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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 64, Iss. 4 — Apr. 1, 1974
  • pp: 495–497

Convolution of a time-dependent driven excitation into the decay curve of an arbitrarily cascaded and blended level

L. J. Curtis  »View Author Affiliations

JOSA, Vol. 64, Issue 4, pp. 495-497 (1974)

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An analysis is presented of the instantaneous emission rate from an atomic level that is populated by arbitrary conditions of both collisional excitation and cascade repopulation. The general solution to the rate equations is obtained in terms of transition probabilities, excitation cross sections, and a simple integral operator, and applications are given for the specific examples of impulsive, stepwise, rectangular, gaussian, and modulated excitation conditions.

L. J. Curtis, "Convolution of a time-dependent driven excitation into the decay curve of an arbitrarily cascaded and blended level," J. Opt. Soc. Am. 64, 495-497 (1974)

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  1. L. J. Curtis, Am. J. Phys. 36, 1123 (1968).
  2. This is actually a Laplace transform with a shifted kernel, but we shall not use its inversion properties in the solution of this problem, considering instead its less-common application to multiple integrals. To make clear what each of a set of nested operators acts upon, we have adopted a notation in which a colon denotes an integral operation over a dummy variable [T in Eq. (3)] which occurs on both sides of the colon.
  3. I. Kaplan, Nuclear Physics (Addison-Wesley, Reading, Mass., 1963), p. 232.
  4. G. M. Lawrence and B. D. Savage, Phys. Rev. 141, 67 (1966).
  5. G. M. Lawrence, Phys. Rev. A 2, 397 (1970).

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