# Would a neutron star-like celestial body made of bosons collapse because of missing Pauli repulsion?

Imagine the neutron star-like celestial body would be built up of bosons (assume that neutrons would be bosons). In that case there would be no Pauli repulsion (the exchange force of the exchange interaction would not be repulsive), so this would apparently lead to an immediate collapse of the neutron star. Whereas the argument for the repulsive exchange force is based on Pauli's principle, in case of bosons could not Heisenberg's uncertainty relation take up a similar role ? If $$n$$ particles are pressed in a smaller and smaller volume $$V$$ according to Heisenberg's uncertainty relation their momentum should increase like $$\Delta p = \hbar \cdot (V/n)^{-1/3}$$, this would generate an enormous pressure and may be prevent the star from collapsing ? I could be even more inquisitive and asking: Has Heisenberg's uncertainty relation ever been tested with bosons? If so, and as I've never heard about an invalidity of the uncertainty relation, can the uncertainty relation save the neutron star from collapsing ? Or is there a flaw in my reasoning ?