This paper presents a semiclassical treatment of the evolution of an initially inverted system into a superradiant state in an extended, optically thick medium. In this process spontaneous emission and background thermal radiation initiate the collective radiative decay and produce a superradiant output pulse of intensity proportional to the square of the number of radiators. The treatment is based on the coupled Maxwell-Schrödinger equations, modified to include a fluctuating polarization source properly constructed to account for the effects of spontaneous emission. Computer results show that for a high-gain system only two parameters significantly influence the evolution process: $T_R$, the characteristic radiation damping time of the collective system; and ${\theta }_0$, a function of the conditions which initiate the superradiant process. In this limit one obtains a normalized emission curve and simple analytical expressions for the time delay, pulse width, and peak intensity of the output radiation. These results are in good agreement with experiments. A comparison of our model with previous treatments of superradiance is given.

It is shown theoretically that Pendellösung fringes exist in the case of Bragg diffraction of circularly polarized light by cholesteric liquid crystals, in analogy with the case of x-ray or neutron diffraction by perfect crystals. The expressions for the fringe separations, both in light wavelength for a given cholesteric thickness and in thickness for a given wavelength, were derived as a function of the physical characteristics of the cholesteric and utilized to interpret experimental data.

An intense relativistic electron beam has been injected into a cylindrical drift tube containing a counterstreaming electromagnetic wave $f_i=9.3\mathrm{}$ GHz and $P_i=170\mathrm{}$ kW). Within a narrow range of axial magnetic field centered at 5 kG, a reflected wave at $f_s\sim 40$ GHz was generated by the interaction of the beam with the incident wave. The reflected wave was observed to have a power of several hundred kilowatts (i.e., greater than the power of the incident wave) and a pulse duration on the order of nanoseconds. All observed experimental characteristics (viz. frequency shift, power amplification, pulse duration, and cyclotron resonance) were consistent with a model of reflection from the discontinuity in refractive index that is associated with an electron beam front near cyclotron resonance. This mechanism could be employed in a new class of short-pulse, ultrahigh power, tunable generators at millimeter and submillimeter wavelengths.

A Landau-Ginzburg free energy is presented that yields a nematic to smectic-$A$ (NA) transition, a nematic to smectic-$C$ (NC) transition, and a Lifshitz point (at the boundary between the NA and NC transitions). Fluctuation enhancements of the Frank elastic constants are calculated. For the NC transition, all three elastic constants $K_1$, $K_2$, and $K_3$ diverge as ${\xi }^2$, where $\xi$ is the correlation length for fluctuations of the smectic order parameter. At the Lifshitz point, $K_1$ and $K_2$ diverge as $\ln \xi$ whereas $K_3$ diverges as $\xi$.

Eikonal approximations to thermodynamic Green's functions are introduced into the functional representations of quantum statistical mechanics. In terms of summations and quadratures over an instantaneous interparticle potential, one obtains explicit representations at reasonably large temperatures for quantum corrections to classical cluster integrals.

A molecular theory, based on first principles, is introduced for the systematic study of the effects of intermolecular forces on optical properties of dielectric molecular fluids. This theory covers a broad range of applications, including (polarized and depolarized) Rayleigh and Raman scattering, absorption spectra, and nonlinear optics. A canonical transformation is presented by which externally applied coherent fields can be separated from internal radiation fields, thus enabling the introduction of radiative corrections (such as retardation) to the intermolecular forces. The polarization of the medium is expressed in terms of a manybody polarizability (or nonlocal susceptibility) operator. The latter quantity contains implicitly all so-called local-field effects (modification of the molecular polarizability by electromagnetic fields due to neighboring molecules). The dipolar contributions, when summed to all orders, yield the familiar Lorentz-Kirkwood factor, involving the retarded dipole tensor.

