Observation of $psi(3686) to p bar{p} eta^{prime}$ and improved measurement of $J/psi to p bar{p} eta^{prime}$

We observe the process $psi(3686) to p bar{p} eta^{prime}$ for the first time, with a statistical significance higher than 10$sigma$, and measure the branching fraction of $J/psi to p bar{p} eta^{prime}$ with an improved accuracy compared to earlier studies. The measurements are based on $4.48 times 10^8$ $psi(3686)$ and $1.31 times 10^{9}$ $J/psi$ events collected by the BESIII detector operating at the BEPCII. The branching fractions are determined to be $B(psi(3686) to p bar{p} eta^{prime}) = (1.10pm0.10pm0.08)times10^{-5}$ and $B(J/psi to p bar{p} eta^{prime})=(1.26pm0.02pm 0.07)times10^{-4}$, where the first uncertainties are statistical and the second ones systematic. Additionally, the $eta-eta^{prime}$ mixing angle is determined to be $-24^{circ} pm 11^{circ}$ based on $psi(3686) to p bar{p} eta^{prime}$, and $-24^{circ} pm 9^{circ}$ based on $J/psi to p bar{p} eta^{prime}$, respectively.