Can degenerate particles scatter from each other?

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zonde
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Can degenerate particles scatter from each other?
To me it seems obvious that they can't but I want to be sure because I have seen people sort of imply the opposite. My reasoning is that after scattering participating particles have to end up in different quantum states and if participating particles don't have energy to end up above Fermi level they only can remain in the same quantum state as before scattering because other possible states are occupied. And so it would mean they are not scattering at all and are basically transparent to each other.
 

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Fermi Dirac distribution of conduction electron gas in metal for T>0 suggests interaction of electrons including degenerate ones.

Two electrons of opposite spins in 1s of helium atom interact by Coulomb force.
 
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zonde said:
My reasoning is that after scattering participating particles have to end up in different quantum states and if participating particles don't have energy to end up above Fermi level they only can remain in the same quantum state as before scattering because other possible states are occupied.
If the particles are in some Fermi level, they are in bound states, and particles in bound states don't scatter to begin with. Scattering requires that the incoming particles are free, not bound.
 
anuttarasammyak said:
Fermi Dirac distribution of conduction electron gas in metal for T>0 suggests interaction of electrons including degenerate ones.
Yes, but "scattering" is not a good term to use to describe their interaction.
 
In astrophysics Fermi Dirac distribution is applied to volume element. I guess this works for conduction electrons in metals as potential is quite homogeneous across metal. This seems strange for particles in bowl like potential as they should spatially redistribute according to energy levels - particles of lowest energy can be only at the center and higher energy particles would tend to be more towards outside. Is it really solid physics to split potential well into volume elements and calculate quantum levels for each volume element separately? How would they be restricted to volume element? Only by scattering from each other, right? Hence was my question of this thread.
I guess it is still good approximation for degenerate electrons as they are interacting with protons via Coulomb potential. There should be some complicated interplay between hydrostatic equilibrium of protons, degeneracy of electrons and interaction between them via Coulomb potential, right? But not so for neutrons.
 
zonde said:
How would they be restricted to volume element? Only by scattering from each other, right?
Um, no, since, as I've already pointed out, particles in bound states can't scatter to begin with--"scattering" is a process involving free particles, not bound ones.
 
zonde said:
they should spatially redistribute according to energy levels - particles of lowest energy can be only at the center and higher energy particles would tend to be more towards outside
No, this is not correct. The spatial distribution of the wave function is more spread out for higher energy levels than lower, but that does not imply what you are saying here. Indeed, in the general case, you can't even say that a specific particle is "in" a particular energy level; the particles are indistinguishable and the actual state is a huge entangled superposition, not a neat little arrangement where the particles gradually fill up the energy levels. That description, even though it (unfortunately) appears in textbooks, is highly heuristic and should not be used to draw actual inferences about the physics.