Subject: What do (special) relativistically contracted electron orbitals look like?

Say I am observing a hydrogenic gold atom moving at relativistic speeds away from
me.  What does the orbital look like? The inner electrons of gold are moving
already at relativistic speeds, so those moving, relative to the nucleus in my
direction are at subrelativistic speeds. Contrawise, those electrons moving
relative to the nucleus away from me are closer to c. These electrons will
appear heavier and so, to be consistant, closer to the nucleus. Does this result
in an additional (to the length contraction of a sphere) breaking of symmetry?
Is this view consistant with the bulk properties of a relativistic gold bar?
We must expect some asymmetry, or else we could make muon atoms with a mere
frame shift, but going from a spherically symmetric atom to one with only one
rotational axis of symmetry seems a bit odd!

Re: What do (special) relativistically contracted electron orbitals look like?