Showing papers in "Physical Review A in 1979"

Importance of classical diffusion in NMR studies of water in biological cells

Abstract: Nuclear-magnetic-resonance measurements of the proton-spin relaxation for water in biological cells are known to exhibit a multiexponential decay. A theory, based on the diffusion equation using the bulk diffusivity of water, is developed to explain this phenomenon. It is shown that multiexponential decay arises simply as a consequence of an eigenvalue problem associated with the size and shape of the cell and that this multiexponential decay can only be observed for samples whose size is of the order of a biological cell. As an example, the theory is applied to a previously published data for rat gastronemius cells. Excellent agreement is obtained, and furthermore, the size of the cell is calculated by fitting the theory to the experiment.

Late stages of spinodal decomposition in binary mixtures

Abstract: The influence of hydrodynamic interactions on the coarsening rate r of a mist of droplets combining through diffusive coalescence is examined in detail. For a sufficiently rarified mist, the competing LifshitzSlyozov or evaporation-condensation mechanism is dominant, but the volume fraction of precipitate actually produced in most off-critical quench experiments probably favors direct coalescence, When the minority phase is continuous, as in a quench at the critical concentration, surface-tension eA'ects lead to a crossover from r -t'" to r -t, where t is the time.

Laser cooling of atoms.

Abstract: Various aspects of the laser cooling of atoms are investigated theoretically. More generally, the authors investigate a process through which the kinetic energy of a collection of resonant absorbers can be reduced by irradiating these absorbers with near-resonant electromagnetic radiation. The process is described here as anti-Stokes spontaneous Raman scattering. Cooling mechanisms, rates, and limits are discussed for both free and bound atoms.

Thermodynamics: A Riemannian geometric model

Abstract: By including the theory of fluctuations in the axioms of thermodynamics it is shown that thermodynamic systems can be represented by Riemannian manifolds. Of special interest is the curvature of these manifolds which, for pure fluids, is associated with effective interparticle interaction strength by means of a general thermodynamic "interaction hypothesis." This interpretation of curvature appears to be consistent with hyperscaling and two-scale-factor universality. The Riemannian geometric model is a new attempt to extract information from the axioms of thermodynamics.

Theory of electromagnetic beams

Abstract: A relatively simple method for calculating the properties of a paraxial beam of electromagnetic radiation propagating in vacuum is presented. The central idea of the paper is that the vector potential field is assumed to be plane-polarized. The nonvanishing component of the vector potential obeys a scalar wave equation. A formal solution employing an expansion in powers of $\frac{{w}_{0}}{l}$ is obtained, where ${w}_{0}$ is the beam waist and $l$ the diffraction length. This gives the same result for the lowest-order components of the transverse and longitudinal electric field of a Gaussian beam that was derived by Lax, Louisell, and McKnight using a more complicated approach. We derive explicit expressions for the second-order transverse electric field and the third-order longitudinal field corrections.

Theory of simple classical fluids: Universality in the short-range structure

Abstract: It is shown to within the accuracy of present-day computer-simulation studies that the bridge functions (i.e., the sum of elementary graphs, assumed zero in the hypernetted-chain approximation) constitute the same universal family of curves, irrespective of the assumed pair potential. In view of the known parametrized results for hard spheres, this observation introduces a new method in the theory of fluids, one that is applicable to any potential. The method requires the solution of a modified hypernetted-chain equation with inclusion of a one-parameter bridge-function family appropriate to hard spheres, and the single free parameter (the hard-sphere packing fraction) can be determined by appealing to the requirements of thermodynamic consistency. The assertion of universality is actually demonstrated via the application of this new method to a wide class of different potentials: e.g., hard spheres, Lennard-Jones, an inverse fifth power (${r}^{\ensuremath{-}5}$) applicable to the helium problem, the Coulomb potential (i.e., the one-component plasma), charged hard spheres, an oscillatory potential proposed for certain liquid metals, and the Yukawa potential.

