Hundís rule

 

Question:

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

 

Answer:

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

 

WHY HIGH S ?

High S values occur when 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 is then antisymmetric, so the Pauli exclusion principle prevents the equivalent electrons from occupying the same region of space.The inter-electron repulsion is thus reduced, increasing the binding.

 

CONCLUSION:

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

 

WHAT ABOUT 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 so 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, e.g., the high spin magnetism in the partially filled 3d shell of ferromagnetic atoms.