Welcome to Physics Forums. The recoil energy is p^{2}/2m, where p=h/λ is the momentum of a lattice photon and m is the mass of an atom or ion trapped in the lattice. The recoil energy is the kinetic energy an atom (or ion) would have after emitting a photon, if initially at rest.
Hi, Recoil energy E=Mv^{2}/2=p^{2}/(2M)=E_{p}^{2}/(2Mc^{2})=([tex]\hbar[/tex]k)^{2}/(2M). M=mass of something (nucleus, atom, ion, etc), which emits photons. v=recoil velocity due to emission of photons. p=momentum. E_{p}= Energy of the emitted photons. c=velocity of light in vacuum. k=wave vector.