Experimental Scheme for Polarizing the Boron Nuclei

TL;DR

This work proposes an optical-pumping scheme to generate nuclear polarization in the spin-3 nucleus $^{10}$B (and its isotope $^{11}$B) to enable searches for exotic gluon states via the double-helicity-flip structure function $\Delta(x,Q^2)$ at the Electron-Ion Collider. By leveraging hyperfine coupling, the authors outline a multi-step pumping sequence that transfers population from the ground hyperfine levels to a fully polarized nuclear state through $J$-, $F$-, and $m_F$-pumping, targeting a closed $|g\rangle \leftrightarrow |e\rangle$ cycling transition. They discuss the substantial technical challenges—high oven temperatures, Doppler broadening, UV laser power limits, and unknown hyperfine constants—and propose strategies such as collimation, buffering, and cavity-enhanced pumping, along with a roadmap of spectroscopy and rate-modeling to optimize polarization. The paper also addresses collider integration, including neutral-atom to polarized-ion conversion, spin-control via Siberian Snakes, polarimetry, and the theoretical framework required to extract the exotic gluon signal, while highlighting the potential to augment $p$-$^{11}$B fusion cross sections with polarized nuclei. If validated, this scheme could provide a new route to study gluon dynamics in nuclei and expand the physics program of the EIC with polarized boron beams and targets.

Abstract

Unravelling the internal structure of hadrons and nuclei in terms of the quarks and gluons of Quantum Chromodynamics is a central focus of current nuclear physics research. Directly observing gluonic states in the nucleus would be groundbreaking and is an objective of the future Electron-Ion Collider (EIC). Over thirty years ago, Jaffe and Manohar identified a new double-helicity flip structure function, directly sensitive to exotic gluons. They pointed out that this could be measured in inclusive high-energy electron scattering from a transversely polarized nuclear target with spin $I \ge 1$. Here, we identify the spin-3 nucleus boron-10 as a particularly interesting system to search for exotic gluons. Leveraging technical advances in atomic physics over the past decade, we outline an experimental scheme to directly optically pump a beam of stable boron atoms to polarize the nuclear spin. Technical challenges to realize a spin-polarized beam of boron-10 in the EIC are discussed. The proposed scheme will also polarize the $^{11}$B nucleus, which could significantly enhance the pB fusion cross section.

Figures (3)

• Figure 1: $^{10}\text{B}$ energy levels. Transition rates $\Gamma$ are reported in Ref. carlsson1994lifetimes. Transition wavelengths are determined from Ref. NIST_ASD. Transitions are characterized in terms of $J$, $F$, and $m_{F}$ pumping steps. The $\ket{g}$ and $\ket{e}$ states are addressed by the $209$ nm transition.
• Figure 2: Experimental schematic to prepare and measure spin polarization. Atoms are heated in an oven to $2000$ K, then collimated to reduce the transverse velocity spread. A pair of Helmholtz coils establishes a quantization axis transverse to the atomic beam motion. To avoid inhomogeneous fields, the coils should be large compared to the apparatus. $249$ nm light pumps atoms to the $\ket{^{2}P_{3/2},F=9/2}$ state. A secondary laser at $209$ nm optically pumps the atoms to the $\ket{^{2}P_{3/2},F=9/2, m_{F} = 9/2}$ state. A third spectroscopy region employs fluorescent detection to determine the state populations and thus nuclear polarization.
• Figure 3: $^{2}P_{3/2}$ energy levels. We diagonalize the Breit-Rabi Hamiltonian $H = A_{HF} I \cdot J + \mu_{B} g_{J} J_{z} B$ to determine the energy spectra. Lower panel: At low field, $F$ is a good quantum number and $E = \mu_{B} g_{F} m_{F} B$. $m_{F}$ pumping to the $\ket{F = 9/2, m_{F} = 9/2}$ state will be employed in this regime. At high fields, the nuclear and electronic spin are decoupled into the $\ket{m_{J}, m_{I}}$ basis. In this regime, $E = A_{HF} m_{J} m_{I} + \mu_{B} g_{J}m_{J} B$ ignoring the much smaller electric quadrupole and nuclear g-factor terms. Nuclear polarization spectroscopy should likely be done in this regime to achieve the best resolution. Upper panel: The splitting for the $\ket{F = 9/2, m_{F} = 7/2, 9/2}$ ($\ket{m_{J} = 3/2, m_{I} = 3, 2}$) states at low (high) magnetic field is plotted. While the splitting increases for larger magnetic fields, it saturates at $A_{HF} m_{J} = 37$ MHz for the $\ket{^{2}P_{3/2}}$ state. Although the energy levels for the $\ket{^{2} D_{5/2}, F' = 11/2}$ states will be qualitatively similar, the hyperfine constant $A_{HF'}$ required to directly calculate the energy structure is unknown to the best of our knowledge.