Evaluation of the beam-induced depolarization of the HJET target at the EIC

The Polarized Atomic Hydrogen Gas Jet Target (HJET) has played a central role in the absolute calibration of proton beam polarization at RHIC and is foreseen as a key component of the hadron polarimetry program at the future Electron--Ion Collider (EIC). The substantially higher beam current, reduced bunch spacing, and shorter bunch length planned for EIC operation motivate a careful reassessment of possible beam-induced depolarization of the jet target. In this paper, the depolarization of ground-state hydrogen atoms caused by the time-dependent magnetic field of the circulating polarized proton beam is quantitatively evaluated. The hydrogen atom is treated as a four-level hyperfine system in a holding magnetic field, and transitions driven by harmonic components of the bunch-induced magnetic field are analyzed using time-dependent quantum-mechanical evolution along atomic trajectories. Numerical tracking of hydrogen atoms through the beam region is performed using nominal EIC beam parameters. It is shown that, for a holding field of $120 \mathrm{mT}$ (as used at RHIC), the resulting depolarization of the jet target at the EIC is negligibly small, $\lesssim 0.01\%$, and well below the level relevant for EIC polarization accuracy requirements. The stability of this result with respect to plausible variations of the EIC proton beam parameters is also evaluated. In addition, possible effects under alternative experimental conditions are also examined.