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.
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.
Introduction The selection rules discussed in Sec. 3.5 forbid many kinds of transitions that are frequently observed or exploited. It must be remembered that these “rules” are based on the approximations of Sec. 3.2, but of course, those can be extended. Such expansions to higher orders of approximation may seem to be little more than a tedious exercise, but this chapter will show that the results are extremely important, because they cause qualitatively different kinds of transitions. Since they involve both the electric and magnetic components of the light, their atomic dipole moments will be identified with the superscript E and B for the remainder of this chapter. The magnetic dipole transitions, called M1, discussed in Sec. 4.2.1 that arise from extension of the electric dipole approximation encompass all of magnetic resonance, including atomic clocks, forced evaporative cooling in Bose–Einstein Condensation (BEC), MRI, and astrophysical processes such as generation of the all-important 21 cm radio frequency line. The electric quadrupole transitions, called E2, discussed in Sec. 4.2.2 describe myriad stellar spectral features as well as the vast majority of nuclear γ-ray transitions. Even with these extensions there are many cases where the relaxation of the electric dipole (E1) selection rules to include M1 and E2 transitions as in Sec. 4.2 still do not account for observed processes. Thus other approximations have to be extended so that their limitations can be relaxed as well. Extension of the perturbation approximation (see Sec. 4.3.1) provides an analytical description of most of non-linear optics, including second harmonic generation, four wave mixing, Raman spectroscopy, and the fabled decay of the hydrogen 2S state. A semi-classical description of the interaction between radiation and atoms can begin with a multipole expansion of the Hamiltonian. The lowest-order term is just from the point charges α located at, and vanishes for neutral atoms. The next-order term is the electric dipole interaction that arises from the non-isotropic distribution of charges induced by the electric field of the light. This term produces the electric dipole transitions (E1) that have been described in some detail in Chap. 3.
The absorbed/emitted radiation will be treated classically, as a monochromatic plane wave, whereas the atomic system that can absorb/emit such radiation will be described quantum-mechanically. However, no incident radiation beam is needed, and the atom “falls down” after a certain time interval to the ground state without any external reason. In the spontaneous emission processes the emitting atom can be thought of as a classical oscillating dipole, whose amplitude decreases due to the energy loss through the radiation. If an ensemble of identical atoms is considered and if, for simplicity, each atom emits radiation with the same spectral shape and full width at half maximum, it is impossible to ascribe a definite spectral component with intensity to a definite atom. In this case, such a broadening is identical for all atoms in the ensemble. On the microscopic scale, absorption of radiation is reduced to the transitions between pairs of energy levels of a discrete atomic spectrum.
Abstract 1. The procedure usually adopted in the Quantum Theory for the estimation of the intensities of a spectrum line includes two stages : (1) the electric moment, p, of the distribution responsible for the spectrum line is calculated by means of Schrodinger’s integrals or some equivalent method ; (2) the rate of loss of energy due to radiation is calculated by the classical formula due to H. Hertz, viz., 2p2/3c3, just as if the distribution were concentrated in a dipole of precisely the same moment p. The first stage involves no difficulties beyond those met with in the evaluation of the integrals or matrices with which we are concerned, the only principles needed being those of the particular quantum theory adopted. But the second stage is open to grave objections and can only be justified on the ground of necessity owing to the absence of any completely satisfactory quantum theory of the electromagnetic field. Sometimes an appeal is made to Bohr’s Correspondence Principle, but this itself involves a somewhat hazardous extrapolation from infinitely large down to small quantum numbers and cannot take the place of a rigorous calculation. A logically consistent method is possible, based on Maxwell’s theory as represented by his electromagnetic equations and their solutions in terms of the classical retarded potential integrals. It may be objected that we do not know how far Maxwell’s equations can be applied to the interiors of atoms, in particular to distributions like those of Schrodinger, but precisely the same objection applies to the customary use of the classical expression for the radiation from an oscillating dipole. Moreover, the attempts made by Heisenberg and Pauli, Dirac and others to formulate a quantum theory of the electromagnetic field have all been based on the assumption that such a theory must be consistent with Maxwell’s equations. The direct application of the methods of classical electromagnetic theory to Schrodinger’s distributions can be justified at least as a rigorous attempt to determine their electromagnetic field and the radiation from them, and the validity of the procedure will have to be judged by the agreement, or otherwise, of the results obtained with experience. In this way we avoid the assumption that a spatially extended distribution can be treated as if its electric moment were concentrated in a point; in fact, the results obtained in this paper for the more important spectrum line series show definitely that the assumption is false, because it leads to results in many cases quite inconsistent with a rigorous application of Maxwell’s theory.
Lux aeterna luceat eis. Let there be light. Take the rest of the week off. Atomic energy levels deduced from optical spectra comprise one of the most precisely known sets of physical measurements that exist. However, the precision of the determinations of the relative oscillator strengths of these spectral lines from the relative intensities of spectral lines is much less precise. Fortunately, time-dependent methods for the study of the dynamics of the emission process exist (and are being developed) that permit the transition probability rates, oscillator strengths, and reaction rates to be determined with ever-increasing precision. In most elementary quantum mechanics textbooks, the section on the emission of radiation is the least satisfactory section of the book. Whereas the development of relationships among various spatial overlap integrals between state vectors for various operators (such as the electrostatic dipole moment) can be formulated in a very elegant ab initio manner, the connection of these matrix elements to the time dependence of the system often seems driven by a posteriori assumptions that are extended beyond their justifiable range of applicability. As Fermi observed in stating his Golden Rule , “the transition probability and energy perturbation can be calculated with the help of perturbation theory ( i.e. , there is no better way known).” The Weisskopf–Wigner approximation offers a scheme for making precise calculations, but does not provide the rigor that has characterized so many other areas of quantum mechanics.
The classical theory of the interaction of light with the electron clouds of atoms and molecules will be discussed in this chapter. The discussion will begin with the interaction of a steady electric field with a collection of point charges, leading to the development of terms describing the electric dipole and quadrupole moments. The classical Lorentz model is then introduced to describe interaction of an oscillating electric field with the electron cloud of an atom, and the concepts of absorption and emission are introduced. The propagation of a light wave through a medium with electric dipoles is then discussed. Finally, the classical theory of radiation from an oscillating dipole is discussed.
A study is made of the spectra of a highly excited hydrogen atom in crossed external l-mixing electric and magnetic fields. A semiclassical model is suggested for the radiative transitions between the perturbed Rydberg levels and the low-lying levels of the atom. The emitted light is shown to be a superposition of radiation of two effective linear vibrators symmetrically placed with respect to the external fields' plane. The interference between the vibrators is the source of rapid oscillations of the observed line intensities and polarization accompanying even small variation of the external fields. The averaged spectral intensity is shown to be unchanged by the presence of the magnetic field, being the same as in Stark splitting.