# Neutron vs electron degeneracy pressure

• I
How is neutron degeneracy pressure able to support a much higher density object such as a neutron star where electron degeneracy pressure only supports a comparatively less dense object such as a white dwarf. Conceptually I would think electron degeneracy pressure to be stronger due to the charge of electrons pushing off another.

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Drakkith
Staff Emeritus
As far as I know, electron degeneracy has little if anything to do with the repulsive force from their like electric charges. Instead it is the result of the electrons running out of low energy states to occupy and being forced into higher energy states. This higher energy state requires more energy, and hence takes more pressure to kick the electron up to that state than lower energy states do.

I think the much greater degeneracy pressure of neutrons is due to their much greater mass, which increases the energy of each of their states.

As always, someone correct me if I'm wrong.

mfb
Mentor
At the same density electron degeneracy pressure is larger. That's why white dwarfs are supported by it. If the electron degeneracy pressure gets too large then electron capture (proton+electron -> neutron+neutrino) become energetically favorable and the electron degeneracy pressure cannot increase more. If the mass is too large the object collapses. The created neutrons don't have a mechanism where they could disappear, their degeneracy pressure can grow to much larger values in a more compact object.

Drakkith
Drakkith
Staff Emeritus
Can you elaborate on why electron degeneracy pressure is larger for the same density, mfb?

mfb
Mentor
Electrons are lighter, their energy states are further apart.
$$P=\frac{(3 \pi^2)^{2/3} \hbar^2}{5 m}\rho^{5/3}$$
This applies separately for each particle type where ##\rho## is the density of free particles of this type and m is their mass. As you can see from the mass in the denominator lighter particles lead to a higher pressure at the same density.

Astronuc and Drakkith
What is the name of this equation and what is the scope of this equation for what it pertains to specifically. Is this for all subatomic particles?

mfb
Mentor
It applies to all cold* fermions. I'm not aware of a special name for it. You can find it e.g. on Wikipedia.

*not highly relativistic

Ken G
Gold Member
Physically, what is happening is that if you specify the particle density, you are setting the interparticle spacing. If you also specify that the particles are degenerate, it implies that the interparticle spacing is comparable to the particle deBroglie wavelength, which is inversely proportional to the particle momentum. Hence the momentum is fixed by the interparticle spacing, but that makes the particle speed inversely proportional to the mass. Pressure relates to momentum flux, not just momentum, so when the momentum per particle is fixed by the particle density, lower mass means higher speed which means higher rate of momentum flux which means higher pressure.

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Drakkith
Can we say Pauli exclusion principle is evident in electron degeneracy pressure.
Also at neutron star stage ,is there too some principle like Pauli exclusion principle at work?

Drakkith
Staff Emeritus