Probing surface distributions of $\alpha$ clusters in ${}^{20}\mathrm{Ne}$ via $\alpha \text{-transfer}$ reaction

Background: Direct evidence of the $\alpha \text{-cluster}$ manifestation in bound states has not been obtained yet, although a number of experimental studies were carried out to extract the information of the clustering. In particular in conventional analyses of $\alpha \text{-transfer}$ reactions, there exist a few significant problems on reaction models, which are insufficient to qualitatively discuss the cluster structure.

Purpose: We aim to verify the manifestation of the $\alpha \text{-cluster}$ structure from observables. As the first application, we plan to extract the spatial information of the cluster structure of the ${}^{20}\mathrm{Ne}$ nucleus in its ground state through the cross section of the $\alpha \text{-transfer}$ reaction ${}^{16}\mathrm{O}({}^6\mathrm{Li},d){}^{20}\mathrm{Ne}$.

Methods: For the analysis of the transfer reaction, we work with the coupled-channel Born approximation (CCBA) approach, in which the breakup effect of ${}^6\mathrm{Li}$ is explicitly taken into account by means of the continuum-discretized coupled-channel method based on the three-body $\alpha +d+{}^{16}\mathrm{O}$ model. The two methods are adopted to calculate the overlap function between ${}^{20}\mathrm{Ne}$ and $\alpha +{}^{16}\mathrm{O}$; one is the microscopic cluster model (MCM) with the generator coordinate method, and the other is the phenomenological two-body potential model (PM).

Results: We show that the CCBA calculation with the MCM wave function gives a significant improvement of the theoretical result on the angular distribution of the transfer cross section, which is consistent with the experimental data. Employing the PM, it is discussed which region of the cluster wave function is probed on the transfer cross section.

Conclusions: It is found that the surface region of the cluster wave function is sensitive to the cross section. The present work is situated as the first step in obtaining important information to systematically investigate the cluster structure.

Figure 1

Illustration of the three-body system.

Figure 2

Calculated transfer cross section of ${}^{16}\mathrm{O}({}^6\mathrm{Li},d){}^{20}\mathrm{Ne}$ at 20.0 MeV (solid line) and 42.1 MeV (dashed line) as a function of the deuteron emitting angle $\theta$ in the c.m. frame by using the MCM wave function. The value of $S_{\mathrm{MCM}}$, which is determined from the ${\chi }^2$ fit of the calculation to the experimental data [7, 8], is given in the legend. At 20.0 MeV the line and the dots are multiplied by 10.

Figure 3

The radial part of the $\alpha \text{−}{}^{16}\mathrm{O}$ relative wave function: ${\varphi }_l^{\left(\mathrm{MCM}\right)}$ of the MCM (solid line) and ${\varphi }_l^{\left(\mathrm{PM}\right)}$ of the PM, with the setups PM1 (dashed lines), PM2 (dotted line), and PM3 (dash-dotted line). Each wave function is normalized to have the norm one.

Figure 4

Calculated cross section with the ${\chi }^2$ fit to be consistent with the experimental data at (a) 20.0 and (b) 42.1 MeV. Each line corresponds to the cross section calculated with the $\alpha \text{−}{}^{16}\mathrm{O}$ wave function shown in Fig. 3.

Figure 5

${\tilde{\varphi }}_l^{\left(\mathrm{MCM}\right)}={\left(S_{\mathrm{MCM}}\right)}^{1/2}{\varphi }_l^{\left(\mathrm{MCM}\right)}$ of the MCM (solid line) and ${\tilde{\varphi }}_l^{\left(\mathrm{PM}\right)}={\left(S_{\mathrm{PM}}\right)}^{1/2}{\varphi }_l^{\left(\mathrm{PM}\right)}$ of PM1 (dashed line), PM2 (dotted line), and PM3 (dash-dotted line). The values of $S_{\mathrm{MCM}}$ and $S_{\mathrm{PM}}$ are adopted from Table 2 in the case of (a) $E_{\mathrm{in}}=20.0$ and (b) 42.1 MeV.

Figure 6

Transfer processes described by the ET (dashed line) and the BT (dotted line) on the cross section at (a) 20.0 and (b) 42.1 MeV. The solid line stands for the result involving both ET and BT, while the dash-dotted line is that of the ET without the BC. (c) The intuitive expression of the breakup effect. See the text for details.