Quantitative description of the ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ reaction as a means of probing the surface $\alpha$ amplitude

Background: The proton-induced $\alpha$ knockout reaction has been utilized for decades to investigate the $\alpha$ cluster formation in the ground state of nucleus. However, even today, the theoretical description of the reaction is not precise enough for the quantitative study. For example, the $\alpha$ spectroscopic factors reduced from $\alpha$ knockout experiments with reaction analyses using phenomenological $\alpha$ cluster wave functions disagree with those given by a structure theory. In some cases they also scatter depending on the kinematical condition of the experiment. This suggests that the theoretical description of the $\alpha$ knockout reaction is insufficient from a quantitative viewpoint.

Purpose: We show that the distorted wave impulse approximation can describe ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ reaction quantitatively if reliable inputs are used; the optical potential, the $p-\alpha$ cross section, and the $\alpha$ cluster wave function. We also investigate the relationship between the $\alpha$ cluster wave function and the $\alpha$ knockout cross section.

Method: The ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ reaction is described by the distorted wave impulse approximation. An input of the calculation, the $\alpha -{}^{16}\mathrm{O}$ cluster wave function, is obtained by the antisymmetrized molecular dynamics and the Laplace expansion method.

Results: In contrast to the previous work, the ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ data at 101.5 MeV is successfully reproduced by the present framework without any free adjustable parameters. It is also found that the knockout cross section is sensitive to the surface region of the cluster wave function because of the peripherality of the reaction.

Conclusions: Using a reliable $\alpha$ cluster wave function, $p-\alpha$ cross section, and distorting potentials, it is found that the ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ cross section is quantitatively reproduced by the present framework. This success demonstrates that the proton-induced $\alpha$ knockout reaction is a quantitative probe for the $\alpha$ clustering.

Figure 1

$\alpha +{}^{16}\mathrm{O}$ RWA of the $0_1^{+}$ state taken from Fig. 2 of Ref. [12].

Figure 2

Kinematical condition of the ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ reaction [15].

Figure 3

$p-\alpha$ differential cross section at 85 MeV obtained by the folding model [35] with the Melbourne $g$-matrix interaction [36] (dashed line). The tuned result at around ${\theta }_{p\alpha }={85}^{\circ }$ is shown in dotted line. The experimental data are taken from Ref. [37].

Figure 4

The comparison between the calculated energy sharing distribution with the AMD-RWA (solid line) and the experimental data taken from Ref. [15].

Figure 5

RWAs constructed by the superposition of two Brink-Bloch wave functions of the $\alpha -{}^{16}\mathrm{O}$ cluster. See text for details.

Figure 6

Real part of the TMD at the recoilless condition: $T_p=67$ MeV. The dashed, dotted, and dot-dashed lines are the results with the RWAs shown by dashed, dotted, and dot-dashed lines in Fig. 5, respectively.

Figure 7

Energy sharing distributions with the RWAs shown in Fig. 5.