Chirality in $(\vec{p},2p)$ reactions induced by proton helicity

Abstract

It is shown that longitudinally-polarized protons can be used to induce chirality in final states of the $(\vec{p},pN)$ reaction at intermediate energies, when there exist three final-state particles with non-coplanar momentum vectors. The analyzing power $A_z$ is proposed as a measure of this effect. Theoretical descriptions to obtain $A_z$ based on an intuitive picture as well as a distorted wave impulse approximation are presented, showing that the helicity of incident protons is coupled to the chirality of the orbital motion of a single-particle wave function, resulting in the chirality of the final states and a large $A_z$ value.

Figures (4)

• Figure 1: A schematic view of initial (left) and final (right) states in the $^{16}$O$(\vec{p},pN)$ reaction, where $0p_{1/2}$ proton having the spin (orbital angular momentum) in parallel with $z$ ($-z$) direction is knocked out. As $C_{zz} \sim 1$, the $\mu_0 = \mu_N$ case is considered. Note that $\mathcal{K}$ must be non-coplanar so as to satisfy $\mathcal{K}\neq\mathcal{\tilde{K}}$. Here we consider the laboratory frame where the nucleus $A$ is at rest.
• Figure 2: Left panel (a): (Inset on top) $\mathcal{K}=(\bm{K}_1,\bm{K}_2,\bm{K}_\mathrm{B})$ in the final state on the $xy$-plane. Note that only the transverse component of $\mathcal{K}$ is shown in the figure, and the longitudinal component of $\bm{K}_2$ is smaller than $\bm{K}_1$. (Middle) A geometrical relation between $\mathcal{K}$ and $\phi$. The absorption is maximum in $3\pi/2 \lesssim \phi \lesssim 2\pi$, where particle 2 ($\bm{K}_2$) goes across the nucleus in this example. (Bottom) A schematic figure of the $\phi$ dependence of $D_{\mathcal{K}}$ as a function of $\phi$ for a certain $(r,\theta)$. Right panel (b): same as (a) but for the mirror partner $\mathcal{\tilde{K}}$. Note that $D_{\mathcal{K}}$ and $D_{\mathcal{\tilde{K}}}$ are both periodic with respect to $\phi$ and related as $D_{\mathcal{K}}(r,\theta,\phi) = D_{\mathcal{\tilde{K}}}(r,\theta,\pi-\phi)$.
• Figure 3: $A_z$ of $^{16}$O$(\vec{p},2p)$ knockout reaction from $0p$ orbits calculated using Eq. \ref{['eq:sigma_pm']}.
• Figure 4: TDXs (top) and longitudinal analyzing powers (bottom) $A_z$ calculated for the $^{16}$O$(\vec{p},2p)$ reaction at 250 MeV as a function of $\phi_{12}$, including the LS term of the optical potential and the $\mu_0 \ne \mu_N$ components. The proton knockout from the $0p_{1/2}$ and $0p_{3/2}$ orbits are labeled as solid and dashed lines, respectively.