A microscopic theory of light scattering developed in a previous publication, which incorporates all intermolecular-force effects, is here extended and applied to specific experimental situations. The consistency between the molecular theory and macroscopic theories of light scattering is established. The formal theory is then elaborated to include explicitly the contributions of higher-multipole hyperpolarizabilities, and of nonlinear effects of the external field. The many-body hyperpolarizabilities are expanded in terms of the corresponding single-particle operators and intermolecular forces. Three specific applications of this formalism are considered: (a) collision-induced forbidden Raman scattering in which higher-multipole polarizabilities are shown to partake; (b) collision-induced second-harmonic generation (SHG) by fluids of centrosymmetric molecules; and (c) SHG by atomic fluids. The latter process is shown to contain direct information on the three-particle correlation function.

The effects of nonlinearity in nematic liquid crystals subject to electric and magnetic fields are emphasized. For the Fréedericks transition, the distortion profile is calculated exactly. For the domain modes, the torque equation can be approximated to a high degree by the nonlinear sine-Gordon equation. An exact two-dimensional periodic solution is found whose consequences are in good quantitative agreement with all experimental observations. The possibility of a first-order transition to a vortex pattern is predicted.

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Through an extensive use of the Poisson summation formula, we have elucidated the description of the phenomenon of Bose-Einstein condensation in finite systems in terms of a "collapse in the thermogeometric space." In particular, we have carried out an explicit evaluation of the temperature dependence of the thermogeometric parameter $y$ for a cubical enclosure under periodic boundary conditions, which in turn enables us to evaluate the temperature dependence of the condensate fraction $\frac{N_0}{N}$ as well as the two-point correlation function $\rho (\overrightarrow{\mathrm{r}},{\overrightarrow{\mathrm{r}}}^{\prime })$ for cubes of arbitrary sizes. Numerical results are given for two specific sizes, $\frac{L}{\overline{l}}=40\mathrm{} \mathrm{and} 100$, where $L$ is the edge length of the enclosure and $\overline{l}$ the mean interparticle distance in the system. In the appropriate limit, our results are in complete agreement with the Fisher-Barber scaling theory for finite-size effects. Application of the Poisson summation formula has also enabled us to extract information of direct physical interest about the growth of long-range order in general cuboidal geometries. The special case of the thin-film geometry has been studied in detail; the resulting formulas provide a considerable improvement over the ones obtained by previous workers.

We have measured the optical Kerr constant and the orientational relaxation times of seven $p$,$p^{\prime }-\mathrm{di}-n-\mathrm{alkoxyazoxybenzene}$ homologous compounds as functions of temperature in the isotropic phase. The observed critical behaviors near the isotropic-nematic transitions agree well with the predictions from the Landau-de Gennes model. Various characteristic parameters of the homologs are deduced from the experiment. Their variations with increase of methylene groups in the alkyl chain are discussed. Our results suggest that neither the mean-field theory of Maier and Saupe nor the Landau expansion of free energy is a good approximation for quantitative description at the isotropic-nematic transition.

The Monte Carlo data of Hansen for the internal energy of the classical one-component plasma in the fluid state is found to satisfy accurately a simple functional form, $\frac{U}{\mathrm{NkT}}=a\Gamma +b{\Gamma }^{\frac{1}{4}}+c$, for $\Gamma >1\mathrm{}$. The fluid static energy is very close to the bcc lattice energy of the solid, and the fluid thermal energy varies as $T^{\frac{3}{4}}$. Simple and accurate expressions for other thermodynamic functions for the plasma fluid are given.

Additional two-photon resonances have been observed and identified in the ${\nu }_2$ bands of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$${\mathrm{H}}_3$ at high Stark fields with the Doppler-free technique. With an excitation energy of 1880.481 ${\mathrm{cm}}^{-1\mathrm{}}$ provided by two C${\mathrm{O}}_2$ 10.4-μm laser quanta [$P\left(14\right)\mathrm{}$ and $P\left(34\right)\mathrm{}$] the observed $({\nu }_2,J,K)\to (\nu _2^{}{}_{}{}^{\prime },J^{\prime },K^{\prime })$ resonances are identified as ($0^{+}$,4,4)→($2^{-}$,4,4) and ($0^{-}$,2,2)→($2^{-}$,2,2). Violation of the parity rule in the former case is induced by the static Stark field.

