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Journal of Physics B Atomic Molecular and Optical Physics

Rayleigh and Raman scattering by hydrogen and caesium

H. R. Sadeghpour, A. Dalgarno

Published Nov 28, 1992• 31 citations
Publisher

Abstract

An inhomogeneous differential equation method is used to calculate the Rayleigh and Raman scattering cross sections for atomic hydrogen and atomic caesium as functions of wavelengths below and above the ionization limits. The profile of the scattering cross section near the 6s-6p resonance of atomic caesium is determined by including an energy-independent radiative width in the scattering formula. The effect of replacing the electric dipole operation by a modified form that takes account of the polarization of the core by the valence electron is explored.

DOI
10.1088/0953-4075/25/22/015

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An inhomogeneous differential equation method is used to calculate the Rayleigh and Raman scattering cross sections for atomic hydrogen and atomic caesium as functions of wavelengths below and above the ionization limits. The profile of the scattering cross section near the 6s-6p resonance of atomic caesium is determined by including an energy-independent radiative width in the scattering formula. The effect of replacing the electric dipole operation by a modified form that takes account of the polarization of the core by the valence electron is explored.
Quantum-mechanical expressions for nonresonance-dipole light-scattering cross sections are related to corresponding expressions for oscillator strengths and refractive indices. In particular, Rayleigh and Raman cross sections for atoms are expressed in terms of oscillator strengths and vector-coupling coefficients. Several of our results, including the relationship between Rayleigh scattering and refractive index, differ in general from the corresponding results of classical dispersion theory. We show that these differences arise from antisymmetric components Ckja = (Ckj − Cjk)/2 of the polarizability tensor, which have been neglected in the classical analyses. Calculated Rayleigh cross sections for cesium and aluminum atoms, and Raman cross sections for aluminum atoms are presented to illustrate our results. The antisymmetric contribution is found to be substantial in all of these cross sections; its most obvious effect is to cause the depolarization (for linearly polarized incident light) to exceed 34 over extended wavelength ranges away from resonance. On the other hand, for atoms initially in states of zero angular momentum, and molecules under conditions which allow the use of Placzek’s polarizability approximation, our results agree with those of classical dispersion theory.
The inelastic Raman scattering of light by hydrogenlike ions has been studied by means of second-order perturbation theory and the relativistic Coulomb Green's-function approach. In particular, we investigate the total and angle-differential Raman cross sections as well as the magnetic sublevel population of the residual (excited) ions. Detailed calculations are performed for the inelastic scattering of photons by neutral hydrogen as well as hydrogenlike xenon and uranium ions, accompanied by the $1{s}_{1/2}\ensuremath{\rightarrow}2{s}_{1/2}$, $1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{1/2}$, and $1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{3/2}$ transitions. Moreover, we discuss how the Raman scattering is affected by relativistic and resonance effects as well as the higher-multipole contributions to the electron-photon interaction.
An experimental and theoretical study is made of Stokes and anti-Stokes Raman scattering from Al, Ga, In, and Tl atoms. Relative phases of 2P01/2,3/2→2D3/2 dipole matrix elements are obtained from the polarization properties of the scattered radiation. For Ga these phases are different from those obtained for Al, In, and Tl, and they are in contrast to what is expected on the basis of single configuration approximations. The experimentally determined phases are used to calculate the Raman cross sections.
The generalized theory of forbidden Raman scattering processes is developed in terms of the multipole expansion of the electromagnetic interaction Hamiltonian. Using the general expressions, the theory of electric dipole–magnetic dipole (E1–M1) Raman scattering is derived in detail. The 1S0→3P1 E1–M1 Raman scattering cross section in atomic magnesium is calculated for two applicable laser wavelengths using published f-value data. Since resonantly enhanced cross sections larger than 10−29 cm2/sr are predicted it should be possible to experimentally observe this scattering phenomenon. In addition, by measuring the frequency dependence of the cross section near resonance, it may be possible to directly determine the relative magnitudes of the A⋅p and A⋅A contributions to the scattering cross section. Finally, possible applications of the effect in atomic and molecular physics are discussed.
We investigate nonresonant contributions to resonant Rayleigh-scattering cross sections of atoms. The problematic nonresonant contributions set a limit to the accuracy to which atomic spectra determine energy levels. We discuss the off-resonance effects in one-photon transitions. We also show that off-resonance contributions for the 1S–2S two-photon transition in atomic hydrogen are negligible at current and projected levels of experimental accuracy. The possibility of a differential measurement for the detection of off-resonance effects in one-photon transitions in atomic hydrogen is discussed. PACS Nos.: 31.15-p, 12.20Ds
The angular distribution of scattered Lyman-$\ensuremath{\alpha}$ photons from atomic hydrogen is calculated as a function of an applied magnetic field. The intensity of the scattered radiation is a function of the energy difference of the excited-2P2P2P levels and shows an extremum at the point where two levels cross. Neglecting hyperfine structure, there are two level crossings of interest: one at 3484 G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\frac{1}{2}}$), and the other 5223G ($2{P}_{\frac{3}{2,\ensuremath{-}\frac{3}{2}}}\ensuremath{-}2{P}_{\frac{1}{2},\ensuremath{-}\frac{1}{2}}$), respectively. The coher$\stackrel{\mathrm{\ifmmode \breve{}\else \u{}\fi{}}}{\mathrm{e}}$nt and incoherent resonance scattering is determined near these crossing points by using a Hamiltonian that includes hyperfine structure and higher-order radiative effects. In the low-field region (3484 G), the hyperfine crossings that contribute to the coherent signal are at 3476.06 and 3491.93 G, respectively. The radiative width of the levels is considerably larger than the hyperfine splittings, and the total scattering intensity has a single peak at 3483.97 G. In the high-field region (5223 G), two hyperfine levels with ${m}_{F}=\ensuremath{-}1$ repel each other (anticross) with a minimum energy separation of 15.3 Mc/sec at 5200.1 G. Resonances occur at 5220.6 and 5223.9 G, and the maximum of the total signal is at 5222.6 G.