Angular Dependence of Matrix Elements for Scattering in III-V Compounds

We have calculated the overlap integral between periodic parts of Bloch functions for two arbitrarily directed crystal momenta

{\vec{k}}_{1}

and

{\vec{k}}_{2}

. Contrary to conjectures in the literature that there is a dependence on the direction of

{\vec{k}}_{1}

in addition to the angle between

{\vec{k}}_{1}

and

{\vec{k}}_{2}

, our results show only an angular dependence on

\frac{({\vec{k}}_{1} \cdot {\vec{k}}_{2})}{(k_{1} k_{2})}

. The final expression obtained is identical in form with results previously deduced by aligning

{\vec{k}}_{1}

with a principal axis of the crystal.

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