Ground State Of Lithium Research Articles

Hyperfine Splitting of the Lithium Ground State

The results of calculations of the hyperfine splitting of the lithium atom ground state are reported. These were done by the Hartree-Fock (HF), unrestricted Hartree-Fock (UHF) and projected UHF approximations to the ground-state eigenfunctions. The exchange polarization effect allowed by the UHF method yields a 34.9% increase in the hyperfine splitting compared to the HF method.

Wave function for the groundstate of lithium

A variational calculation for the groundstate of the lithium atom is carried out with an anti-symmetrical wave function built up out of the core function exp[−K/2(r1+r2] (1+br12) and the valence electron function\(\exp \left[ { - \frac{K}{2}\left( {r_1 + r_2 } \right)} \right]\left( {1 + br_{12} } \right)\) and the valence electron function\(r_3 e^{ - \frac{a}{2}r_3 } \). The resulting improvement in the total energy of the atom is considerable. But contrary to expectation the calculated value of the ionisation potential is much inferior to those previously obtained with simple hydrogen-like core functions. The numerous integrals occurring in the problem are discussed from a uniform viewpoint. A few simple integrals involving either one or two of the inter-electronic distances are first evaluated with the help of two general formulas (D) and (E) of Section 4, and from them the remaining ones are obtained by repeated differentiation with respect to parameters occurring in the exponential part of the integrand. Considerable simplification is achieved thereby and possibilities of errors are also largely eliminated.

Wave Function for the Ground State of Lithium

A variational calculation of the ground state $1{s}^{2}2s^{1}S$ of Li is carried out with the wave function $\ensuremath{\Psi}=\mathrm{exp} (\ensuremath{-}\frac{\ensuremath{\alpha}k{r}_{3}}{2})\mathrm{exp} [\ensuremath{-}\frac{k({r}_{1}+{r}_{2})}{2}][a+bk{r}_{12}+c{k}^{2}{({r}_{1}\ensuremath{-}{r}_{2})}^{2}+dk{r}_{3}]\ensuremath{-}\mathrm{exp} (\ensuremath{-}\frac{\ensuremath{\alpha}k{r}_{2}}{2})\mathrm{exp} [\ensuremath{-}\frac{k({r}_{1}+{r}_{3})}{2}][a+bk{r}_{13}+c{k}^{2}{({r}_{1}\ensuremath{-}{r}_{3})}^{2}+dk{r}_{12}]$The energy comes out to be -14.914 Rh, compared with the value -14.838 Rh obtained by the best wave function not containing terms like ${r}_{12}$ and ${r}_{13}$, and the spectrocopic value -14.956 Rh.

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\ifmmode\pm\else\textpm\fi{}0.007 ev against an observed 5.364 ev.

Wave Functions for the Ground State of Lithium and Three-Electron Ions

Improved wave functions and ionization potentials have been obtained for the configuration 1s2 2s, by using the variation method with a variation function containing four parameters. The wave function for the whole atom is of the determinant form, built up of K and L single-electron functions. The K function used is hydrogen-like with one parameter, the effective nuclear charge, and the L function is of the form αre—ηr—e—ζr. A simple rule is obtained by means of which it is possible to write down the wave function for any three-electron ion without further calculation. The deviation of the calculated ionization potentials from the observed values is 0.9 percent for Li I and decreases to 0.3 percent for C IV. Comparison is made with the results of other investigators and curves showing the wave functions and electron density functions are given.