The accurate measurements obtained with Fabry-Perot spectrometry allowed a detailed determination of the main hyperfine interactions in the (0-0) $B{}_{}{}^1{}_{}{}^{}\Pi \to X{}_{}{}^1{}_{}{}^{}\Sigma$ transition of the LuF molecule. The corresponding parameters are $Q_{0,0}=-35\mathrm{}\pm 5$ mK, $Q_{1,1}=-30\mathrm{}\pm 4$ mK, $Q_{1,-1}=-34\mathrm{}\pm 3$ mK, $G_{\mathrm{Lu}}=53\mathrm{}\pm 3$ mK, and $G_{\mathrm{F}}\le 7$ mK. Then it is shown that these parameters give important information on the LuF bond and its origin: high ionicity (> 95%), high $c$ tendency for the excited ${}_{}{}^1{}_{}{}^{}\Pi$ state, probable atomic origin of molecular configurations: $6s6p\left(\mathrm{Lu}\mathrm{II}\right)\to \left(6s\sigma \right)\left(6p\pi \right)$ and $6s^2\left(\mathrm{Lu}\mathrm{II}\right)\to {\left(6s\sigma \right)}^2$.

We report on calculations of the third-order optical harmonic coefficients for atomic hydrogen and helium, using $R$-matrix expansions for the excited spectra. The results obtained are in excellent agreement with previous theoretical and experimental determinations. The method is readily applicable to the calculation of other multiphoton processes for other atomic systems.

The cross sections for electron-field pair production by photons (triplets) are studied in helium and in two helium-neon mixtures with a streamer chamber at an incident photon energy of 2.614 MeV. The streamer chamber is triggered by the coincidence between the electron and the positron detectors. The chamber is located between two Helmholtz coils giving a magnetic field of 300 G. A detailed analysis of the false triplet events is performed by using new kinematical criteria. The results are the following: (1) Experimental differential energetic distributions for the two electrons and the positron are consistent with those recently calculated by Mork and Haug. (2) These cross sections are very different for pair and triplet production. (3) Differential angular cross sections agree with the distribution predicted by Mork and Haug. (4) The measured cumulative integral cross sections in helium and in the helium-neon mixtures, compared with Mork and Jarp's theoretical predictions and within experimental uncertainties, are consistent with the total cross section of 12.8 μb/electron predicted by Mork and Haug. (5) An upper limit for the total multiplet cross section in Ne was determined to be ${10}^{-8\mathrm{}}$ b/electron.

Model calculations are presented for nonadiabatic passage of an oriented spin through a reversing solenoidal magnetic field; these are useful for comparison with experiments described elsewhere. The model corresponds closely to the well-known Landau-Zener-Stueckelberg model of a two-state curve crossing in molecular collision theory; various modifications appropriate to the Majorana problem are considered. The resulting transition amplitudes are discussed for the $F=1\mathrm{}$ hyperfine component of the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ metastable state of atomic hydrogen as an example.

Analytical and numerical results are presented which are related to the following higher-order atomic processes: retardation effects in two-photon bound-bound transitions, evaluation of the Bethe logarithm in excited states, and multiphoton ionization. These calculations are carried out within the framework of the conventional perturbation theory by using different representations of the Coulomb Green's function, each representation offering its own particular advantages.

Floquet's theorem and a corresponding perturbation theory are derived for Hamiltonians periodic in time. The resulting theory is then applied to the interaction of stationary and moving, neutral two-level atomic or molecular systems with monochromatic linearly and circularly polarized electromagnetic radiation.

The mapping of operator equations into $C$-number differential form by means of the atomic coherent-state representation leads to mathematical difficulties that have no counterpart in the case of the Glauber-Sudarshan representation for Bose systems. We give sufficient conditions for the solutions of $C$-number equations in the atomic coherent-state representation to be physically meaningful.

A method of producing inversion by multistage x-ray pumping of low-$Z$ elements is described. A detailed numerical model of the physical processes involved has been created and applied to boron. It is shown that significant inversion of the 255-eV $K\alpha$ transition of hydrogen-like boron may be produced with an optical pump laser, producing on the order of 5 × ${10}^{16}$ W/${\mathrm{cm}}^2$. Demonstration of x-ray lasing will require a pump laser power of at least 20 TW and the solution of several technological problems which are briefly discussed.

