The system experiences a spherically symmetric potential russell saunders coupling pdf. In this model the atomic Hamiltonian is a sum of kinetic energies of the electrons and the spherically symmetric electron-nucleus interactions. That is, they are conserved properties of this approximate model of the atom.
A rigid rotor has a well-defined, time-independent, angular momentum. These two situations originate in classical mechanics. However, all rules of angular momentum coupling apply to spin as well. If two or more physical systems have conserved angular momenta, it can be useful to combine these momenta to a total angular momentum of the combined system—a conserved property of the total system. Application of angular momentum coupling is useful when there is an interaction between subsystems that, without interaction, would have conserved angular momentum. By the very interaction the spherical symmetry of the subsystems is broken, but the angular momentum of the total system remains a constant of motion.
Use of the latter fact is helpful in the solution of the Schrödinger equation. When there is interaction among the subsystems, the total Hamiltonian contains terms that do not commute with the angular operators acting on the subsystems only. Collections of particles also have angular momenta and corresponding quantum numbers, and under different circumstances the angular momenta of the parts couple in different ways to form the angular momentum of the whole. Angular momentum coupling is a category including some of the ways that subatomic particles can interact with each other. One of its effects is to separate the energy of internal states of the atom, e. This interaction is responsible for many of the details of atomic structure.
This is an approximation which is good as long as any external magnetic fields are weak. LS coupling term becomes small. In heavier atoms the situation is different. In atoms with bigger nuclear charges, spin-orbit interactions are frequently as large as or larger than spin-spin interactions or orbit-orbit interactions. Term symbols are used to represent the states and spectral transitions of atoms, they are found from coupling of angular momenta mentioned above.