  We hypothesize that in a non-metallic crystalline structure under extreme
pressures, atomic wavefunctions deform to adopt a reduced rotational symmetry
consistent with minimizing interstitial space in the crystal. We exemplify with
a simple numeric variational calculation that yields the energy cost of this
deformation for Helium to 25%. Balancing this with the free energy gained by
tighter packing we obtain the pressures required to effect such deformation.
The consequent modification of the structure suggests a decrease in the
resistance to tangential stress, and an associated decrease of the crystal's
shear modulus. The atomic form factor is also modified. We also compare with
neutron matter in the interior of compact stars.
