between and is , twice as the separation between and is . As for the spin-spin interaction responsible for the hyperfine structure, because the Hamiltonian of the hyperfine interaction can be written as where is the nuclear spin and is the total angular momentum, we also have an interval rule: where is the total angular momentum . The derivation is essentially the same, but with nuclear spin , angular momentum and total angular momentum . Limitations The interval rule holds when the coupling is weak. In the LS-coupling scheme, a weak coupling means the energy of spin-orbit coupling is smaller than residual electrostatic interaction: . Here the residual electrostatic interaction refers to the term including electron-electron interaction after we employ the central field approximation to the Hamiltonian of the atom. For the hyperfine structure, the interval rule for two magnetic moments can be disrupted by magnetic quadruple interaction between them, so we want . For example, in helium, the spin-spin interactions and spin-other-orbit interaction have an energy comparable to that of the spin-orbit interaction. References Atomic physics