Expanding exp(ik⋅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(ik⋅r), and keeping the first two terms, the matrix element for a forbidden transition becomes ⟨f|ϵ⋅pexp(ik⋅r)|i⟩≃i⟨f|(ϵ⋅p)(k⋅r)|i⟩. 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…
