Electronic Properties of Tin and Bismuth from Angular Correlation of Annihilation Photons

A linear slit setup has been used to obtain results of angular-correlation measurements in (a) tin single crystals in three orientations: [001], [100], and [110], (b) bismuth single crystals in four orientations: [111], [100], [1¯10], and [2¯1¯1], (c) solid and liquid tin and bismuth, and (d) deformed bismuth.

For both metals, the single-crystal angular-correlation curves lie near to the free-electron parabola. The tin curves show more anisotropy than the bismuth curves. An important result is the clear anisotropy found in the high-momentum part of the curves—the tails—for both metals. Little agreement is found between simple theoretical models and these results.

A calculation of the curves based on the one-electron theory of valence electrons in metals would be highly desirable. The peaks of the liquid-metal curves are narrower than the peaks of the polycrystalline curves. The tails of the liquid-metal curves are smaller and of another form than the tails of polycrystalline curves; no Gaussian with only one adjustable constant factor can give a fit to both tails.

No useful method for interpreting liquid-metal angular-correlation curves seems to exist. Two deformed bismuth samples gave angular-correlation curves nearly equal to the polycrystalline curves.