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$\cdot $3 (1$^{1}$S-2$^{1}$P), 537$\cdot $0 (1$^{1}$S-3$^{1}$P) and 591$\cdot $4 angstrom (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 angstrom 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$\cdot $3339, 537$\cdot $0293 and 591$\cdot $4121 angstrom with an estimated accuracy of $\pm $ 0$\cdot $0005 angstrom. For $^{3}$He the corresponding figures, obtained by adding the measured shifts to the $^{4}$He wavelengths, are 584$\cdot $3640, 537$\cdot $0577 and 591$\cdot $4466 angstrom. The term values of the upper states of these lines relative to the ionization limit have been redetermined by a new measurement of the Bergman series 3$^{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: $ \matrix \text{I.P.}\ (^{4}\text{He})=198310\cdot 8_{2}\pm 0\cdot 15\,\text{cm}^{-1}, \\ \text{I.P.}\ (^{3}\text{He})=198300\cdot 3_{2}\pm 0\cdot 15\,\text{cm}^{-1}. \endmatrix $ The isotope shift of the ground state, 10$\cdot $50 $\pm $ 0$\cdot $05 cm$^{-1}$, agrees closely with the theoretical prediction. Experimental values for the Lamb shift are obtained by comparing the observed ionization potentials with those obtained from the Dirac theory not including quantum electro-dynamic effects. Using Kinoshita's 39-parameter value, one finds a Lamb shift of - 0$\cdot $7$_{9}$ and - 0$\cdot $8$_{2}\pm $ 0$\cdot $15 cm$^{-1}$ for $^{4}$He and $^{3}$He, respectively. [Added in proof: Using Pekeris's 203-parameter value one finds - 1$\cdot $1$_{9}$ and -1$\cdot $2$_{3}$ cm$^{-1}$, respectively.] The value predicted by Kabir, Salpeter & Sucher is - 1$\cdot $3$_{3}\pm $ 0$\cdot $2 cm$^{-1}$.