On the Ground State of Lithium

Wave functions of several forms have been applied to the treatment to the ground state of Li. It is found that errors in the representation of the $K$ shell have but little effect on the computed ionization energy, and that a satisfactory orbital for the $L$ electron can be constructed in a very simple form. The best wave function in which the relative positions of the $K$ and $L$ electrons are not taken into account gives an ionization energy in error by 0.05 ev. To take account of inter-shell polarization effects the Hylleraas method has been extended, and a wave function has been constructed which depends on the relative positions of all the electrons. A total energy in error by 0.068 ev (0.034 percent) has been computed, and the theoretical value of the ionization energy is fixed as 5.363±0.007 ev against an observed 5.364 ev.