Elastic scattering and target recoil

[copernicus1]

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.

 

[mfb]

I understand that in elastic scattering, the incident particle leaves the interaction with the same magnitude of momentum it had initially.

That is wrong (it would mean no collision happened). If the momentum transfer is small compared to the momentum of the particle, it might be negligible, even if the target momentum is not negligible afterwards. This can happen with very fast and/or very light particles.

1) the target particle acquires energy from the interaction between the two particles (for example, from the electromagnetic field for Rutherford scattering), or

That is not possible in the way you describe. The electric field is conservative.

Elastic scattering just means that both particles stay the same afterwards. There is always energy and momentum transfer (otherwise it is no interaction at all).

 

[copernicus1]

I'm confused. The Wikipedia article on elastic scattering states that the kinetic energy of the incident particle is conserved. If the incident particle's energy doesn't change, and if, from what you say, the target can't acquire energy except through exchange with the incident particle, then what is the point of defining "elastic scattering," if it never actually happens?