The Decay of Resonance Radiation by Spontaneous Emission

A critical examination of the theory of resonance radiation has been carried through, employing the mathematical technique of Laplace and Stieltjes transforms. Particular attention has been devoted to the question of the temporal behavior of the excited state. With no restrictions on the interaction between atom and radiation field other than that it be real, and that processes of sufficiently high frequency contribute only negligible effects, one can prove that the probability amplitude of the excited state cannot decay according to the general law ${\Sigma }_{\mu ,\nu }{C}_{\mu \nu }{t}^{{\lambda }_{\mu }}{e}^{-{\beta }_{\nu }t},$ where the ${\lambda }_{\mu }$ and ${\beta }_{\nu }$ are complex constants lying in the right half-plane and the $C_{\mu \nu }$ are arbitrary complex coefficients. The deviation from the law just cited can be termed a straggling phenomenon since exact analysis shows that the probability amplitude, for sufficiently long times, is greater than that defined according to the radioactive decay law.