Ionization Energy of Metastable ^{3}He (2 ^{3}S_{1}) and the Alpha- and Helion-Particle Charge-Radius Difference from...

The current experimental and theoretical values of the ionization energy of metastable ^{4}He [(1s)(2s) ^{3}S_{1}] differ by 9σ, which prevents the determination of the alpha-particle charge radius from spectroscopic measurements in ^{4}He. To help clarify the origin of this discrepancy, we report on a precision measurement of hyperfine-resolved transitions from the (1s)(2s) ^{3}S_{1} metastable state of ^{3}He to high np Rydberg states converging on the F^{+}=0, 1 hyperfine levels of the ^{3}He^{+} (1s) ^{2}S_{1/2} ground state. Rydberg-series extrapolation using multichannel quantum-defect theory (MQDT) enabled the determination of the ionization energy of the (1s)(2s) ^{3}S_{1} state of ^{3}He [E_{I}(^{3}He)/h=1 152 788 844.6154(77)_{stat}(25)_{sys}  MHz] and of the corresponding isotopic shift [(E_{I}(^{4}He)-E_{I}(^{3}He))/h=53 898.093(9)  MHz]. The MQDT analysis also permitted the quantification of singlet-triplet mixing in the np series induced by the hyperfine interaction. From the isotopic shift of the ionization energy of He, the difference δr^{2} between the squared charge radii of the helion and alpha particles is determined to be 1.060(10)  fm^{2}.