The dynamics of a multimode high-intensity gas laser including some velocity-changing-collision effects is investigated theoretically. Using a spatial Fourier expansion method for the density matrix of the active medium, one obtains the system of equations which contain only the Fourier components of the population inversion. To obtain the approximate solutions in the high-intensity case, the saturation terms due to hole burning and the population-pulsation terms are treated separately. The former are calculated exactly and the result is equivalent to the rate-equation approximation. The latter are treated by the perturbation method. The equations of motion for mode amplitudes have a similar form to those of Lamb's perturbation theory but can be applied to a high-intensity multimode laser. Experimental results of three-mode oscillation of a He-Ne laser are compared with the theory.

We use the inverse method to investigate initial optical pulses suitable for forming compact zero-area outputs. We find that nonseparating and nonspreading pulses can be formed.

We study the effects of statistical broadening and population loss on the dynamics of strongly excited three-level quantum systems. The results of both analytic and numerical treatments of the three-level Schrödinger equation are displayed. In order to allow for statistical broadening, solutions are required for arbitrary detuning of the two very intense monochromatic lasers. The most efficient statistically averaged population depletion occurs when the Rabi frequency of the second transition is greater than that of the first.

A quantitative treatment is carried out for the exact operator expressions derived in a previous paper. The formalism of the dressed atom and the concept of level crossings (anticrossings) are used throughout and provide a basis for the quantitative investigation of the resonant three- and four-photon ionization of cesium. The numerical results obtained within this framework are in excellent agreement with experimental observations.

Using the exact solution for a sine-driven two-level system we have calculated the nonlinear absorption coefficient of a gas of two-level molecules with homogeneous (hard collisions, spontaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms. We have studied the dependence of the form of the absorption lines on relaxation parameters, on the strength of the electric field, and for various ratios between the homogeneous and inhomogeneous linewidths. We include considerations about saturation of the medium caused by the external field that gives rise to the so-called power broadening of the spectral lines. The dependence of the linewidth on the saturation parameters and on the relaxation parameters is determined. These parameters appear in the ratio of the purely homogeneous and purely inhomogeneous linewidths. Asymptotic behaviors of this linewidth for the homogeneous limit and for the inhomogeneous limit are also determined.

We have calculated the gain of a free-electron laser in the small-gain-per-pass limit by using the single-particle model. The electron equations of motion reduce to that of a simple pendulum. As operating levels increase, the theory predicts that by varying the amount of detuning, gain enhancement should occur. In addition, we calculate the electron energy and phase distributions at the output of the amplifier assuming the electrons entering are monoenergetic and have a uniform phase distribution. Above a certain operating level, the theory predicts and explains for the first time the occurrence of discontinuities in both distribution functions. The effect of these discontinuities in storage-ring high-power applications is not yet known.

It is proved that the superradiant phase transition cannot occur in a general system of atoms or molecules if only charges (not intrinsic magnetic moments) of the particles interact with a finite number of radiation modes in the dipole approximation.

A method for optimizing usual kinetic modeling techniques for determination of the dynamic structure factor from a given kinetic equation is investigated. The procedure has the potential to significantly reduce the calculational effort, thereby permitting future study of more complex kinetic equations currently being developed for dense gases. The exact low-density kinetic equation with step potential interaction including finite-collision-time effects is derived for calculation of the self-structure factor and used to illustrate and test the kinetic modeling.

Some local characteristics of the Schrödinger equation for two-electron atomic systems, as a functional, are investigated from a mathematical point of view and the possibility of their application to the semiempirical determination of energy levels is examined.

New upper and lower bounds for Van der Waals coefficients using even and odd oscillator-strength sum rules are derived.

First-principles fully nonlocal pseudopotentials which predict good phonon spectra and elastic shear constants for Li, Na, and K were used to obtain the effective ion-ion pair potentials at the melting-point density. The pair potential $U\left(r\right)\mathrm{}$ was used to make a Monte Carlo determination of the static structure factor $S\left(q\right)\mathrm{}$ and pair-correlation function $g\left(r\right)\mathrm{}$ for liquid alkali metals. The results for Na and K compare well with the experimental data of Greenfield and Wiser.

