# Elastic scattering and target recoil

• copernicus1
In summary, elastic scattering is a type of collision where both particles involved in the interaction remain unchanged afterwards. However, there can still be energy and momentum transfer between the particles, even though the kinetic energy of the incident particle is conserved. This transfer can occur through exchange with the incident particle or through the interaction between the particles. The definition of elastic scattering serves as an approximation for when the target particle is much heavier than the incident particle, but it can still occur in other scenarios with small momentum transfer.
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.

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).

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?

## 1. What is elastic scattering?

Elastic scattering is a type of scattering process in which the kinetic energy and momentum of the scattered particles are conserved. This means that the total energy and momentum of the particles before and after the scattering event are the same.

## 2. What is target recoil?

Target recoil refers to the backward motion of a target particle after an elastic scattering event. This recoil is caused by the transfer of momentum from the incident particle to the target particle during the scattering process.

## 3. What factors affect elastic scattering?

The factors that affect elastic scattering include the mass and velocity of the incident particle, the mass and composition of the target particle, and the angle of incidence. The type of interaction between the particles and the energy of the incident particle can also play a role.

## 4. How is elastic scattering used in scientific research?

Elastic scattering is used in a variety of scientific research fields, including nuclear physics, materials science, and particle physics. It is used to study the structure and properties of atoms and nuclei, as well as to investigate the interactions between particles and materials.

## 5. What is the difference between elastic and inelastic scattering?

Elastic scattering is a type of scattering in which the total energy and momentum of the particles are conserved. Inelastic scattering, on the other hand, involves a transfer of energy and/or momentum between the particles, resulting in a change in their total energy and momentum.

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