The absolute impact-parameter dependence of $K$-shell ionization probability $I\left(p\right)\mathrm{}$ has been measured in the range ${10}^{-12\mathrm{}}$-${10}^{-11\mathrm{}}$ cm at incident proton energies of 1 and 2 MeV with Al, Cu, and Ti targets. In the first part we give a condensed survey of previous results showing that a detailed investigation of $I\left(p\right)\mathrm{}$ behavior at very small impact parameters is required for a better understanding of this problem. Such a study provides a useful check on the accuracy of classical and semiclassical ionization theories in a region where they are more likely to fail. Our results, obtained by a coincidence method, are compared with the presently available theories: the binary-encounter approximation and the semi-classical approximation. A systematic deviation is found between experimental and theoretical data which is not accounted for when relativistic effects and the actual projectile trajectory are included in the binary-encounter-approximation model.

Starting with a $1s$ vacancy in the neon atom, Auger rates are calculated for transitions to the final $\mathrm{LS}$-coupled states of ${\mathrm{Ne}}^{++}$. Electron correlations are found to have a significant effect on these rates. Although the configuration mixing of ${\mathrm{Ne}}^{++}$ ${\mathrm{}\left(1s\right)\mathrm{}}^2{\mathrm{}\left(2s\right)\mathrm{}}^2{\mathrm{}\left(2p\right)\mathrm{}}^4 {}_{}{}^1{}_{}{}^{}S$ and ${\mathrm{}\left(1s\right)\mathrm{}}^2{\mathrm{}\left(2p\right)\mathrm{}}^6 {}_{}{}^1{}_{}{}^{}S$ is important, good results are only obtained by also considering the other correlation effects representing mixing with other configurations. The ratios of calculated Auger rates relative to the $1s-2s2s {}_{}{}^1{}_{}{}^{}S$ rate are in close agreement with experiment. However, the calculated absolute rates are all higher than the experimental values of Mehlhorn, Stalherm, and Verbeek by factors ranging from 1.4 to 1.5.

The ($e, 2e$) reaction is used to investigate the binding energies and angular correlations for electrons ejected from the $4p$ and $4s$ orbitals of krypton. Configuration interaction in the ion eigenstates is the dominant feature in the ejection of a $4s$ electron. Only (30±3)% of the strength of the $4s$ hole state is contained in the ion eigenstate with the dominant configuration $4s4p^6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$. The angular correlations calculated with the distorted-wave off-shell impulse approximation, and using the Hartree-Fock wave functions of Froese-Fischer, agree very well with the observed angular correlations. In addition, relative to a $4p^{-1\mathrm{}}$ spectroscopic factor of unity, the $4s^{-1\mathrm{}}$ spectroscopic factors for the various excited ion eigenstates sum to 0.99 ± 0.08. Data are also presented on the binding energies of electrons ejected from the outer $s$ and $p$ orbitals in neon and argon, and the role of configuration interaction in the $s^{-1\mathrm{}}$ states is discussed. Incident electron energies are approximately 200, 400, and 800 eV.

The angular correlations and binding-energy spectra have been measured for electrons ejected from the valence shells of He, Ne, Ar, and Xe in the coplanar symmetric geometry. The data have been analyzed with the distorted-wave off-shell impulse approximation using the Hartree-Fock wave functions of Froese-Fischer. The sensitivity of the coplanar symmetric cross section to distortion of the electron waves has enabled us to verify that the distortion effects are small and consistent with the optical model for elastic scattering. Large correlation effects are observed in the xenon $5s^{-1\mathrm{}}$ and argon $3s^{-1\mathrm{}}$ states, but correlation is negligible for the neon $2s^{-1\mathrm{}}$ state. Spectroscopic factors and single-particle binding energies are determined for the neon, argon, and xenon $s$ states.