Absolute cross sections are reported for the resonant charge-transfer reaction ${\mathrm{He}}^{+}$+He→He+${\mathrm{He}}^{+}$ at collision energies between 0.1 and 187 eV. The results, obtained using a new merging-beam apparatus at Rice University, are in agreement both with theory and with measurements made using other experimental techniques. The experimentally determined cross sections between 0.5 and 187 eV fall about a line given by ${\sigma }^{\frac{1}{2}}\left({\AA }^2\right)=5.09-2.99\mathrm{} \ln W$, where $W$ is the collision energy in eV. Considerable attention is paid to the configuration and operation of the apparatus. Tests and calculations which confirm the interpretation of the experimental data in a merging-beam experiment are discussed.

Through a method using a change of variables for frequencies occurring in nonlinear phenomena, we show that no dispersion relation can be established between different phenomena and that the only dispersion relation for a well-defined phenomenon is a relation of Kramers-Kronig type.

When a smectic-$A$ phase is composed of chiral molecules, it exhibits an electroclinic effect, i.e., a direct coupling of molecular tilt to applied field. The pretransitional behavior of the electroclinic effect in the $A$ phase is used to study the critical behavior near the second-order, smectic-$A$—smectic-$C$ phase transition. This behavior is measured by monitoring the change in birefringence of a sample as the electroclinic effect causes a tilt of the molecules. A large pretransitional effect is measured, and constants describing the critical behavior are determined.

It is found that light undergoing double scattering in a fluid introduces a spurious curvature in the semilog plot of the time-dependent correlation function versus time. The amount of curvature to be expected is calculated as a function of the parameters of the experiment. This permits the correction of experimental data by the subtraction of the double-scattering contribution. Alternatively, we express the results of our calculation in frequency space by exhibiting the deviation to be expected from a Lorentzian spectrum. A further description of the double scattering is given in terms of a continuous distribution of relaxation rates. Also included, as a by-product, is a brief treatment of the double-scattering correction for the equal-time correlation function. Small-angle approximations, valid in the extreme critical region, lead to analytic results which are found to be in good agreement with numerical computations of Bray and Chang. As in their work, our calculations are limited to the 90° scattering geometry.

A calculation of the Maier-Saupe model is given in terms of the random-phase approximation. The influence of the range of the intermolecular potential is analyzed. Notably, attention is paid to short-range-order effects in the isotropic phase. It appears that light-scattering data can be understood using a short-range potential.

A generalized, multielectron version of the Planck-Larkin convergent hydrogenic partition function is presented. It is shown that compensation between bound and scattering states leads naturally to convergent expressions for multielectron bound-state partition functions. The nature of the compensation is studied by comparing a high-temperature expansion of the bound-state sum with a perturbation expansion in the coupling parameter $\beta e^2$ of the complete trace. The analytic form of high-order quantum perturbation terms is determined from a parametrized pseudopotential method. Rigorous evaluation of low-order quantum perturbation expressions is used to determine parameter values.

The highly collimated beams of energetic neutral atoms used in controlled thermonuclear fusion research (CTR) require the virtual elimination of space-charge forces in the primary ion beam in order to minimize the angular divergence. A model is presented which describes the behavior of an intense ion beam passing through a gas cell. This theory is used to derive the space-charge field produced by such a beam and shows how its effect can be minimized. This model agrees well with experimental measurements and enables emittance-dominated beams of very high brightness to be obtained which could find applications in fields other than CTR.

It is shown that the measurements of Edwards et al. do not demonstrate the existence of two independent self-generated magnetic fields in the laser-target interaction region. On the contrary, these results illustrate, once more, the two-phase expansion of the magnetic fields spatial configuration: diffusion within the photoionized background followed by convection with the laser plasma.

Analysis of a spin-rotation model illustrates how transitions between adiabatic channel states stem from the second, rather than from the first, rate of change of these states, provided that appropriate identification of channels and scaling of the independent variable are used. These remarks, like the earlier development of a post-adiabatic approach, aim at elucidating the suprising success of approximate separation of variables in the treatment of complex mechanical systems.