Stochastic model for induced consecutive transitions with application to Rydberg angular momentum transfer

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Abstract
Theory is offered for a stochastic model describing induced excitation and transfer, decay, and subsequent detection of particles occupying a finite manifold of states. In intense excitation‐transfer fields k the observed particle density for excited states becomes ρ″∝kt−1/σΔl, where t is the excitation time and σΔl is a phenomenological cross section characteristic of transfer between states in the manifold. Formulas are derived which relate σΔl simply to parameters governing the experiment, and thus provide insight to values of σΔl measured for electron impact excitation and angular momentum transfer of high‐Rydberg atoms. A problem is posed wherein the model is generalized to include a variable dimensionality as one way of introducing nonlinearity for transition cross sections connecting states in the manifold.