence of $\left|F\right|$. The solid (open) circles are the result determined from the experimental data at 71 (200) MeV. The solid line is a result of $V\left(\zeta \right)=-25exp[-{(\zeta /1.41)}^2]$. Experimental data are taken from Refs. [5, 15, 16] for 71 MeV and Refs. [6, 7] for 200 MeV.

Figure 3

${\theta }_{\mathrm{c}.\mathrm{m}.}$ dependence of predicted $A_y$ for $\vec{p}+{}^6\mathrm{He}$ scattering at 200 MeV. See the text for closed and open circles.

Figure 4

$q$ dependence of measured $A_y$ (closed circles) for $\vec{p}+{}^4\mathrm{He}$ scattering at $E_{\mathrm{lab}}=72$ MeV and measured $A_y$ (open circles) for $\vec{p}+{}^6\mathrm{He}$ scattering at $E_{\mathrm{lab}}=71$ MeV. Data are taken from Ref. [5] for ${}^6\mathrm{He}$ and Ref. [16] for ${}^4\mathrm{He}$.

Figure 5

${\theta }_{\mathrm{c}.\mathrm{m}.}$ dependence of $d\sigma /d\mathrm{\Omega }$ and $A_y$ for $\vec{p}+{}^{4,6}\mathrm{He}$ scattering at $E_{\mathrm{lab}}=200$ MeV/nucleon. In the left panel, the solid line is a result of our fitting based on the optical potential model (OPM). In the right panel, the solid and dashed lines denote results of CF model (CFM) with and without $U_{p{n}_1}$ and $U_{p{n}_2}$, respectively. Experimental data are taken from Ref. [7] for ${}^4\mathrm{He}$ and Ref [6] for ${}^6\mathrm{He}$.

Figure 6

$q$ dependence of $d\sigma /d\mathrm{\Omega }$ for $\vec{p}+{}^{4,6}\mathrm{He}$ scattering at $E_{\mathrm{lab}}=200$ MeV/nucleon in the upper panel and the form factor $\left|F\right(Q\left)\right|$ in the lower panel. Experimental data are taken from Ref. [7] for $\vec{p}+{}^4\mathrm{He}$ scattering and Ref. [6] for $\vec{p}+{}^6\mathrm{He}$ scattering.

Figure 7

$q$ dependence of $A_y$ for $\vec{p}+{}^6\mathrm{He}$ scattering at $E_{\mathrm{lab}}=200$ MeV/nucleon. The solid line denotes a result of the CF-folding model, while $U_{p{n}_1}$ and $U_{p{n}_2}$ are switched off in the dashed line. The thin solid line is a result of the fitting for $\vec{p}+{}^4\mathrm{He}$ scattering at $E_{\mathrm{lab}}=200$ MeV/nucleon. Open circles show the experimental data [7] for $\vec{p}+{}^4\mathrm{He}$ scattering. In $0.9\lesssim q\lesssim 2.4{\mathrm{fm}}^{-1}$, open circles can be regarded as measured $A_y$ for the $\vec{p}+{}^6\mathrm{He}$ scattering at $E_{\mathrm{lab}}=200$ MeV/nucleon. Experimental data are taken from Ref. [7] for ${}^4\mathrm{He}$.

Figure 8

$q$ dependence of $d\sigma /d\mathrm{\Omega }$ and $A_y$ for $\vec{p}+{}^{4,6}\mathrm{He}$ scattering at $E_{\mathrm{lab}}\approx 71$ MeV/nucleon in the upper and middle panels and the form factor $\left|F\right(Q\left)\right|$ in the lower panel. The solid and dashed lines denote results of CF model with and without $U_{p{n}_1}$ and $U_{p{n}_2}$ for ${}^{,6}\mathrm{He}$, respectively. The thin solid line denotes the result of fitting for ${}^4\mathrm{He}$. Data are taken from Refs. [5, 15] for ${}^6\mathrm{He}$ and from Ref. [16] for ${}^4\mathrm{He}$.