Mass of helium-4 at 9 ppt from the cyclotron frequency ratio ⁴He⁺/¹²C³⁺

We report a precision measurement of the cyclotron frequency ratio ⁴He⁺/¹²C³⁺ using a cryogenic Penning ion trap, producing an atomic mass of ⁴He with fractional uncertainty of 9 x 10^-12. This result enables future Penning trap measurements of the ratio of electron spin-flip frequency to cyclotron frequency in ⁴He⁺ to yield a value for the electron atomic mass with uncertainty below  1 x 10^-11. Our measurement, which effectively references ⁴He directly to ¹²C, combined with our previous measurements of the ⁴He⁺/D₂⁺ and ⁴He⁺/H₂D⁺ ratios [1], adds extra validation to the recent generation of high-precision atomic mass measurements of stable and long-lived isotopes of hydrogen and helium.

[1] M. Medina Restrepo, M.  Fernandez Davila, C. A. Navarro, and E. G. Myers, Phys. Rev. A 112, L040801 (2025).