The theory of far-infrared generation by optical mixing of focused Gaussian beams is developed, taking into account the effects of diffraction, absorption, double refraction, and multiple and total reflections at the boundary surfaces. Results of numerical calculations are presented. It is shown that focusing of the pump beams appreciably enhances the far-infrared output despite the strong far-infrared diffraction. In a 1-cm-long crystal, the optimum focal-spot size is approximately equal to or smaller than the far-infrared wavelength for an output at frequency less than 100 ${\mathrm{cm}}^{-1\mathrm{}}$. Double refraction of the pump beams is relatively unimportant. Both far-infrared absorption and boundary reflections have major effects on the far-infrared output and its angular distribution. The former is often the factor which limits the output power. We show that a simple model treating the nonlinear polarization as a constant-$\frac{1}{e}$-radius Gaussian distribution of radiating dipoles is a good approximation to the problem. We also compare the results of our calculations with those for second-harmonic generation.

The trilinear Hamiltonian of Tucker and Walls, governing the parametric amplification, leads to three coupled nonlinear Heisenberg equations in terms of creation and annihilation operators. Using the Manley-Rowe relations the equations are reduced to a single nonlinear equation in terms of one of the number operators. Thereafter, it is solved by means of a perturbation method around the diagonal, allowing calculation of the mean number of photons and the variance of the amplified field. The short-time approximation, the parametric approximation, and the classical limit are reobtained by suitable limiting processes.

The coherent interaction of two smoothly varying, near-resonant, two-photon pulses with a three-level system can be described by "two-photon damped Bloch equations" which are analogous to those for a one-photon transition in a two-level system except for the presence of a two-photon coupling and a frequency shift. These equations are solved for the cases ${\gamma }_1$, ${\gamma }_2\ll \Omega$, ${\gamma }_1={\gamma }_2$, and $\frac{{\gamma }_2{k}^2{\epsilon }^4}{{\Omega }^2}$, ${\gamma }_1\ll \Omega$, where ${\gamma }_1$ and ${\gamma }_2$ are the atomic energy and phase relaxation widths, respectively, and $\Omega$ is the Rabi frequency. The leading contribution to the refractive index is intensity dependent, caused by the level shifts inherent in multiphoton processes; it includes a relaxation dependent part which is important at times shorter than ${\gamma }_1^{-1\mathrm{}}$. The second-order contributions depend on the square of the intensity and the time-integrated square of the intensity. The latter contribution, which is relaxation dependent, causes line asymmetry at the long-wavelength wing; it consists of a term proportional to ${\gamma }_2-{\gamma }_1$ and only important at early times and a term proportional to $2{\gamma }_2-{\gamma }_1$.

Second-harmonic generation in a degenerate two-level gaseous system is considered with atomic motion taken into account. The diagonal elements of the dipole matrix are assumed to be present. We find the photon statistics of the second-harmonic field to be considerably influenced by the detuning in the two-photon absorption. The threshold condition is discussed. We obtain the average second-harmonic photon number and thus calculate the dimensionless intensity parameter. The output variance of the second-harmonic field is discussed.

A unified Landau theory is introduced for the nematic, smectic $A$, and smectic $C$ phases using the director $\overrightarrow{\mathrm{n}}$ for the nematic order parameter, the complex order parameter $\psi$ for the smectic planes, and the vector $\overrightarrow{\beta }$ for the smectic $C$ dipolar order. The phase diagram is studied and a possible second-order triple point is predicted. The liquid structure factor near the nematic-smectic $C$ phase transition is calculated and found to be in semiquantitative agreement with the x-ray experiments. All three Frank elastic constants are predicted to diverge near a second-order nematic-smectic $C$ transition. The compressive instability near the smectic $A$-smectic $C$ phase transition is explained in the present model.

The radial distribution function and static structure factor of liquid potassium at temperatures of 338 and 408 K have been calculated by a Monte Carlo method using a realistic ion-ion potential. The agreement between the calculated liquid structure factor and recent x-ray diffraction measurements is excellent.

