The Migdal effect in solid crystals and the role of non-adiabaticity

We systematically apply the Born-Oppenheimer approximation to show that the Migdal effect in a solid crystal is entirely due to non-adiabatic effects, namely the deviation of the wave function from exact factorization of the electronic and nuclear contributions. The matrix element obtained this way matches exactly the result found by means of a previously derived low energy effective theory.