Hundís rule

 

In systems with multiple electrons within an LS coupled subshell, terms with high S and low L tend be the most tightly bound.

 

Low L means elliptic orbits, which spend more time close to the nucleus.

 

WHY HIGH S ?

 

High values of S occur when the electron spins are aligned (all have the same ms), causing the spin portion of the wave function to be symmetric.

 

The space portion of the wave function must then be antisymmetric, and the Pauli exclusion principle prevents the equivalent electrons from occupying the same region of space.

 

Thus the inter-electron repulsion is reduced thereby increasing the binding.

 

CONCLUSION:A Bose condensation in spin-space produces a Pauli exclusion in configuration space.

 

 

WHEREAS FOR LOW S,

 

For systems with low S, the spins are anti-aligned pairwise, with anti-symmetric wave functions.

 

Thus the spatial wave function is symmetric and the equivalent electrons can overlap in space, increasing their repulsive interaction.

 

CONCLUSION: A Pauli exclusion in spin-space produces a Bose condensation in configuration space.

 

 

Ferromagnetism

 

The high S of the ground state has implications in, eg, the high spin magnetism in the partially filled 3d shell of ferromagnetic atoms.