Investigating $\alpha$ clustering on the surface of ${}^{120}\mathrm{Sn}$ via the $(p,p\alpha )$ reaction, and the validity of the factorization approximation

The ${}^{120}\mathrm{Sn}(p,p\alpha ){}^{116}\mathrm{Cd}$ reaction at 392 MeV is investigated with the distorted wave impulse approximation (DWIA) framework. We show that this reaction is very peripheral, mainly because of the strong absorption of $\alpha$ by the reaction residue ${}^{116}\mathrm{Cd}$, and the $\alpha$ clustering on the nuclear surface can be probed clearly. We investigate also the validity of the so-called factorization approximation that has frequently been used so far. It is shown that the kinematics of $\alpha$ in the nuclear interior region is significantly affected by the distortion of ${}^{116}\mathrm{Cd}$, but it has no effect on the reaction observables because of the strong absorption in that region.

Figure 1

Coordinates of $\mathrm{A}(p,p\alpha )\mathrm{B}$ reaction.

Figure 2

Comparison between the $d{\sigma }_{p\alpha }/d{\mathrm{\Omega }}_{p\alpha }$ calculated by the single-folding model calculation and the experimental data [24, 25] at 297 and 500 MeV.

Figure 3

Calculated energy sharing cross section of ${}^{66}\mathrm{Zn}(p,p\alpha ){}^{62}\mathrm{Ni}$ reaction at 101.5 MeV. The experimental data are from Ref. [12].

Figure 4

The test of the LSCA and the AMA. The real part of ${\chi }_{2,{\mathit{K}}_2}^{*(-)}$ with no approximation (solid line), with the LSCA (dashed line), and with the AMA (dotted line) are plotted. In Figs. 4 and 4, the propagation from $(7\mathrm{fm}, {61}^{\circ }, {180}^{\circ })$ and $(7\mathrm{fm}, {29}^{\circ }, 0^{\circ })$ are investigated, respectively; $({\theta }_2,{\varphi }_2)=({61}^{\circ },{180}^{\circ })$ is chosen for the kinematics of the $\alpha$ particle.

Figure 5

TDX as a function of the recoil momentum. The solid (dashed) line corresponds to the calculation without (with) the factorization approximation. The TDX calculated with the PWIA divided by 200 is also shown by the dotted line.

Figure 6

$\left|I\right(R\left)\right|$ at $p_{\mathrm{R}}=0$ (solid line), the same but calculated with only the $\alpha -{}^{116}\mathrm{Cd}$ distorting potential $U_{\alpha }$ (dashed line), and the result with PWIA (dotted line). The results are normalized to unity at the peak position.

Figure 7

Same as Fig. 5 but with changing $R_{\min }$. The solid, dashed, dotted, dot-dashed, and two-dot-dashed lines correspond to $R_{\min }=$ 0, 6, 6.5, 7, and 8 fm, respectively.

Figure 8

$\left|J\right(\mathit{R}\left)\right|$ on the $z-x$ plane for $y=$ 0, 1, 3, 5, 6, and 7 fm. The kinematical condition is the same as in Fig. 6.

Figure 9

The TDXs with different $r_0$. The solid (dotted) line is the TDX with $r_0=1.40$ (1.14) fm. The dashed line is the same as in Fig. 5 for comparison.