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American Journal of Physics

Coulomb phase shift

Charles W. Clark

Published Aug 1, 1979• 9 citations
Publisher

Abstract

The relationship between the energy derivative of the Coulomb phase shift and the classical expression for the time delay is discussed.
DOI
10.1119/1.11721

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Using a time-dependent scattering theory for light the authors obtain expressions for the time that light spends in a finite dielectric medium surrounded by vacuum, the so-called dwell time. Given an incoming wavepacket, they focus upon the light scattered in an arbitrary direction. In view of the similarity between Maxwell's equations and the Schrodinger equation, some useful results are derived for the case of Schrodinger potential scattering as well. They show that the dwell time of a Schrodinger particle is a derivative of the phase shifts with respect to the potential, rather than to energy as is the case for the phase-delay time. They indicate the relation to absorption arguments. Because the potential for classical waves is energy dependent, derivatives of the phase shift with respect to potential enter into the phase-delay time for classical waves.
We show that the optical dephasing time T2{T}_{2}T2​ can be obtained from a measurement of the time delay T0{T}_{0}T0​ between two shifts of $\ifmmode\pm\else\textpm\fi{}\frac{\ensuremath{\pi}}{2}$ in the phase of the exciting laser for which a null occurs in the jump in the nonlinear transmission through a sample. The phase shift is imposed upon a single-mode cw laser by applying a rectangular voltage pulse to an electro-optic phase modulator placed in the laser beam. The time delay at which the null occurs is proportional to T2{T}_{2}T2​, which is given by the expression T2=(2ln2)T0{T}_{2}=(\frac{2}{\mathrm{ln}2}){T}_{0}T2​=(ln22​)T0​. The method is demonstrated in atomic sodium and iodine vapor and the separation of third-order optical transients from linear transients induced by the phase shift is discussed. An analytic expression for the jump in the nonlinear transmission, induced by the second phase shift, as well as for the transient in transmission following a single phase shift of a laser which weakly saturates an optically thin sample is derived. It is also shown that optical dephasing rates may be inferred from the variation of the integral of the transmitted light in a double-phase-switching experiment.
A relationship between the low-energy antiproton-atom scattering parameters and Coulomb level shifts is derived. The corresponding scattering lengths are calculated for the p\ifmmode\bar\else\textasciimacron\fi{}-He+{\mathrm{He}}^{+}He+ system on the basis of energy level shifts evaluated earlier by means of the Born-Oppenheimer approximation.