How do neutrons gain energy from phonon scattering?

[FillBill]

So during neutron scattering in a crystal, a neutron can interact with 0, 1, or more phonons. First of all, what is the actual mechanism by which they interact? My textbook just kind of glosses over that.

Second of all, when a neutron goes in it can absorb a phonon and come out with more energy than it came in with. This must mean the energy comes from the crystal, right? But what energy, just the thermal energy of the atoms?

So, if you scattered neutrons off a solid at 0K, would it only give energy to the crystal, not take it at all?

 

[snorkack]

So during neutron scattering in a crystal, a neutron can interact with 0, 1, or more phonons. First of all, what is the actual mechanism by which they interact? My textbook just kind of glosses over that.

Simple nucleon-nucleus scattering - same as when neutron scatters in a gas. Mainly strong interaction, with some contributions from electromagnetic and weak.

Second of all, when a neutron goes in it can absorb a phonon and come out with more energy than it came in with. This must mean the energy comes from the crystal, right? But what energy, just the thermal energy of the atoms?

Yes. Thermal energy in a crystal consists of phonons.

Basically, whenever a neutron scatters off a loose nucleus in a gas, it transfers some momentum to the nucleus. But the effect on neutron energy depends on the velocity of the gas. In a gas where temperature is 0 and all nuclei are stationary in one frame, in that frame the neutrons can only lose energy, not gain.

In a crystal, the nuclei are unable to have a free choice of momentum and energy. The neutron may scatter off a nucleus so that the whole crystal takes the rebound momentum. Or else the neutron creates phonons - quantized movements inside the crystal. Or else phonons give energy to the neutrons.

So, if you scattered neutrons off a solid at 0K, would it only give energy to the crystal, not take it at all?

Yes. There is no energy to take at all.

 

[RedSonja]

Phonons are the vibrational modes of the crystal lattice. The mechanism for inelastic scattering of neutrons may be very simply described as this: When the neutron hits the nucleus of an atom in the crystal, energy may be transferred from the neutron to the nucleus and it will start oscillating. Due to EM interactions this motion will make the nearby atoms oscillate as well, the motion will spread out over the lattice and the effect is that a phonon is excited. Depending on the properties (interatomic distances) of the lattice only phonons of certain frequencies can be created.

If the nuclei are already oscillating (i.e. there is a phonon) the neutron may steal the vibrational energy upon collision.

So, if you scattered neutrons off a solid at 0K, would it only give energy to the crystal, not take it at all?

Yes! At temperatures below ~10 K there are no thermally excited phonons present, therefore you will only see scattered neutrons with less energy than the incoming neutrons.