The Einstein A and B Coefficients

Abstract

Consider an ensemble of identical atoms whose states are quantized with energies W _i , W _j , W _k ,..., and with statistical weights W _i , W _j , W _k ,..., respectively. The statistical weight of a level refers to the fact that it may consist of a number w of degenerate states each of which plays its part in any statistical process involving that level. For example, for an atomic level of angular momentum specified by J, there are 2J + 1 states which are degenerate in zero magnetic field. The statistical weight of this state is w = 2J + 1. In general there can be other contributions to the statistical weight such as unresolved hyperfine structures. Consider an atom of two levels only, a lower level of energy W _i and an upper level of energy W _k ,between which radiative transition is allowed. Let it experience an environment of radiation containing the frequency v _ik = (W _k − W _i )/h According to the quantum rules of atom-radiation interaction established in Chapter 7 absorptive transitions are stimulated from level i to level k, and emissive transitions are stimulated from level k to level i. But even if no radiation is present, it is known from observation that spontaneous transitions from level k to level i also occurs.