The nonlinear-response theory of acoustic pulse generation by linear spectroscopy developed in an earlier paper [Phys. Rev. A 29, 1453 (1984)] is extended to the case of solids. Viscoelastic equations for the dynamics of the fluctuations are obtained by explicitly including the stress tensor into the macroscopic description of the system, as well as correlation-function forms for the coupling constants linking the incident optical pulse to the local stress relaxation. Since transverse waves propagate in solids, absorption-driven transverse shear waves are obtained and their properties are discussed.

The ratio of the transverse-diffusion coefficient to the mobility determines the transverse Gaussian spreading of a pencil beam of ions pulled through a buffer gas by a uniform electric field. The mathematical basis for this effect is reviewed and a precision apparatus to measure the transverse spread is described. Measurements of the transverse diffusion of ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}^{2+}$ in Ar in the pressure range from 0.2 to 0.6 Torr at room temperature for $\frac{E}{N}$ values ranging from 30 to 290 Td are presented and discussed ($1 \mathrm{Td}\equiv {10}^{-17\mathrm{}} \mathrm{V}$ ${\mathrm{cm}}^2$).

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

We consider a Pólya random walk, i.e., an unbiased, nearest-neighbor walk, on a $d$-dimensional hypercubic lattice and study the scaling behavior of the mean end-to-end resistance of the walk as a function of the number of steps in the walk. The resistance of the walk is generated by assigning a constant conductance to each step of the walk. This problem was recently proposed by Banavar, Harris, and Koplik, and may be useful for understanding the physics of disordered systems. We develop a position-space renormalization-group approach, a generalization of the one developed for percolation conductivity, and study the problem and a modification of it proposed here in one, two, and three dimensions. Our results are in good agreement with the numerical estimates of Banavar et al.

The scope of the quasiclassical procedure previously used by us for estimating atomic-electron momentum densities exclusively from the knowledge of electron densities has been extended to diatomic molecules. This procedure yields a spherically averaged molecular-electron momentum density from which the corresponding Compton profile and $〈p^n〉$ expectation values may be computed. The procedure has been tested for the molecules ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$. The Compton profiles and $〈p^n〉$ values thus obtained compare well with their wave-function and experimental counterparts.

New and simple extrapolation techniques are introduced, of relevance to variational calculations in atomic and molecular physics. The inverse of the number of independent basis functions usually used as the independent variable in the extrapolation to infinite basis sets is replaced by a measure of the goodness of the representation that a basis set offers. This approach will, in some cases, provide a remarkable improvement in the stability and accuracy of the extrapolation. Two different methods are presented with numerical examples.

Recently Pathak and Gadre discussed the relationship between the electron density $\rho \mathrm{}\left(r\right)\mathrm{}$ and the expectation values $〈p〉$ and $〈p^{-1\mathrm{}}〉$. In previous work by the author, using the Na atom as an example, the Thomas-Fermi-Dirac energy-density functional has been used to assess the effect of the (modified) Weizsäcker, and the combined effect of the (modified) Weizsäcker and Hodges gradient expansion corrections on $\rho \mathrm{}\left(r\right)\mathrm{}$. In this paper use is made of the respective electron densities, and the effect of the gradient expansion corrections on the expectation values $〈p〉$ and $〈p^{-1\mathrm{}}〉$ is assessed. It is found that the effect of the (modified) Weizsäcker correction is significant, while the effect of the Hodges correction is more modest.

The results of a calculation of the muonium hyperfine structure for the $n=2\mathrm{}$ level are reported here. This calculation includes all recoil corrections through order ${\alpha }^5$. The results presented here differ markedly with those previously reported. The reason for this difference is explained. A further discussion indicates that results presented here are appropriate for an experimental comparison.

The arguments for the exactness of the quantization effects of modern physics are discussed. Some comments are made on past and possible experiments which combine these quantum effects.

Cross sections for elastic scattering of 25-, 50-, and 100-keV protons by helium atoms are calculated in the Glauber approximation. The results agree well with experiments at 25 keV, but they are larger than experimental results by about a factor of 2 and 4 at 50 and 100 keV, respectively, at all scattering angles of measurements.

A modified local-plasma model, based on the works of Lindhard and Winther, and Bethe, Brown, and Walske is established. The Gordon-Kim model for molecular-electron density is used to calculate stopping power of ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and water vapor for protons of energy ranging from 40 keV to 2.5 MeV, resulting in good agreement with experimental data. Deviations from Bragg's rule are evaluated and are discussed under the present theoretical model.

The dependence of the differential cross section for laser-assisted elastic electron-hydrogen scattering on the direction of propagation of the laser beam is studied by discarding the usual dipole approximation for the incident electron wave function. Representative numerical results are presented for a Nd-glass laser, which display a significant dependence at intensities of the order of ${10}^{11}$-${10}^{12}$ W/${\mathrm{cm}}^2$.

A general differential-cross-section formula for the inelastic scattering of relativistic spin-½ particles by heavy atoms is derived in the Born approximation and the structure and polarization of the incident particle is incorporated. The results reduce to those of Fano and of Turner et al. in well-known limiting cases.

Calculations of the proton ionization cross section of ${\mathrm{Li}}^{1+}$, ${\mathrm{C}}^{1+}$, and ${\mathrm{N}}^{1+}$, done in the plane-wave Born approximation, are compared with recent measurements. Agreement to 25% or better is found above 100 keV. Comparison of the explicit calculations with scaled neutral-atom $2s$ and $2p$ subshell cross sections show that the scaled cross sections will underestimate the measurements by a factor of 2.

Photoionization calculations of the first excited $d$ states of the alkali-metal atoms are performed within the Hartree-Fock approximation with full exchange. Effects of the variation of the asymptote of the initial excited-state wave functions on the photoionization cross sections are studied. Results are presented indicating that a small inaccuracy in the asymptote of the excited-state wave function leads to a disagreement between length and velocity results, the latter being more reliable. It is recommended that both the length and velocity results be reported to indicate the accuracy of calculations.

Explicit expressions for the constants of motion and the complete solution for the time evolution of the density matrix of a three-level system excited by two laser fields whose amplitudes are sinusoidally modulated and have a phase difference of $\frac{\pi }{2}$ are presented.

The exact fluorescence spectrum for two atoms in a monochromatic driving field is analyzed. The dipole-dipole interaction is treated in the small-sample approximation, and finite detuning from the atomic resonance is also allowed for. The terms dominating the high-field spectrum are given explicitly, as well as a Lorentzian decomposition valid for the case of well-separated peaks.

We have shown that classical three-wave mixing equations can be recast into a form which is isomorphic to Lorenz equations for turbulence. The possibility of Lorenz-type optical chaos is predicted.

Several aluminum lines observed in the Princeton Large Torus tokamak discharges have been identified as intersystem transitions, establishing the energies of the Al VIII $2s2p{}_{}{}^{35}{}_{}{}^{}S$, Al IX $2s2p{}_{}{}^{24}{}_{}{}^{}P$, and Al X $2s2p{}_{}{}^3{}_{}{}^{}P$ terms. Some observations of isoelectronic transitions in scandium and titanium ions are also reported.

The Landau theory of twist-induced biaxiality in cholesteric liquid crystals is presented. Results are given for the asymmetry parameter ${\eta }_C$ as a function of temperature and chirality. These are compared with the experimental data of Yaniv et al. and the Maier-Saupe-type calculation of Lin-Liu and Lee. While the theoretical curves are qualitatively similar to those reported experimentally, the magnitude of the latter is as much as an order-of-magnitude greater than the theoretical prediction. Some possible reasons for this discrepancy are discussed.