The Fine Structure of HE as a Test of the Spin Interactions of Two Electrons

Abstract

A tentative expression for the quantum Hamiltonian of two electrons has been set up in a previous paper. The equation is discussed again. It is shown that the last term in it is subject to doubt. The Hamiltonian is tested by applying it to the calculation of the fine structure of the He $2^{3}P$ level. It is found that the above mentioned term in ${e}^{4}$ is in contradiction with experiment. Removing the term from the equation one is left essentially with Heisenberg's old Hamiltonian. The spin interaction in it is shown to agree well with experiment. The calculation has been applied also to ${\mathrm{Li}}^{+}$.The essential improvements on previous work are: (1) an increase in the precision of the unperturbed eigenfunctions; (2) a determination from experimental data of a constant $D$ which depends directly on spin---spin interactions (see Eq. (1) below) and which can be calculated with fair accuracy. Comparing the theoretical and empirical values of $D$ a clearer test of the magnitude of spin---spin interactions can be obtained than by calculating the relative positions of the three components of the triplet. The reason for this is that the relative positions of the lines depend also on another constant $C$ which is a difference of two approximately equal numbers and is more difficult to calculate accurately.