Editing Population inversion (section)

== Selection rules ==
{{Main|Selection rule}}
Many transitions involving electromagnetic radiation are strictly forbidden under quantum mechanics. The allowed transitions are described by so-called [[selection rule]]s, which describe the conditions under which a radiative transition is allowed. For instance, transitions are only allowed if Δ''S''&nbsp;=&nbsp;0, ''S'' being the total spin angular momentum of the system. In real materials, other effects, such as interactions with the crystal lattice, intervene to circumvent the formal rules by providing alternate mechanisms. In these systems, the forbidden transitions can occur, but usually at slower rates than allowed transitions. A classic example is [[phosphorescence]] where a material has a ground state with ''S''&nbsp;=&nbsp;0, an excited state with ''S''&nbsp;=&nbsp;0, and an intermediate state with ''S''&nbsp;=&nbsp;1. The transition from the intermediate state to the ground state by emission of light is slow because of the selection rules. Thus emission may continue after the external illumination is removed. In contrast [[fluorescence]] in materials is characterized by emission which ceases when the external illumination is removed.

Transitions that do not involve the absorption or emission of radiation are not affected by selection rules. The radiationless transition between levels, such as between the excited ''S''&nbsp;=&nbsp;0 and ''S''&nbsp;=&nbsp;1 states, may proceed quickly enough to siphon off a portion of the ''S''&nbsp;=&nbsp;0 population before it spontaneously returns to the ground state.

The existence of intermediate states in materials is essential to the technique of optical pumping of lasers (see below).