A result in atomic theory stating that the square of the magnitude of the total wavefunction for a full subshell or a half-full subshell in which all the spins of the electrons of the half subshell are parallel spins (i.e. all s-subshells, p-subshells with 3 or 6 electrons, d-subshells with 5 or 10 electrons, f-subshells with 7 or 14 electrons) is spherically symmetric. This theorem determines which atoms are spherical. It was first stated and proved by the German astrophysicist Albrecht Unsöld (1905–95) in 1927, using results concerning the addition of spherical harmonics. Unsöld’s theorem can also be proved in an equivalent way using group theory.