C${\mathrm{H}}_2$ and Al targets were irradiated at ${10}^{16}$ W/${\mathrm{cm}}^2$ with a focused Nd: glass laser to study the dependence of x-ray emission on laser-pulse parameters. Complementary optical diagnostics indicated that 60-80% of the incident laser energy was absorbed in the planar targets. X-ray intensities spanning eight orders of magnitude were measured from 1 to above 100 keV by the multiple absorption foil method. The spectral shapes for C${\mathrm{H}}_2$ targets were independent of pulse length for 21- and 250-psec pulses.

A cell model in which the cell size is constant at fixed temperature and pressure is utilized to calculate melting data and gas-liquid critical constants. Interactions between vacancies are taken into account and the variation of vibrational free energy with vacancy concentration is incorporated into the model. The calculated results agree well with experiment for the hard-sphere transition and melting and condensation of argon. The pair correlation function for argon computed from the model is in good agreement with experiment with reasonable values of the parameters in the calculation. The calculations indicate that vacancy defects exist in liquids and play an essential role in determining melting conditions.

The detailed spatial dependence of the director field $\overrightarrow{\mathrm{n}}\left(\overrightarrow{\mathrm{r}}\right)$ for the metastable cholesteric storage mode is calculated as a function of plate spacing and surface energy coefficient. These calculations are first performed subject to the constraint that $\overrightarrow{\mathrm{n}}$ is confined to a plane perpendicular to the plates. Upon waiving the planarity constraint and solving the complete Euler-Lagrange equations, we find that the departure of $\overrightarrow{\mathrm{n}}$ from the plane is less than 7° with the largest values occurring in the immediate vicinity of the plates. Employing our results for $\overrightarrow{\mathrm{n}}\left(\overrightarrow{\mathrm{r}}\right)$, we calculate the dependence of the electrical capacitance on plate spacing. We also propose a mechanism for the decay of the storage mode as well as a simple semiphenomenological expression for its lifetime. For a suitable choice of parameters our theoretical expressions are in reasonably good agreement with the capacitance and lifetime measurements of Hulin for variable plate spacing.

It is pointed out that, for a system of $N$ particles which can associate reversibly with a molecule, to second order in perturbation the standard free energy is linear in each particle density plus terms in their pairwise products. This means that, because of symmetry, only $\frac{N(N+1\mathrm{})\mathrm{}}{2}$ standard chemical potential parameters need be determined. The system is, therefore, highly overdetermined by available experimental studies. Furthermore, this form for the standard chemical potential is sufficiently orthogonalized so that evaluation of the individual elements of the chemical potential matrix can be made from data without noteworthy accuracy. Such a fitting process is carried out using data for hemoglobin, with oxygen, hydrogen ions, chloride ions, and 2,3 diphosphoglyserate as the associating particle systems. The analysis allows one to fit the Hill index, the Bohr effect, the equilibrium association constants, the shift of the oxygen gas pressure axis with changes in the $p\mathrm{H}$, the chloride ion and diphosphoglyserate solute concentrations, and with temperature. The oxygenation data taken in a hyperbaric environment are interpreted to yield changes in the hemoglobin molecule's volume as the number of associating particles is varied.

Numerical solutions have been obtained for the electron distribution function as a function of both energy and position for the case of a uniform stream of electrons being absorbed at a collecting electrode under the influence of a uniform electric field. Solutions are obtained from the Boltzmann equation for various power-law dependences of the momentum-transfer cross section on electron energy. It is found that the electron density distribution obtained by integrating the distribution function over energy varies significantly from the conventional solution obtained by solving the electron continuity equation with drift velocities and either transverse or longitudinal diffusion coefficients taken to be independent of position. The average electron energy increases by ∼ 50% near the boundary for a cross section increasing linearly with energy making the effective drift and diffusion coefficients a function of position.

The ballast resistor is a simple, one-dimensional device which has an instability far from equilibrium. The steady-state solutions of the energy-conservation equation show a first-order phase transition. We derive a potential function which is minimized in the steady state. The probability distribution of different states of the system is related to this potential.