Good point, I forgot the Lennard-Jones potential (often used as a proxy for these kinds of forces) goes repulsive at close distance. It's electrostatic, the fact that the particles are bosons merely means that their ground state is the zero point kinetic energy. Perhaps we should say that the ground state of bosons acts like they have springs between nearest neighbors, whereas the ground state of fermions acts like a Fermi sea and is generally reached while the interparticle forces are still attractive.But they don´t. While in solid diprotium, the molecules do tunnel to rotate around in their positions, the electrons are trapped in molecules. Solid hydrogen is an insulator.
For comparison: He-4 atoms are bosons. But while all He-4 atoms do occupy the same state, they do not occupy the same volume - despite consisting of indistinguishable bosons, ground state helium has a finite density. They still repel.
So it's the compressibility of a material that determines whether the relationship between pressure and density is proportional or something else? If so, is there a way to calculate the amount of compressibility that would give a proportional relationship?Compressibility is more of a local property of matter. If the density is independent on pressure, so pressure increases suddenly for practically no change of density, then the density is constant. If density increases with square of pressure then the planet does not change in radius with added mass.
And if density increases proportional to pressure, as is the case for isothermal ideal gas, then the planet will shrink by itself, without any added mass.