Maris polarization in the ($p,pd$) reaction

Proton-induced knockout reactions at intermediate energies provide a clean probe for nuclear clusters with relatively small theoretical uncertainties. The Maris polarization, which is the effective polarization of a particle inside a nucleus arising from nuclear absorption and spin-orbit coupling, has been used in proton knockout to determine the total angular momentum $j$ of the removed protons. However, its manifestation in cluster knockout remains unexplored. We theoretically demonstrate that the Maris polarization can be observed via the vector analyzing power $A_y$ of the proton-induced deuteron knockout ($p,pd$) reaction in imbalanced kinematics. We first compute the spin-correlation coefficient $C_{y,y}$ of $p$-$d$ elastic scattering, which is an elementary process, to identify suitable kinematics for the Maris polarization. We then calculate $A_y$ of the ($p,pd$) reaction at $250$~MeV in forward kinematics for deuteron-cluster orbits with $j = 1$, $2$, and $3$. The large positive $C_{y,y}$ values around $p$-$d$ scattering angles of $\sim 40^\circ$ are consistent with the experimental data. In the corresponding ($p,pd$) kinematics, the calculated $A_y$ is positive for $j = 3$ and negative for $j = 1$, indicating effective upward and downward polarizations of the deuterons in the nucleus, respectively. The calculated $A_y$ for $j = 2$ lies between these and is not yet fully understood. We theoretically demonstrate that the Maris polarization occurs in the ($p,pd$) reaction under imbalanced kinematics. This work will provide an indicator of the presence and orbital motion of deuteron clusters in nuclei, which have not yet been established. Further experimental and theoretical studies are required to improve the quantitative understanding of this effect, particularly for $j = 2$.