I understand that in elastic scattering, the incident particle leaves the interaction with the same magnitude of momentum it had initially. But, can there also be a target particle recoil in this case? If the kinetic energy of the incident particle is conserved, how does the target particle acquire kinetic energy in recoiling? I see two possibilities: 1) the target particle acquires energy from the interaction between the two particles (for example, from the electromagnetic field for Rutherford scattering), or 2) the target particle acquires energy from the incident particle, in which case this doesn't meet the definition of elastic scattering. If this is the case, is "elastic scattering" really just an approximation for when the target particle is really heavy compared to the incident particle? Thanks.