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\sect{Fermions in gravitation field of a star}

Consider a neutron star as non-relativistic gas of non-interacting
neutrons of mass ${\mathsf{m}}$ in a spherical symmetric equilibrium
configuration. The neutrons are held together by a gravitational
potential ${\frac{-\mathsf{m}MG}{r}}$ of a heavy object of mass M
and radius ${r_{0}}$ at the center of the star (${G}$ is the gravity
constant and ${r}$ is the distance from the center).

Assume that the neutrons are classical (Boltzmann) particles at
temperature ${T}$ and find their density ${n\left(r\right)}$ at
${r>r_{0}}$. Is the potential confining? [By definition, for a
confining potential there a solution with ${n\left(r\right)-->0}$ at
${r-->\infty]}$. Next, consider the neutrons as fermions at ${T=0}$,
and find ${n\left(r\right)}$. Is the potential confining??? Extend
your result to the case ${T\neq 0}$, and discuss the connection with
the Boltzmann limit.


