The stability of the electrons in an atom itself is not related to the exclusion principle, but is described by the quantum theory of the atom. The underlying idea is that close approach of an electron to the nucleus of the atom necessarily increases its kinetic energy, an application of the uncertainty principle of Heisenberg. However, stability of large systems with many electrons and many nuclei is a different matter, and requires the Pauli exclusion principle.
It has been shown that the Pauli exclusion principle is responsible for the fact that ordinary bulk matter is stable and occupies volume. This suggestion was first made in 1931 by Paul Ehrenfest, who pointed out that the electrons of each atom cannot all fall into the lowest-energy orbital and must occupy successively larger shells. Atoms therefore occupy a volume and cannot be squeezed too closely together.
A more rigorous proof was provided in 1967 by Freeman Dyson and Andrew Lenard, who considered the balance of attractive (electron-nuclear) and repulsive (electron-electron and nuclear-nuclear) forces and showed that ordinary matter would collapse and occupy a much smaller volume without the Pauli principle. The consequence of the Pauli principle here is that electrons of the same spin are kept apart by a repulsive exchange interaction, which is a short-range effect complemented by the long-range electrostatic or coulombic force. This effect is therefore partly responsible for the everyday observation in the macroscopic world that two solid objects cannot be in the same place in the same time.
However, Dyson and Lenard did not consider the extreme magnetic or gravitational forces which occur in some astronomical objects. In 1995, Elliott Lieb and coworkers showed that the Pauli principle still leads to stability in intense magnetic fields such as in neutron stars, although at a much higher density than in ordinary matter. It is a consequence of General Relativity that in sufficiently intense gravitational fields, matter collapses to form a black hole.
Astronomy provides another spectacular demonstration of this effect (the Pauli_exclusion_principle), in the form of white dwarf stars and neutron stars. For both bodies, the usual atomic structure is disrupted by large gravitational forces, leaving the constituents supported by "degeneracy pressure" alone. This exotic form of matter is known as degenerate matter. In white dwarfs, atoms are held apart by electron degeneracy pressure. In neutron stars, which exhibit even more intense gravitational forces, electrons have merged with protons to form neutrons. Neutrons are capable of producing an even higher degeneracy pressure, albeit over a shorter range.
Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. The force provided by this pressure sets a limit on the extent to which matter can be squeezed together without it collapsing into a neutron star or black hole. It is an important factor in stellar physics because it is responsible for the existence of white dwarfs.
An effect of degeneracy pressure is to raise the energy of the neutrons, so yes---it does cause more collisions (which occur via coulomb and strong interactions). Degeneracy pressure itself is a purely quantum-mechanical/statistical effect, its not 'communicated' via any of the fundamental forces.but how is the degeneracy communicated in a neutron star. I mean, if there is that pressure, does it generate collisions to other neutrons? in such collisions, what is the force involved?