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The polarized spectrum of hydrogen in the presence of electric and magnetic fields

R. Casini, Egidio Landi Degl’Innocenti

Published Sep 1, 1993• 9 citations
OpenAlex

Abstract

The polarization properties of a beam of radiation interacting with a hydrogen atom subject to simultaneous stationary electric and magnetic fields are investigated, assuming no constraints on the direction of the two fields. The problem of determining the energy eigenstates is solved within the theory of Rayleigh-Schrodinger for the stationary perturbations (the contributions of the fine and hyperfine structure of the energy spectrum are also accounted for). Then the polarized transition rates (for absorption, spontaneous emission and stimulated emission) are evaluated according to the methods of non-relativistic quantum electrodynamics, adopting the density matrix formalism which allows one to deal with partially polarized states of the atomic and the radiation field systems

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Journal of Physics B Atomic and Molecular Physics•Apr 21, 1974•5 citations
The polarization properties of a beam of radiation interacting with a hydrogen atom subject to simultaneous stationary electric and magnetic fields are investigated, assuming no constraints on the direction of the two fields. The problem of determining the energy eigenstates is solved within the theory of Rayleigh-Schrodinger for the stationary perturbations (the contributions of the fine and hyperfine structure of the energy spectrum are also accounted for). Then the polarized transition rates (for absorption, spontaneous emission and stimulated emission) are evaluated according to the methods of non-relativistic quantum electrodynamics, adopting the density matrix formalism which allows one to deal with partially polarized states of the atomic and the radiation field systems
This paper examines two theoretical aspects of the measurement of polarization of the quenched radiation which comes from the application of a weak electric field to the 2s2s2s state of hydrogen. Specifically, it outlines the justification of the Bethe-Lamb phenomenological analysis of this problem from the external field approximation of quantum electrodynamics. Further, it includes the lowest-order effects of the JJJ-breaking part of the hyperfine structure in Rayleigh-Schr\"odinger perturbation theory. While it was expected that these terms would contribute to the polarization fraction a correction to the lowest order of the relative size of the ratio of the hyperfine splittings to the fine-structure splitting of the n=2n=2n=2 state or about one part in 103{10}^{3}103, cancellations occur and these JJJ-breaking terms give a correction in the fourth place of the polarization fraction.
A density-matrix approach has been developed for the angular distribution and polarization of radiative emission during single-photon atomic transitions for a general set of steady-state excitation processes in an arbitrary arrangement of static (or quasistatic) electric and magnetic fields. Particular attention has been directed at spectroscopic observations in the intense fields of the high-power ion diodes on the Particle Beam Fusion Accelerator II (PBFA II) and SABRE devices at Sandia National Laboratories and at magnetic-field measurements in tokamak plasmas. The field-dependent atomic eigenstates are represented as expansions in a complete basis set of field-free bound and continuum eigenstates. Particular emphasis has been given to directed-electron collisional excitations, which may be produced by an anisotropic incident-electron velocity distribution. We have allowed for the possibility of the coherent excitation of the nearly degenerate field-dependent atomic substates, which can give rise to a complex spectral pattern of overlapping Stark-Zeeman components. Coherent excitations may be produced by a beam of electrons that are spin-polarized at an angle with respect to the propagation direction or by nonparallel electric and magnetic fields. Our main result is a general expression for the matrix elements of the photon-polarization density operator representing the total intensity, angular distribution, and polarization of the atomic radiative emission. For the observation of radiative emission in the direction of the magnetic field, the detection of linearly polarized emission, in addition to the usual circularly polarized radiation, can reveal the presence of a perpendicular electric field or a coherent excitation mechanism.
In a previous paper, it was explained that the absorption and emission process (AE-process) of Bohr’s model of the hydrogen atom must involve an electric charge (i.e., electron) transiting between atomic energy levels instead of quantum jumping; otherwise, there is no way to use the AE-process to predict the fine structure constant. In this paper, it is shown that (1) a complete oscillation of the atomic electron (i.e., an electric charge) and of the induced magnetic field must occur for Bohr’s hydrogen atom to emit electromagnetic radiation, and (2) an atomic electron (i.e., electric charge) of Bohr’s hydrogen atom can transit between energy levels without the atom emitting electromagnetic radiation.
The hyperfine levels for the ground state of hydrogen are normally connected by magnetic dipole transitions. However, for astrophysical applications, it may be that two-photon electric dipole processes are also important over cosmological distances. This thesis sets up a general mathematical formalism for the calculation of two-photon processes within the hyperfine structure of an atom with spin 1/21/21/2, and applies it to the ground state of hydrogen. Rates are calculated for both spontaneous emission and absorption of radiation. Due to an extraordinary degree of cancellation in the matrix elements, the rates turn out to be too small to have a significant impact on astrophysical processes involving the absorption and emission of radiation. The results are nevertheless important in reducing the uncertainty due to possible contributions from these processes. Other two-photon processes involving Raman scattering are also considered and the relevant cross sections calculated. The calculations of the decay rate, absorption coefficient and Raman scattering cross section are extended to heavier hydrogenic ions as a function of the nuclear charge ZZZ, using an approximate interpolation formula for the hyperfine splitting in the ground state. Results are presented for the hydrogenlike ions from He+^++ to Pb81+^{81+}81+. Modifications for the case of isotopes with a nuclear spin greater than 1/21/21/2 are briefly considered
The lineshape theory of optically detected RF-induced electric resonance transitions in hydrogen is concluded with the treatment of the detection process within the framework of the density matrix formalism. An optical detection function is derived from which can be determined the intensity, polarisation, and angular distribution of the detected decay radiation, subject to constraints of apparatus efficiency and geometry, in terms of the initial atomic density matrix elements and variables of the radiofrequency electric field.