It is Bohr and Mottelson's discovery that the atomic nuclei is not spherical. This is quite surprising.
A natural question is then, can the atom also be non-spherical?
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https://en.wikipedia.org/wiki/Atomic_orbital. Insufficient effort or am I missing the core of your question? – CuriousOne Aug 08 '16 at 13:58
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Non spherical atoms : http://chemistry.stackexchange.com/questions/13766/why-are-atom-spherical-in-shape no offence meant, I am sure you already know this, but the spherical harmonic functions are not generally spherical, so the atom won't be spherical on that basis. – Aug 08 '16 at 14:09
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Please define what defines the shape of an atom - to me, the assumption of it having a discrete shape itself is surprising. – Sanya Aug 08 '16 at 14:15
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You are thinking classically, the concept of shape (as noted above) is meaningless on this scale. When we see an STM image of an atom in a corral, are we actually seeing the atom, or just a computer produced image based around a region of electric charge? – Aug 08 '16 at 15:03
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The reasons for the existence of pear shaped nuclei are discussed in Why are pear-shaped nuclei possible? and Do pear-shaped nuclei really have anything to do with time travel? The tl;dr version is that the weak force is important in determining the nucleus shape and the weak force violates parity, so it's possible to have a ground state that is not parity symmetric.
However the weak force is too short range to have any effect on the shape of the electronic structure of an atom, so atoms are spherical to within experimental error. In principle there will be deviations from spherical symmetry, but in practice these will be too small to be measurable.
John Rennie
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