Total charge-exchange cross sections for ${\mathrm{Kr}}^{+}$ and ${\mathrm{Xe}}^{+}$ incident on Cs have been measured. The energy of the incident ion was in the range 1.0-28.7 keV for ${\mathrm{Kr}}^{+}$ and in the range 1.0-17.2 keV for ${\mathrm{Xe}}^{+}$. The cross section ${\sigma }_{+0\mathrm{}}$ for ${\mathrm{Kr}}^{+}$ incident on Cs is (884 ± 86) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 1.0 keV, and increases to (1171 ± 41) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 5.0 keV. From 5.0 up to 28.7 keV, the cross section lies between 1100 × ${10}^{-17\mathrm{}}$ and 1200 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$. The cross section ${\sigma }_{+0\mathrm{}}$ for ${\mathrm{Xe}}^{+}$ incident on Cs is (942 ± 53) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 1.0 keV, and increases to (1297 ± 71) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 7.2 keV. From 7.2 to 17.2 keV, the cross section lies between 1250 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ and 1440 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$.

The total cross section for charge exchange or breakup when ${\mathrm{D}}_2^{+}$ is incident on Cs has been measured in the energy range 3.0-23 keV. The cross section has a value of (1362 ± 80) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 3 keV and falls rapidly with increasing energy, reaching a value of (594 ± 40) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 23 keV. The equilibrium fraction of ${\mathrm{D}}^{-}$ obtained when ${\mathrm{D}}_2^{+}$ is incident on Cs has also been measured. The equilibrium fraction of ${\mathrm{D}}^{-}$ is (10.5 ± 2.0)% at 3 keV, (7.3 ± 1.6)% at 5 keV, (3.4 ± 0.7)% at 11.5 keV, (2.0 ± 0.4)% at 17.3 keV, and (1.5 ± 0.3)% at 23 keV. The equilibrium fraction of ${\mathrm{D}}^{-}$ obtained when ${\mathrm{D}}_2^{+}$ is incident on Cs at an energy $E$ is shown experimentally to be the same as the equilibrium fraction of ${\mathrm{D}}^{-}$ obtained when ${\mathrm{D}}^{+}$ is incident on Cs at an energy $\frac{1}{2}E$. The angular distribution of the reaction products when ${\mathrm{D}}_2^{+}$ ions are incident on Cs includes appreciable scattering into angles which are larger than 1°. An explanation of these large scattering angles is offered.

It is shown that the previous parametric-instability explanation of the jump in the Stokes intensity $I_S$ as a function of laser intensity $I_L$ in stimulated Raman scattering experiments is valid for many solids, liquids, and gases (with high optical dispersion $\frac{\mathrm{dn}}{d\lambda }$ and high Raman frequency ${\omega }_f$), while a few materials (low $\frac{\mathrm{dn}}{d\lambda }$ and ${\omega }_f$) should show an enhanced gain, $I_S\sim \exp I_L^2$, which is greater than the usual stimulated-Raman gain but not as great as the jump result. The previously anomalous experimental results of Grun, McQuillan, and Stoicheff and of others, which show the jump in $I_S$, and of Hagenlocker, Minck, and Rado, which show both types of behavior, are explained. The instability is expected to be important in laser damage of Raman-active crystals and possibly in determining the limiting diameter of self-focused beams. The transient solution for the case of high dispersion indicates that the steady state is not reached until a time much greater than the Raman phonon-relaxation time. It is also shown that a phonon parametric instability studied previously in another context can reduce the Stokes intensity. Experiments to detect the phonon instability and measure the magnitude and temperature dependence of "half-frequency" phonons $Q$ (with frequencies ${\omega }_Q+{\omega }_{-Q}={\omega }_f$) are suggested.

Cross sections for ionization of the $L_{\mathrm{I}}$, $L_{\mathrm{II}}$, and $L_{\mathrm{III}}$ subshells in Ta, Au, and Bi have been measured for proton energies from 1.0 to 5.5 MeV and $\alpha$-particle energies from 1.0 to 11.0 MeV. X-ray spectra recorded with a Si(Li) detector were used to deduce the subshell ionization cross sections: $L\alpha$ components give $L_{\mathrm{III}}$ subshell ionization cross sections ${\sigma }_{L_3}$, and $L\gamma$ components were computer analyzed into $L{\gamma }_5$, $L{\gamma }_1$, $L{\gamma }_{2+3}$, and $L{\gamma }_4$ to give the $L_{\mathrm{II}}$ and $L_{\mathrm{I}}$ subshell ionization cross sections, ${\sigma }_{L_2}$ and ${\sigma }_{L_1}$, respectively. The data are compared with simple model calculations. The necessity of including some small but significant additional effects in the plane-wave Born-approximation treatment, particularly wave functions more realistic than the normally assumed hydrogenic forms, is discussed.

