Ionization potentials and Lamb shifts of the ground states of 4 He and 3 He

Abstract
In order to obtain an experimental value for the Lamb shift of the ground state of helium it is necessary to determine a very precise value for the ionization potential. For this pur­pose the wavelengths of the far ultra-violet lines 584·3 (1 1 S -2 1 P ), 537·0 (1 1 S -3 1 P ) and 591·4 Å (1 1 S -2 3 P 1 ) of 4 He have been redetermined with much improved accuracy and those of 3 He have been measured for the first time. The standards used were lines of C + and A + in the region 610 to 520 Å which were derived by means of the combination principle from lines at longer wavelengths. The final results for the wavelengths of the 4 He lines are 584·3339, 537·0293 and 591·4121 Å with an estimated accuracy of ± 0·0005 Å. For 3 He the corresponding figures, obtained by adding the measured shifts to the 4 He wavelengths, are 584·3640, 537·0577 and 591·4466 Å. The term values of the upper states of these lines relative to the ionization limit have been redetermined by a new measurement of the Bergman series 3 3 D – n 3 F , of the intercombination lines 2 3 P –3 1 D and 2 1 P –3 3 D and a remeasurement of the near ultra-violet 2 1 P – n 1 D and 2 3 P – n 3 D series. Combining these results with those of the far ultra-violet lines the following values for the ionization potentials of 4 He and 3 He are obtained: I. P. ( 4 He) = 198310·8 2 ± 0·15 cm -1 , I. P. ( 3 He) = 198300·3 2 ± 0·15 cm -1 . The isotope shift of the ground state, 10·50 ± 0·05 cm -1 , agrees closely with the theoretical prediction. Experimental values for the Lamb shift are obtained by comparing the observed ioniza­tion potentials with those obtained from the Dirac theory not including quantum electro-dynamic effects. Using Kinoshita’s 39-parameter value, one finds a Lamb shift of —0·7 9 and —0·8 2 ± 0·15 cm -1 for 4 He and 3 He, respectively. [ Added in proof : Using Pekeris’s 203-parameter value one finds —1·1 9 and —1·2 3 cm -1 , respectively.] The value predicted by Kabir, Salpeter & Sucher is —1·3 3 ± 0·2 cm -1 .

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