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

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 (11S-21P), 537·0 (11S-31P) and 591·4 Å (11S-23P1) of 4He have been redetermined with much improved accuracy and those of 3He 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 4He lines are 584·3339, 537·0293 and 591·4121 Å with an estimated accuracy of ± 0·0005 Å. For 3He the corresponding figures, obtained by adding the measured shifts to the 4He 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 33D–n3F, of the intercombination lines 23P–31D and 21P–33D and a remeasurement of the near ultra-violet 21P–n1D and 23P–n3D series. Combining these results with those of the far ultra-violet lines the following values for the ionization potentials of 4He and 3He are obtained: I. P. (4He) = 198310·82 ± 0·15 cm-1, I. P. (3He) = 198300·32 ± 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 —0·79 and —0·82 ± 0·15 cm-1 for 4He and 3He, respectively. Added in proof: Using Pekeris’s 203-parameter value one finds —1·19 and —1·23 cm-1, respectively. The value predicted by Kabir, Salpeter & Sucher is —1·33 ± 0·2 cm-1.