A theory of coherent two-photon resonance is developed by applying a canonical transformation on the Heisenberg equation of atomic motion. The theory leads both to the optical Bloch equation and the second-order induced polarization which drives the classical Maxwell's equation. The expressions for the Rabi frequency and the induced polarization are given explicitly for two-photon absorption and Raman effect. The results are applied to coherent steady-state propagation, and two kinds of pulses are derived for different-frequency two-photon absorption, including the atomic frequency shift.

The characteristics of a laser with an intracavity absorption cell have been calculated for the case in which the gain atoms are homogeneously broadened and the absorber atoms are inhomogeneously broadened. The sensitivity of the laser intensity to the density of absorbers is determined.

In this paper we present a new approach to the problem of unstable laser resonators. We consider a stable resonator in which we insert a thin diverging lens near one mirror. By varying the focal length of the lens, the lens-resonator system can go from stable to unstable. We expand the field in the lens-resonator system in terms of the normal modes of the original stable resonator. The polarization of the lens causes coupling of the stable modes. The present method allows one to introduce the active lasing medium in a natural way, as is shown. The normal modes of the unstable resonator are obtained numerically, along with analytic solutions in certain limiting cases. A physical discussion of the unstable resonator problem is given in terms of a pseudospin picture.

The Kubo response-function formalism is utilized to obtain expressions for the magnetization created in a plasma by a circularly polarized electromagnetic wave. This effect, the inverse Faraday effect, has previously been studied only in the dipole approximation. The present treatment includes plasma polarization effects and allows consideration of the thermal motion and relativistic effects associated with high-powered laser radiation. A physical interpretation of the results is presented in which the angular momentum stored in the plasma is shown to be the basis of the effect.

A novel fluid-transport calculation by computer simulation, via nonequilibrium molecular dynamics, of laboratory methods of transport measurement is described. Shear viscosity of soft-sphere ($r^{-12\mathrm{}}$ potential) and Lennard-Jones particles ($r^{-12\mathrm{}}-r^{-6\mathrm{}}$ potential) has been obtained from molecular dynamic modeling of Couette flow. Soft-sphere deviations from Enskog theory are similar to those found for hard spheres by Alder, Gass, and Wainwright, using time-correlations of equilibrium molecular dynamic system fluctuations. For the Lennard-Jones shear viscosity near the triple-point region, there is agreement between the equilibrium calculation of Levesque, Verlet, and Kurkijarvi and the nonequilibrium results using 108 atoms in a cube. However, systems two and three cubes wide give lower results, which, when extrapolated with inverse width, yield close agreement with the experimental argon shear viscosity. Comparison of the Lennard-Jones shear viscosity with experimental argon data along the saturated vapor-pressure line of argon confirms our successful simulation of macroscopic viscous flow with few-particle nonequilibrium molecular dynamic systems. A new result of the nonequilibrium molecular dynamics is the characterization of nonequilibrium distribution functions, which might provide the basis for a perturbation theory of transport. Since momentum transport is primarily accomplished by the repulsive potential core for high temperatures, the Lennard-Jones shear viscosity must behave like the soft-sphere system for high temperatures [viscosity divided by ${\left(\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\right)}^{\frac{2}{3}}$ is a function of density divided by ${\mathrm{}\left(\mathrm{temperature}\right)\mathrm{}}^{\mathrm{¼}}$]. In fact, the calculated excess shear viscosity (that part above the zero-density temperature dependence) has been successfully correlated in terms of the 12th-power scaling variables for temperatures as low as the critical value (along the freezing line). The utilization of soft-sphere scaling variables yields relatively simple functions for describing both the excess shear viscosity and the thermal-conductivity behavior throughout the fluid phase. The introduction of these scaling variables also clearly reveals two features: (i) weak temperature dependence, and (ii) the sign of the temperature derivative at constant density (negative for shear viscosity and positive for thermal conductivity). While both of these features have been experimentally observed in simple fluid experimental data, their cause has not been previously traced to the dominance of the core potential. Thus, the soft-sphere scaling variables should be useful for correlating experimental data.

