We analyze beam-induced depolarizing effects in the hydrogen jet target (HJET) at the relativistic heavy ion collider (RHIC), which has been used for absolute hadron beam polarimetry and shall be employed at the electron-ion collider (EIC). The EIC’s higher bunch repetition frequencies and shorter bunch durations shift beam harmonics to frequencies that can resonantly drive hyperfine transitions in hydrogen, threatening to depolarize the target atoms. Using frequency-domain analysis of beam harmonics and hyperfine transition frequencies, we establish a photon emission threshold above which beam-induced fields are too weak to cause significant depolarization. For EIC injection (23.5 GeV) and flattop (275 GeV), beam-induced depolarization through the bunch structure renders operation at the current RHIC magnetic guide field at the target ( B 0 = 120 mT ) untenable. Increasing the magnetic guide field at the target to B 0 ≈ 400 mT moves all hyperfine transition frequencies to at least 3 times the cutoff frequency, ensuring reliable absolute beam polarimetry with the required 1% precision at the EIC.

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. The posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

Polarized ion beams at the Electron Ion Collider are essential to address some of the most important open questions at the twenty-first century frontiers of understanding of the fundamental structure of matter. Here, we summarize the science case and identify polarized $^2$H, $^3$He, $^6$Li and $^7$Li ion beams as critical technology that will enable experiments which address the most important science. Further, we discuss the required ion polarimetry and spin manipulation in EIC. The current EIC accelerator design is presented. We identify a significant R\&D effort involving both national laboratories and universities that is required over about a decade to realize the polarized ion beams and estimate (based on previous experience) that it will require about 20 FTE over 10 years (or a total of about 200 FTE-years) of personnel, including graduate students, postdoctoral researchers, technicians and engineers. Attracting, educating and training a new generation of physicists in experimental spin techniques will be essential for successful realization. AI/ML is seen as having significant potential for both acceleration of R\&D and amplification of discovery in optimal realization of this unique quantum technology on a cutting-edge collider. The R\&D effort is synergistic with research in atomic physics and fusion energy science.