Manifestation of $\alpha$ clustering in ${}^{10}\mathrm{Be}$ via $\alpha$-knockout reaction

Background: Proton-induced $\alpha$-knockout reactions may allow direct experimental observation of $\alpha$ clustering in nuclei. This is obtained by relating the theoretical descriptions of clustering states to the experimental reaction observables. It is desired to introduce microscopic structure models into the theoretical frameworks for $\alpha$-knockout reactions.

Purpose: Our goal is to probe the $\alpha$ clustering in the ${}^{10}\mathrm{Be}$ nucleus by proton-induced $\alpha$-knockout reaction observables.

Method: We adopt an extended version of the Tohsaki-Horiuchi-Schuck-Röpke wave function of ${}^{10}\mathrm{Be}$ and integrate it with the distorted-wave impulse approximation framework for the calculation of $(p,p\alpha )$-knockout reactions.

Results: We make the first calculation for the ${}^{10}\mathrm{Be}(p,p\alpha ){}^6\mathrm{He}$ reaction at 250 MeV by implementing a microscopic $\alpha$-cluster wave function, and we predict the triple-differential cross section (TDX). Furthermore, by constructing artificial states of the target nucleus ${}^{10}\mathrm{Be}$ with compact or dilute spatial distributions, the TDX is found to be highly sensitive to the extent of clustering in the target nuclei.

Conclusions: These results provide reliable manifestation of $\alpha$ clustering in ${}^{10}\mathrm{Be}$.

Figure 1

Coordinates of the ${}^{10}\mathrm{Be}(p,p\alpha ){}^6\mathrm{He}$ reaction.

Figure 2

Charge distribution of ${}^{10}\mathrm{Be}$ nucleus for the (a) artificial shell-model-like state with parameter ${\beta }_{\alpha ,z}=1.0$ fm, (b) the physical ground state with variational optimized parameter ${\beta }_{\alpha ,z}=2.6$ fm, and (c) artificial gaslike cluster state with parameter ${\beta }_{\alpha ,z}=6.0$ fm.

Figure 3

The approximated RWA of ${}^{10}\mathrm{Be}$ nucleus for the three values of ${\beta }_{\alpha ,z}$.

Figure 4

The TDX of the ${}^{10}\mathrm{Be}(p,p\alpha ){}^6\mathrm{He}$ reaction at 250 MeV. The kinetic energy of particle 1 is fixed at 180 MeV and its emission angle is set to $({\theta }_1,{\varphi }_1)=(60.9^{\circ },0^{\circ })$. ${\varphi }_2$ for particle 2 is fixed at ${180}^{\circ }$ and ${\theta }_2$ is varied around ${51}^{\circ }$. $P_R$ is the recoiled momentum.

Figure 5

TMD of the ${}^{10}\mathrm{Be}(p,p\alpha ){}^6\mathrm{He}$ reaction at 250 MeV for $P_R=0$.