Half-cycle pulse acting on a one-dimensional Rydberg atom: Semiclassical transition amplitudes in action and angle variables
- 1 February 1995
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 51 (2) , 1030-1041
- https://doi.org/10.1103/physreva.51.1030
Abstract
In this paper we derive the expression for the transition coefficient used in the preceding paper [C. D. Schwieters and J. B. Delos, Phys. Rev. A 51, 1023 (1995)] for principal-quantum-number transitions in one-dimensional hydrogen caused by half-cycle pulses. We briefly review the methods of Miller [Adv. Chem. Phys. 25, 69 (1974)] and Marcus [Chem. Phys. Lett. 7, 525 (1970); J. Chem. Phys. 54, 3965 (1971)], and then derive the result using the methods of Maslov and Fedoriuk [Semi-Classical Approximation in Quantum Mechanics, (Reidel, Dordrecht, 1981)]. Also, we examine the approximate reduction of hydrogen from three to one dimension and we find a hitherto unknown correction due to the residual motion of one of the ignored degrees of freedom. We discuss the regime of validity of this one-dimensional approximation.Keywords
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