Positron Annihilation in Yttrium and Zirconium

The angular dependence of the positron annihilation radiation along the [0001] direction has been studied in yttrium and zirconium by the augmented-plane-wave method. The calculation was performed using a mesh of 250 points distributed uniformly throughout the $\frac{1}{24}$ zone. A set of 32 reciprocal lattice vectors was used to determine the eigenvalues and eigenfunctions. Exchange was treated in the Slater's ${\rho }^{\frac{1}{3}}$ approximation. The calculated curve for yttrium shows a fairly good agreement with the experimental results of Williams and Mackintosh. The theory predicts a more pronounced hump in the curve near the zone boundary than is observed experimentally. The experimental data for zirconium are not available, but the calculation shows that the hump almost disappears as the $d$ shell starts filling in.