where ⟨ ⟨ m ⟩ ⟩ is the average atomic mass, ω ω κ κ p , α α and d κ κ p , α α are the frequency and atomic displacement due to a phonon with polarization α α and momentum κ κ p , and | κ κ e , i ⟩ ⟩ is the electron wavefunction for an electron with momentum κ κ e in band i. From Fermi's golden rule