Consequences of the conservation of matrix element in an APW interpolation scheme for Fermi surfaces

Abstract Using the ‘on the Fermi sphere’ approximation for the matrix elements in an APW interpolation scheme for Fermi surfaces, the existence of focus points, recently introduced by O.K. Andersen, is shown to follow from the conservation of these matrix elements at varying the value of the Fermi energy parameter E F . In this approximation the slopes ∂α ι /∂ E F of the logarithmic derivatives α ι can be calculated and the focus point radii S ι can be found. Without this approximation it is found that there still remains a strong correlation between the experimental ∂α ι /∂ E F . Finally it is shown empiricly that neither the focus point parameter set { S ι , α ι ( S ι )} nor the linear approximation to the experimental α ι can be used for an accurate description of the Fermi surfaces of white tin and copper over a large range of E F .