Abstract
There are two essential objectives in our work for helium. The first objective is the verifi- cation of the Lamb shift. The Lamb shift is included in the α5, α6, and α7 terms in the QED theoretical calculation where the uncertainty of the Lamb shift ranges from 0.5 to 2 MHz for the n = 2 states and is mainly due to the term in α7. The second objective is the determination of the finite nuclear size. The uncertainty from the QED calculation becomes much smaller for the isotope shift in the same transition. The difference of the nuclear charge radius between isotopes can be derived from the isotope shift. We present the precision measurements for 21S0 - 31D2 two photon transitions in both 3He and 4He. Using an optical frequency comb (OFC) for the frequency metrology, the central frequencies of the 21 S0 -31 D2 in 3 He and 4 He are 594 384 761.556(12) MHz and 594 414 291.803(13) MHz respectively. The experimental uncertainty in our results is better than 13 kHz, which is near the limit of the natural linewidth of 10.36 MHz. In combination with the theoretical ionization energy of the 3D state, the most precise ion- ization energy of the 21S0 state in 4He is determined to be 960 332 040.823(24) MHz, mainly limited by the theoretical uncertainty of the 3D states (20 kHz). Then, the deduced 21S0 and 23S1 Lamb shifts are 2806.864(24) MHz and 4058.130(24) MHz, which are 1.6 times better than previous determinations. The separation of 33D1-31D2 for 4He is 101 143.889(29) MHz, improving the precedent determination by a factor of 11. For the first time, the hyperfine structure of 31D2 state in 3He can be resolved. The measured hyperfine separation is 139.873(7) MHz. Furthermore, the isotope shift of 3He and 4He in the transition is 29.530 246(18) GHz. Therefore, the difference of the nuclear charge radius of 3He and 4He can be deduced to be 1.061(25) fm2. The separation of 33D1-31D2 for 3He is 101 058 203(56) kHz, improving the previous work by a factor of 90.