Accurate values of the Lamb shift can be derived from measurements of the anisotropy in the angular distribution of the radiation accompanying the electric field induced $2s$-$1s$ transition of hydrogen. Calculations of the anisotropy, including relativistic and hyperfine structure corrections, are presented for the hydrogenic ions up to ${\mathrm{S}}^{15+}$. The data enable the calculation of the Lamb shift from a measured value of the anisotropy.

We report measurements of the change in the work function of a $pH-2\mathrm{}$ water surface upon spreading a monolayer of pentadecanoic acid. The measurements were made as a function of density at a temperature of 20.1°C, which is below the critical temperature for this monolayer. Large variations in the work function were observed in the density range corresponding to the region in which the liquid and vapor phases of the monolayer coexist, offering further evidence for the presence of two distinct phases.

The single-electron capture cross sections in proton-helium collisions have been calculated using a one-parameter Hylleraas wave function and also a refined Byron-Joachain wave function for the helium atom in the approximate integral form of the close-coupling formalism. We have considered both the prior and post forms of the interaction in evaluating the input Born-Oppenheimer exchange amplitude. The discrepancy in the results obtained by using the two forms of interaction have been studied for each wave function. The simple Hylleraas wave function with the post form of interaction is found to be quite adequate for the scattering calculation of the system ${\mathrm{H}}^{+}+\mathrm{He}\left(1\mathrm{}{s}^2\right)\to \mathrm{H}\mathrm{}\left(1s\right)+{\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$.

A solution is presented for the damped optical Bloch equations under the excitation of a smooth pulse by first deriving three independent third-order equations of the Bloch vector components. Each equation is reduced to quadratures by assuming that the logarithmic time derivative of the field amplitude is small compared to the Rabi frequency. This results in an approximate summation of the infinite-order time-dependent perturbation in the field amplitude. The relaxation-dependent induced damping of the population inversion is calculated. Also calculated are additional relaxation-dependent contributions to the intensity-dependent refractive index. The time-integrated intensity contribution tends to cause line asymmetry, which becomes, at later times, linear in ${\gamma }_2$ when ${\gamma }_2\gg {\gamma }_1$ and zero when $2{\gamma }_2={\gamma }_1$, where ${\gamma }_1$ and ${\gamma }_2$ are the atomic energy and phase-changing relaxations, respectively. The dependence of the spectral broadening on pulse length, pressure, and length of the sample is discussed.

The proofs of the noncrossing rule and the problems inherent in the application of the rule are discussed. It is shown that avoided crossings cannot be rigorously predicted by the noncrossing rule. The determination of spurious avoided crossings by variational calculations is discussed. A rule is developed which establishes when variational calculations will necessarily predict avoided crossings regardless of whether the exact states cross or avoid crossing.

The one-dimensional three-body problem interacting with a pairwise $\delta$ function is investigated. For the general three-body problems, conditions on the masses and the interacting strengths for the existence of a simple type of exact solution are obtained. It is immediately clear that the "helium" atom does not possess such an exact solution. For the "helium" atom, an upper bound to the exact ground-state energy is obtained. This is close to, but slightly better than, the Hartree-Fock calculation which can be carried out exactly.

Static dipole polarizabilities are calculated from pseudonatural orbital configuration expansion wave functions for the ground states of the atoms Na through Ca with an accuracy estimated to about 2%. The resulting values are (in the order Na-Ca) 165.02, 71.32, 56.27, 36.32, 24.52, 19.60, 14.71, 11.096, 287.6, and 153.9 a.u. The influence of the electron correlation on the polarizabilities is shown to reflect its influence on the radial distribution of the electrons.