Nuclear Physics – Why Neutron Degeneracy Pressure is Stronger than Electron Degeneracy Pressure

Question

I am asking about Pauli Exclusion Principle stating that no two fermions can have the same 4 quantum numbers which is why we have periodic table of elements, but straight to my question: despite Pauli Exclusion Principle is not an actual force then why neutron degeneracy pressure is much stronger than electron degeneracy pressure?

Answer 1

Let $\sim$ denote equality to within dimensionless factors dimensional analysis can't determine. Consider a star where the degeneracy pressure is due to $N$ fermions of a mass-$m$ species comprising a proportion $p$ of the stellar mass; for a neutron star, we can take $p=1$, whereas $p$ is very small when the degeneracy pressure is due to electrons.

A gravity pressure $\sim G(Nm/p)^2/R^4$ balances a degeneracy pressure $\sim\hbar^2n^{5/3}/m$, with $n:=N/R^3$ the number density of the relevant species. Hence $R^4\sim\frac{\hbar^2p^2}{Gm^3N^{1/3}}$, and the pressure $\sim G^5N^{10/3}m^{14}/(\hbar^8p^{10})$.

So it's a matter of comparing values of $N^{10/3}m^{14}/p^{10}$. The values of $m/p$ are similar in the two star types, so the neutron's greater mass is crucial. (Also, the neutron star will have greater $N$.)