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I have a problem to solve in Cosmology which says:

*"Write the formulas for the quantum kinetic energy of neutrons, protons and electrons as well as the formula for the gravitational energy for a neutron star that is comprised of free neutrons, protons and electrons in a ratio of N*

The numerical coefficients should be these for homogeneous density."

_{n}: N_{p}: N_{e}= 93,4 : 6,6 : 6,6 (N_{ν}=N_{n}+N_{n}=1,8x10^{57})The numerical coefficients should be these for homogeneous density."

Attempt for solution

I find in the book "From Quarks to Quasars" by E.N.Economou that the total quantum kinetic energy of neutrons is 92,14% of the total, U

_{k,tot}=U

_{k,n}/0,9214=(α

_{κ}/0,9214)ħ

^{2}N

^{5/3}/(m

_{n}R

^{2}). The coefficients are a

_{κ}=1,1.

This equation is derived from the total kinetic energy of N fermionic particles (s=1/2) that are similar and non relativistic.

And my question is:

**How can this equation be used for neutrons (and protons) which are bosons and don't follow Fermi's exclusion principle (where this equation is derived from)?**