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.
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.