Expanding \(\exp(\,{\rm i}\,{\bf k}\!\cdot\!{\bf r})\), and keeping the first two terms, the matrix element for a forbidden transition becomes \[\label{e13.146} \langle f|\epsilon\!\cdot\!{\bf p}\,\ex...Expanding \(\exp(\,{\rm i}\,{\bf k}\!\cdot\!{\bf r})\), and keeping the first two terms, the matrix element for a forbidden transition becomes \[\label{e13.146} \langle f|\epsilon\!\cdot\!{\bf p}\,\exp(\,{\rm i}\,{\bf k}\!\cdot\!{\bf r})|i\rangle \simeq {\rm i}\,\langle f|(\epsilon\!\cdot\!{\bf p})\,({\bf k}\!\cdot\!{\bf r})|i\rangle.\] Hence, if the residual matrix element on the right-hand side of the previous expression is non-zero then a “forbidden” transition can take place, albeit at a mu…