This paper describes the results of a theoretical and experimental investigation of the tensor dielectric susceptibility of a plasma in which some of the participating atoms exhibit population inversion. The measurement of the real part of the tensor dielectric susceptibility in the vicinity of an optical resonance has previously been very difficult due to the large absorption near resonance; however, by examining a resonance for which the levels exhibit population inversion we have obtained a direct measure of the real part of the susceptibility by observing the "negative" Faraday rotation, i.e., "negative" circular birefringence associated with the resonance. We also observed for levels with inverted populations the complement of the inverse Zeeman effect, that is, we observed a Zeeman splitting of the gain curve in the amplifying medium. The high-gain $5d[\frac{3}{2}]_{1}^{}{}_{}{}^{0}\ensuremath{-}6p{[\frac{3}{2}]}_{1}$ transition of atomic xenon at 2.026 \ensuremath{\mu} in a helium-xenon mixture was used for these measurements. The observed results were consistent with the theory.
The propagation of light in an optically pumped vapor is determined semiclassically by the expectation value of a dielectric susceptibility operator. We present explicit formulas for the dielectric susceptibility of a vapor of alkali atoms. The qualitative features of the susceptibility are illustrated for the specific case of
Rb87. The theory of this paper is essential for a clear understanding of phenomena such as the birefringence of alkali vapors and the microwave modulation of light by alkali vapors. Some experimental observations of birefringence in rubidium vapor are interpreted with the semiclassical theory.
Measurements of relative values of the nuclear magnetic susceptibility of
He3 vapor have been made by a pulsed resonance technique for several values of vapor density at 2 and 3.1\ifmmode^\circ\else\textdegree\fi{}K. The results of these measurements show that deviations from Curie's law are considerably smaller than those expected for a perfect Fermi gas. A theoretical expression is derived for the susceptibility at vapor densities sufficiently low that only binary collisions are important; a modification of the calculation of the second virial coefficient is used to evaluate the effect of direct interactions. The susceptibility is related to the difference between two virial coefficients, that of
He3 and that calculated for a hypothetical
He3 with zero spin. The theoretical results are in good quantitative agreement with the experimental data. They indicate that the perfect-Fermi-gas theory is not applicable to the calculation of the susceptibility of
He3 vapor at low density except at temperatures lower than 0.002\ifmmode^\circ\else\textdegree\fi{}K. Moreover, from the theoretical results it is concluded that deviations from Curie's law in the vapor are expected to be less than about 1% whenever higher order collisions do not contribute significantly to the interaction between
He3 atoms.
1.General mathematical theory.---Modifications are given in the general derivation of the Langevin-Debye formula by means of quantum mechanics published in part I which are required by the moment now being magnetic rather than electric. The main additions are the appearance of a diamagnetic term, and allowance for the fact that the magnetic moment consists of two parts arising respectively from orbital electronic motions and from the electrons' internal spins. These parts cannot always be treated as rigidly coupled to form a "permanent" resultant moment. The Hamiltonian function used for the internal spin is that of a spherical top.2.Diamagnetism.---The writer's previous claim that Pauli's formula for the diamagnetic susceptibility can be applied to molecules as well as atoms is shown to be invalid because of the anomalous fact that the square of the angular momentum, unlike the average angular momentum, does not vanish even in
S states when there is more than one nucleus. Pauli's formula is instead an upper limit to the diamagnetism in non-monatomic molecules and is a good approximation when the Schr\"odinger wave function has nearly as much symmetry as in an atomic
S state.3.Paramagnetism of atoms.---Limiting values for the paramagnetic susceptibilities of atoms are $\ensuremath{\chi}=N\frac{[4s(s+1)+k(k+1)]{\ensuremath{\beta}}^{2}}{3kT}$ and $\ensuremath{\chi}=[\frac{N{g}^{2}j(j+1){\ensuremath{\beta}}^{2}}{3kT}]+N\ensuremath{\alpha}$ where $\ensuremath{\beta}$ is the Bohr magneton and $\ensuremath{\alpha}$ is a constant. These two formulas are rigorously applicable when the multiplet intervals are respectively very small or very large compared to
kT, and are valid regardless of whether the magnetic field is strong enough to change the quantization by producing a Paschen-Back effect. The formula for small multiplets yields susceptibilities slightly different from those given by Laporte and Sommerfeld's expression for this case, and is much simpler, as they overlooked the contribution of the portion of the magnetic moment which is perpendicular to the invariable axis.4.Paramagnetism of molecules.---The susceptibility is calculated on the basis of the Hund theory of molecular quantization. Formulas are given applicable to his couplings of type (a) and type (b) provided in the former the multiplet intervals are either very large or very small compared to
kT. The experimental susceptibilities for
O2 and Cl
O2 are in accord with the assumption that the normal states are respectively
3S and
2S terms. In the particular case of
S terms the numerical results are the same in the atomic and molecular formulas, but, unlike previous theories, it is not necessary to suppose the orbits are as freely oriented in molecules as in atoms. Polyatomic molecules may have lower paramagnetic susceptibilities than diatomic ones because the dissymmetry causes large fluctuations in electronic angular momentum.5.Paramagnetism of nitic oxide.---Spectroscopists have recently found that the normal states of the NO molecule are
2P terms separated by 120.9 ${\mathrm{cm}}^{\ensuremath{-}1}$. This permits an unambigous calculation of the susceptibility of NO which agrees with the experimental value within 1.5 per cent. Deviations from Curie's law are calculated which result from the doublet interval being comparable with
kT. These deviations should be detectable experimentally if the susceptibility of NO could be measured over a wide temperature range.
In this work the electromagnetic field in a dielectric medium is quantized in a simple and straightforward way based on the classical expression for the energy density for the case of weak absorption. The quantized field leads to expressions for spontaneous and stimulated emission rates, and gain and absorption coefficients, for the general case of a dispersive dielectric host medium. Local field corrections, when they apply, arise in the same manner as in classical electromagnetic theory. The theory also leads to a radiative level shift dependent on the dispersion of the dielectric, and this shift may be interpreted as a van der Waals interaction between the guest atom and the atoms of the host medium.>