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Physical Review

Multiple Nature of Elementary Sources of Radiation—Wide-Angle Interference

Simon Freed, S. I. Weissman

Published Sep 15, 1941• 58 citations
Publisher

Abstract

It has been shown possible in wide-angle interference experiments to analyze radiation with respect to its multipole character. The fluorescence from ions of europium in solution consisted of different kinds of radiation in that they possessed different interference properties. From the behavior of the fringe systems, one group of spectral lines was identified as arising from magnetic dipoles while two other groups had their origin in the forced oscillations of electric dipoles. The multipole character of the radiation of a quantum transition was found modified by a change in the microscopic fields about the emitting ions.

DOI
10.1103/physrev.60.440

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It has been shown possible in wide-angle interference experiments to analyze radiation with respect to its multipole character. The fluorescence from ions of europium in solution consisted of different kinds of radiation in that they possessed different interference properties. From the behavior of the fringe systems, one group of spectral lines was identified as arising from magnetic dipoles while two other groups had their origin in the forced oscillations of electric dipoles. The multipole character of the radiation of a quantum transition was found modified by a change in the microscopic fields about the emitting ions.
It is shown that, assuming conservation of energy and momentum in individuai transitions, radiation must be regarded as propagated by linearly directed quanta. Evidence is brought forward in favour of the view that these quanta are spatially localised longitudinally as well as laterally. As these conclusions seem unavoidable, an attempt is made to see if there is any possibility of accounting for interference effects in terms of quants possessing periodic properties. The idea that a single quantum can produce interference effects is untenable. The conception of the phase of a quant is introduced, and it is supposed that atoms may absorb a quant in a given phase provided they are in a “state” corresponding to that phase. Considering radiation emanating from a point, it is shown that a tentative explanation of interference may be obtained if the quants have a constant phase at emission, and if they give atoms at any point an impulse towards the state corresponding to their phase at the point. According as these impulses reinforce or oppose each other, bright or dark parts of a fringe System are obtained. Practically the whole nomenclature and method of the wave theory may be taken over and applied to the quant phase field surrounding an emitting source. Essentially, on this view, an explanation of interference is sought in terms of different quants, and the dark and bright parte of a fringe system are to be explained, not in terms of different numbers of quante arriving at them, but in different phase relations of quante which do arrive. Quante are characterised by a magnetic and electric vector, whose magnitudes and directions define the state of polarisation and the phase. Electron orbite may also be regarded as characterised by two vectors in terms of which it seems as if the “state” may be specified. The relation between transition character and type of radiation emitted is finally considered and it is shown that the evidence so far available renders plausible an explanation of interference of the kind put forward. Much further experimental work, particularly in connection with the Stark and Zeeman effects, is, however, necessary, before sufficient precision can be given to the views put forward to make them satisfying. On the other hand, it seems premature to suppose that only a formal treatment is possible of the physical phenomena involved.
Almost everything we know about atomic energy levels comes from the spectra resulting from radiative transitions between these levels. It is possible that the electric dipole moment of a charge distribution may vanish, in which case the radiation depends on the higher moments. The source of magnetic dipole radiation is a circulating current that reverses direction harmonically, as in a loop antenna. Since a steady-current loop can be regarded as equivalent to a static magnetic dipole, the oscillating current is equivalent to an oscillating dipole. If the electric dipole radiation is impossible, but magnetic dipole radiation can occur, the radiative process would be classed as "forbidden" because of its low intrinsic intensity. An oscillating linear dipole emits no radiation along the direction of its axis of vibration. Although the physical origin of magnetic moments is circulating currents, the effect of an oscillating circular current can be calculated by considering an equivalent linear magnetic dipole.
General expressions for the dependence of the polarization of the radiation emitted in an atomic electronic transition upon the angle of emission are derived on the basis of a vector-spherical-harmonic/Bessel-function description of the photon. The concept of a photon of a specific multipolarity, i.e. quadrupole, octupole, etc, and identifiable as such, is found to be unviable. The angular distribution and dependence upon distance from the source of the transverse and parallel components of the electric and magnetic fields arising from E1, E2, M1 and M2 atomic electronic emissions are elucidated.
The absorption of single photons by coupled pairs of ions in rare-earth solids was first observed by Varsanyi and Dieke.1 They noticed that weak absorption of light occurred in PrCl3 at frequencies close to the sum of transition frequencies of individual Pr ions, giving rise to rare-earth fluorescence. This effect was explained by the perturbation theory of Dexter.2 He showed that weak multipole or exchange interactions between rare-earth ions permitted the simultaneous promotion of two ions to excited states by the action of one absorbed photon in an electric dipole allowed transition. Similarly, two ions initially in excited states could emit one sum frequency photon in a cooperative manner.
An ion is located in a crystal at a site that is not a centre of inversion, with a Zeeman field directed at right angles to the crystal axis c. Periodic intensity variations in the optical spectrum that occur when the crystal is rotated about c are due to magnetic dipole transitions between levels of different type and to electric dipole transitions between levels having admixed opposite-parity parts of different type. Use of an antiunitary operator that commutes with the total Hamiltonian demonstrates that interference between electric and magnetic dipole radiation (or interference between any opposite-parity multipole radiation) does not occur for transitions appearing in the axial spectrum, but does occur for those appearing in the pi or sigma transverse spectrum. Depending on the site symmetry, two or four of the Zeeman components of a doublet-doublet transition have an additional periodicity as a result of this interference. Eigenstates are constructed that show the relationship between the M values of a Zeeman level, the crystal quantum number that labels it, and its type, and are used to calculate the angular dependence of certain doublet-doublet dipole transitions for ions at sites of point symmetries D 2d and C 3h . With explicit expressions for dipole matrix elements, it is discovered that two Zeeman components having the same angular dependence when interference is neglected exhibit dissimilar angular behaviour when the interference cross-term is included.