Fermi Surfaces of Thorium and Actinium

The results of a theoretical study of the energy bands and the Fermi surface of thorium calculated by the relativistic-augmented-plane-wave (RAPW) method and of actinium (rigid-band approximation) are reported. A muffin-tin version of the crystal potential was used and the exchange was included in the full ${\rho }^{\frac{1}{3}}$ Slater approximation. A set of 36 reciprocal-lattice vectors was used in the expansion of the wave function, and with this set the energy eigenvalues were converged to within 0.003 Ry at the points of high symmetry. The calculated bands were interpolated by the method of "spline-fits" to obtain the density of states and the Fermi energy. The Fermi surface consists of three distinct pieces: a hole surface shaped like a rounded cube centered at $\Gamma$, electron surface shaped like pairs of lungs centered on the symmetry lines $\Gamma K$, and hole surfaces shaped like dumbbells centered on the symmetry lines $\Gamma L$. The de Haas-van Alphen frequencies are determined and the results compared with the existing experimental data. Assuming a rigid-band model, the present results have been used to predict the Fermi surface of actinium.