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At the Relativistic Heavy-Ion Collider (RHIC), the Polarized Atomic HydrogenGas Jet Target polarimeter (HJET) is employed for the precise measurement ofthe absolute transverse (vertical) polarization of proton beams, achieving lowsystematic uncertainties of approximately $\sigma^\text{syst}_P/P\leq0.5\%$.The acquired experimental data not only facilitated the determination of single$A_\text{N}(t)$ and double $A_\text{NN}(t)$ spin analyzing powers for 100 and255 GeV proton beams but also revealed a non-zero Pomeron spin-flipcontribution through a Regge fit. Preliminary results obtained for forwardinelastic $p^{\uparrow}p$ and elastic $p^{\uparrow}A$ analyzing powers will bediscussed. The success of HJET at RHIC suggests its potential application forproton beam polarimetry at the upcoming Electron-Ion Collider (EIC), aiming foran accuracy of 1\%. Moreover, the provided analysis indicates that the RHICHJET target can serve as a tool for the precision calibration, with therequired accuracy, of the $^3$He beam polarization at the EIC.

Polarization Measurements of $p^{\uparrow}$ and $^3$He$^\uparrow$ Beams at RHIC and Future EIC Using the Polarized Atomic Hydrogen Gas Jet Target