Investigation of $\alpha$ clustering with knockout reactions

Background: Nuclear clustering has been one of the main interests in nuclear physics. In order to probe the $\alpha$ clustering through reaction observables, $\alpha$ transfer and $\alpha$ knockout reactions have been studied. It is very important to probe the $\alpha$ cluster amplitude at nuclear surface since the $\alpha$ spectroscopic factor is not necessarily a direct measure of the $\alpha$ clustering.

Purpose: Our goal is to reveal how the $\alpha$ cluster amplitude is probed through $\alpha$ knockout reactions depending on reaction conditions, e.g., the incident energy.

Method: We consider ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ and ${}^{120}\mathrm{Sn}(p,p\alpha ){}^{116}\mathrm{Cd}$ at 100–400 MeV within the distorted wave impulse approximation (DWIA) framework. We introduce a masking function, which shows how the reaction amplitude in the nuclear interior is suppressed and defines the probed region of the $\alpha$ cluster wave function.

Results: It is clearly shown by means of the masking function that the $\alpha$ knockout reaction probes the $\alpha$ cluster amplitude in the nuclear surface region, which is the direct measure of well-developed $\alpha$ cluster states. The incident energy dependence of the masking effect is investigated, using a simplified form of the masking function.

Conclusions: The $\alpha$ knockout reaction can probe the $\alpha$ cluster amplitude in the nuclear surface region by choosing proper kinematics owing to the masking effect originated from absorptions of distorting potentials, and is a suitable method to investigate how $\alpha$ cluster states are spatially developed.

Figure 1

$\alpha$ cluster wave function obtained by solving Eq. (11). The solid, dashed, and dotted lines correspond to ${\varphi }_{\alpha }^{40}\left(R\right)$, $R{\varphi }_{\alpha }^{40}\left(R\right)$, and $R^2{\varphi }_{\alpha }^{40}\left(R\right)$, respectively. The dashed line is equivalent to the PM1 in Fig. 3 of Ref. [3].

Figure 2

TDX of ${}^{20}\mathrm{Ne}(p,p\alpha ){}^{16}\mathrm{O}$ at 392 MeV as a function of the recoil momentum.

Figure 3

(a) Masking function $\left|D_{00}\left(R\right)\right|$ defined by Eq. (15). The solid, dashed, and dotted lines represent $\left|D_{00}\left(R\right)\right|$ of DWIA, DWIA without Coulomb interactions, and PWIA, respectively. The dot-dashed line shows the eikonal-masking function $\left|D_{00}^{\mathrm{EK}}\left(R\right)\right|$ discussed in Sec. 3d. (b) Same as (a) but $I\left(R\right)$ and that with the eikonal approximation $I^{\mathrm{EK}}\left(R\right)$.

Figure 4

The same as Fig. 3 but for ${}^{120}\mathrm{Sn}(p,p\alpha ){}^{116}\mathrm{Cd}$ reaction.

Figure 5

Incident energy $T_0$ dependence of $C_{\mathrm{abs}}$.