Direct measurement of the ${}^3$He${}^{+}$ magnetic moments

Abstract

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics [1, 2, 3], nuclear and atomic structure [4, 5], magnetometry and metrology [6] as well as chemistry and medicine [7, 8]. In particular, ${}^3$He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry [6, 9]. This requires a high-accuracy value for the ${}^3$He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of $12$ parts per billon (p.p.b.) [10,11]. Here we investigate the ${}^3$He${}^{+}$ ground-state hyperfine structure in a Penning trap to directly measure the nuclear $g$-factor of ${}^3$He${}^{+}$ $g_I^{\prime }=-4.2550996069(30{)}_{stat}(17{)}_{sys}$, the zero-field hyperfine splitting $E_{\mathrm{HFS}}^{\exp }=-8665649865.77(26{)}_{stat}(1{)}_{sys}$ Hz and the bound electron $g$-factor $g_e^{\text{exp}}=-2.00217741579(34{)}_{stat}(30{)}_{sys}$. The latter is consistent with our theoretical value $g_e^{\text{theo}}=-2.00217741625223(39)$ based on parameters and fundamental constants from [12]. Our measured value for the ${}^3$He${}^{+}$ nuclear $g$-factor allows for the determination of the $g$-factor of the bare nucleus $g_I=-4.2552506997(30{)}_{stat}(17{)}_{sys}(1{)}_{theo}$ via our accurate calculation of the diamagnetic shielding constant [13] ${\sigma }_{{}^{3}H{e}^{+}}=0.00003550738(3)$. This constitutes the first direct calibration for ${}^3$He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value [14] and enables us to determine the Zemach radius [15] to $r_Z=2.608(24)$ fm.

References in corpus (23)

• Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm
• High-precision measurement of the atomic mass of the electron
• Complete two-loop correction to the bound-electron g factor
• Frequency metrology in quantum degenerate helium: Direct measurement of the 2 3S1 - 2 1S0 transition
• Muon (g-2) Technical Design Report
• High-precision measurement of the proton's atomic mass
• Testing fundamental interactions on the helium atom
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• First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a Penning trap
• Resolution of Single Spin-Flips of a Single Proton
• Penning-trap mass measurements of the deuteron and the HD+ molecular ion
• Anomalous magnetic moment of a bound electron
• Hyperfine structure in hydrogen and helium ion
• Extraction of the electron mass from $g$ factor measurements on light hydrogenlike ions
• QED theory of the nuclear magnetic shielding in hydrogen-like ions
• Ultrasensitive 3He magnetometer for measurements of high magnetic fields
• Zemach moments of 3He and 4He
• Sympathetic Cooling of Protons and Antiprotons with a Common Endcap Penning Trap
• Nuclear Corrections to Hyperfine Structure in Light Hydrogenic Atoms
• QED calculation of the nuclear magnetic shielding for hydrogen-like ions
• Zeeman effect of the hyperfine structure levels in hydrogenlike ions
• Fragility of surface states in topological superfluid ${}^3$He

Cited by in corpus (17)

• Penning-Trap Mass Measurement of Helium-4
• Testing Standard Model extensions with few-electron ions
• Precision spectroscopy on ${}^9$Be overcomes limitations from nuclear structure
• Higher-order QED corrections to the hyperfine splitting in ${}^3$He
• Nuclear polarizability effects in ${}^3$He${}^{+}$ hyperfine splitting
• Nuclear magnetic shielding in heliumlike ions
• Improved bound-electron g-factor theory through complete two-loop QED calculations
• Accurate determination of ${}^{6,7}$Li nuclear magnetic moments
• Measurement of the g factor of ground-state 87Sr at the parts-per-million level using co-trapped ultracold atoms
• Hadronic vacuum polarization correction to the bound-electron $g$ factor
• Trap-integrated fluorescence detection based on silicon photomultipliers in a cryogenic Penning trap
• Axion detection via superfluid ${}^3$He ferromagnetic phase and quantum measurement techniques
• Smallness of the nuclear polarization effect in the hyperfine structure of heavy muonic atoms as a stimulus for next-generation experiments
• Quantum science with arrays of metastable helium-3 atoms
• Precision magnetometry at cryogenic temperatures with gaseous 3He NMR probes
• Magnetic shielding in the atomic hydrogen anion
• Extended Kalman Smoothing of Free Spin Precession Signals for Accurate Magnetic Field Determination