我們在 Helium 上的絕對頻率量測有兩個重要的目標，第一個目標是驗證蘭姆位移 (Lamb shift)，蘭姆位移包含在 QED 理論計算中的 5, 6 和 7 階中，對於氦原子 n = 2 個能 階，蘭姆位移計算的不準確度在 0.5 到 2MHz 範圍內，並且主要是由第 7 項貢獻，第二 個目標是推論氦原子核尺寸，藉由測量同一躍遷中的同位素偏移，此時 QED 計算的不 準度很高的項目很大程度上會被消除，並且它給出了同位素之間核電荷半徑的差異。
我們測量了 3He 和 4He 中的 21S0 - 31D2 雙光子躍遷，以 OFC 作為絕對頻率的基準 值，3He 和 4He 中 21S0 - 31D2 的中心頻率分別為 594 384 761.556(12)MHz 和 594 414 291.803(13)MHz，在我們的實驗結果中量測不準度優於 13kHz。在 4 中，我們決定了 目前最精確的 21S0 能階的電離能 (Ionziation energy) 為 960 332 040.823(24)MHz，其 不準度主要受限於理論計算的 3D 能階(20 kHz)的不準度。進一步的推導出 21S0 和 23S1 蘭姆位移分別為 2806.864(24)MHz 和 4058.130(24)MHz，比先前的決定值要 好 1.6 倍，在 4He 的量測中我們也間接決定了 33D1-31D2 為 101 143.889(29)MHz，改 進了先前的結果 11 倍。
在 3He 的實驗量測中，31D2 能階的超精細結構 (Hyperfine structure) 首次被解析， 其測量超精細分離是 139.873(7)MHz。經由我們的測量決定 3He 和 4He 的同位素 移位為 29.530±246(18)GHz。因此，3He 和 4He 的核電荷半徑差 (Difference in the nuclear charge radii) 可以推導為 1.061(25)fm2，另外，結合其他的量測結果，3He 的 33D1-31D2 為 101 058 203(56)kHz，這個決定值改進了先前的結果 90 倍。

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.

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