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arXiv:1707.06518

Red shift of spectral lines of hydrogen atoms caused by its electrical polarization

V. S. Severin

Published Jul 20, 2017• 0 citations
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Abstract

A system of Lorentz oscillators is considered to interpret of spectral lines of hydrogen atoms. The dielectric permittivity of this system, which takes into account its electric polarization, is considered. The substance is examined in the gas state or in the form of small dust of matter. It is shown that the considering of the electric polarization results in a redshift of spectral lines of the substance and the appearance of dip of curve of spectrum. This dip takes place in the blue side with respect to the spectral position of the already shifted line. The magnitude of the red shift of spectral line and the width of this dip in the spectrum depend strongly on the concentration of hydrogen atoms that create this spectrum and on the spectral position of line that not shifted.

DOI
10.48550/arxiv.1707.06518

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A system of Lorentz oscillators is considered to interpret of spectral lines of hydrogen atoms. The dielectric permittivity of this system, which takes into account its electric polarization, is considered. The substance is examined in the gas state or in the form of small dust of matter. It is shown that the considering of the electric polarization results in a redshift of spectral lines of the substance and the appearance of dip of curve of spectrum. This dip takes place in the blue side with respect to the spectral position of the already shifted line. The magnitude of the red shift of spectral line and the width of this dip in the spectrum depend strongly on the concentration of hydrogen atoms that create this spectrum and on the spectral position of line that not shifted.
We extend previous work on the algebraic first-order moments of polarization profiles of hydrogen lines in the presence of external fields, to include the effect of configuration mixing induced by the applied fields. An algebraic formula for hydrogen line shifts due to the quadratic Stark effect is derived, under the assumption that the applied electric field is weak enough that line quenching induced by field ionization can be neglected. The derivation of such a formula is made possible by an aimed use of standard techniques of projection-operator algebra and of the fundamental implications of the spectral theorem. The results of this paper should help in decreasing the amount of numerical work needed in the calculation of line shifts of hydrogen lines induced by the presence of electric fields, as the preliminary numerical calculation of the Hamiltonian eigenvalues and eigenvectors is avoided, thus making calculations tractable for lines of higher hydrogen series than considered so far, e.g., in applications of pressure-broadening theory.
The Lorentz-Lorenz equation predicts that the dispersion feature of an isolated optical resonance should have a density-dependent frequency shift toward the red end of the spectrum. We have investigated the dispersion feature experimentally by observing the frequency dependence of the Fresnel reflection (selective reflection) from the boundary between a dense atomic potassium vapor and the window of the vessel containing the vapor. We find that the selective-reflection features of both the S1/2-P1/2 (770.1 nm) and S1/2-P3/2 (766.7 nm) lines of potassium shift increasingly toward the red and broaden as the number density of the vapor is increased to 2 × 1017 atoms/cm3. We compare the results of the experiment to theoretical predictions for the selective reflection. The broadening is well described by conventional binary collision theory; however, the observed red shift of both of the lines is somewhat larger than that predicted by the Lorentz-Lorenz equation. It is possible that other mechanisms that lead to frequency shifts are occurring.