{c}
{title2=$E_F-E_{F-1}=aF$}

For dimensionless <angular momentum operators> and a <Hamiltonian> $H=a\mathbf I\cdot\mathbf J$ at fixed $I,J$, <addition of angular momentum> gives $E_F=a[F(F+1)-I(I+1)-J(J+1)]/2$. Subtracting neighbouring <energy levels> proves the displayed rule. For <fine structure> substitute $\mathbf L,\mathbf S$ and total $J$; for magnetic-dipole <hyperfine structure> use electronic $J$, <nuclear spin> $I$ and total $F$. Electric-quadrupole interactions and mixing with nearby <energy levels> can violate the rule.


 Landé interval rule (source code)