A detailed theoretical and simulation study of resonant absorption in a hot plasma is presented which isolates the behavior of the plasma for times short compared to an ion response time. The extent to which an electron fluid model can describe the absorption process in the kinetic regime is discussed. At high intensities the absorbed energy is observed to be deposited in a suprathermal tail of electrons whose energy varies approximately as the square root of the incident power. The density profile modification due to the ion response to the pondermotive force is also discussed.

The relationship between a second-rank tensor anisotropy and the orientational order in a cholesteric liquid crystal is derived. The results are confirmed by nuclear-magnetic-resonance (NMR) second-moment measurements on both the cholesteric and nematic phases of a mixture of cholesteryl chloride and $p$-azoxyanisole. The dipole NMR line shape of this sample in the cholesteric phase is explained entirely by the static cholesteric structure.

A relativistic electron beam entering a metallic drift tube filled with neutral gas at low pressure (e.g., 0.1-0.5 Torr ${\mathrm{H}}_2$) creates a potential well which may result in acceleration of ions to several times the beam energy. We have studied this process computationally, with emphasis on the modeling of a number of recent experiments. The code agrees with most of the experimental results, and verifies a recently proposed model for the acceleration process.

The neutron inelastic scattering from orthobaric liquid neon at 26.9 °K has been measured with a triple-axis crystal spectrometer operating in its constant-$Q$ mode. The scattering was measured as a function of frequency $\nu$ for 34 values of $Q$ in the range 0.8-12.5 ${\mathrm{\AA }}^{-1\mathrm{}}$. Corrections for residual multiple scattering and instrumental resolution were applied to the theoretical cross sections before comparing with experiment. In the region of collective behavior, $Q\lesssim 4$ ${\mathrm{\AA }}^{-1\mathrm{}}$, the quasielastic peak that is observed is in qualitative agreement with the Kerr - Singwi theory and with the memory-function theory, which is applied to neon in the present work. The observed scattering at constant $Q(<\mathrm{}1.6\mathrm{}{\AA }^{-1\mathrm{}})$ shows a pronounced inelastic wing at values of $\nu$ where the memory-function theory predicts a small inelastic peak. No such wing is contained in the Kerr-Singwi theory. The latter theory evidently overestimates the damping of the collective motion while the former underestimates it. The observed scattering in the region $Q>\mathrm{}4\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ is characteristic of single-particle scattering. The peak position follows, but lies somewhat lower than, the recoil frequency $\frac{\hslash Q^2}{4\pi m}$, where $m$ is the mass of a neon atom, and the width of the scattering function increases approximately linearly with $Q$. Superimposed on this general behavior are well-defined oscillations characteristic of the coherent nature of the scattering. The single-particle scattering in liquid neon is very similar to that observed in liquid helium. The data in the single-particle region are in reasonable agreement with the Kerr-Singwi model and in even better agreement with a truncated Gram-Charlier expansion. The earlier data of Chen et al. are corrected for the nonlinearity inherent in a time-of-flight experiment and are found to agree with the present results in showing that there are no well-defined propagating excitations in liquid neon for $Q>~0.8$ ${\mathrm{\AA }}^{-1\mathrm{}}$.

We propose here a molecular theory of liquid crystals based on well-known theory of classical liquids. The method of calculation involves the simultaneous solution of two coupled nonlinear integral equations. The one- and two-particle distribution functions are obtained, as are order parameters as functions of density and temperature. The results are compared with those of mean-field calculations.

Absolute cross sections for $K$-shell ionization by 50- to 600-keV ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ incident on C${\mathrm{H}}_4$, ${\mathrm{N}}_2$, and Ne were measured by Auger-electron spectroscopy. Previous results obtained in our laboratory for C${\mathrm{H}}_4$ and ${\mathrm{N}}_2$ are compared with these new values which are measured with an improved apparatus. The projectile $Z$ dependence of the cross section was reanalyzed using the new data.

An explicit expression for the fourth frequency moment of the spectral function of the energy-density fluctuation correlation function, and hence for the energy-density correlation f0323;nction, has been derived for a classical system of particles interacting through a two-body potential. It has been found to contain correlations up to four particles only. An expression in the long-wavelength limit for the eighth frequency moment of $S(q, \omega )$ has also been given.