Stark structure of the Rydberg states of alkali-metal atoms

Abstract: The authors describe practical methods for calculating the Stark structure of Rydberg states of the alkali metals based on diagnolization of the energy matrix. A survey of Stark structures is presented for all of the alkali metals in the vicinity of $n=15$. Topics discussed include general methods for evaluating radial matrix elements, the treatment of fine structure, oscillator-strength distribution, scaling laws, the structure of a level anticrossing, and sources of error. Experimental Stark maps are compared with calculated results for lithium and cesium. Experimental studies of the oscillator-strength distribution within a Stark manifold and the structure of a level anticrossing are also presented.

Origin of the nonlinear second-order optical susceptibilities of organic systems

Abstract: An all-valence-electron self-consistent-field linear-combination-of-atomic-orbitals molecular-orbital procedure including configuration interactions for calculating the magnitude and sign of the nonlinear second-order molecular susceptibility components (hyperpolarizability) for substituted dipolar aromatic molecular systems is reported. Three fundamentally important examples, aniline, nitrobenzene, and $p$-nitroaniline, are considered. Analysis of the microscopic origin of their molecular second-order susceptibilities provides a direct means for understanding the macroscopic nonlinear optical response of organic molecular solids which have already been observed to possess exceptional nonlinear optical properties. The important excited states of aniline, nitrobenzene, and $p$-nitroaniline have been identified and examined in their relationship with the molecular second-order susceptibility-tensor components ${\ensuremath{\beta}}_{\mathrm{ijk}}$. The detailed nature of the charge separation accompanying these states has been discussed in terms of both the configurations composing the excited states, and also the one-electron molecular orbitals which determine those configurations. These results demonstrate how the bond-additivity approximation is inappropriate for $p$-nitroaniline. Finally, the frequency dependence of the ${\ensuremath{\beta}}_{\mathrm{ijk}}$ components in each case shows that the Kleinman relations are valid approximations only at relatively low frequencies.

Ground state of a spin-½ charged particle in a two-dimensional magnetic field

Abstract: We prove that a spin-\textonehalf{} charged particle moving in a plane under the influence of a perpendicular magnetic field has ($N\ensuremath{-}1$) zero-energy states, where $N$ is the closest integer to the total flux in units of the flux quantum. The ($N\ensuremath{-}1$) independent wave functions are calculated explicitly. The result, which is extremely simple to prove, is an example of the Atiyah-Singer index theorem when applied to the Euclidean two-dimensional Dirac equation.

Multiplicative stochastic processes in statistical physics

Abstract: For a large class of nonlinear stochastic processes with pure multiplicative fluctuations the corresponding time-dependent Fokker-Planck-equation is solved exactly by analytic methods. A universal eigenvalue spectrum and the corresponding set of eigenfunctions are obtained in closed form. The eigenvalue spectrum consists of a discrete as well as a continuous part. To emphasize the significance of the model proposed for the description of more-general stochastic processes the authors investigate its stability with respect to the inclusion of weak additive fluctuations. A discussion of the differences in the static as well as the dynamic behavior of multiplicative and additive stochastic processes is given in detail. It is shown explicitly how internal as well as externally imposed fluctuations can lead to multiplicative stochastic processes. The applications of the results to various fields such as nonlinear optics---subharmonic generation, parametric three-wave mixing, Raman scattering---electronic devices, autocatalytic chemical reactions, and population dynamics are given. In particular, a comparison with recent experiments by S. Kabashima et al., who investigated the statistical properties of electronic parametric oscillators driven by external noise, is carried out.

L-shell Coulomb ionization by heavy charged particles

Abstract: The theory of Coulomb ionization of $L$ shells by low-velocity heavy charged particles whose atomic number is small compared to the atomic number of the target atom is extended to projectiles with velocities comparable to or larger than the $L$-shell orbital velocities. At large impact parameters projectiles polarize the shell, and at small impact parameters they increase the binding energies of the electrons to be excited. The polarization effect is incorporated in accordance with the perturbed stationary-state (PSS) approximation. The effect of the repulsion between the projectile and the target nucleus is accounted for by a Coulomb-deflection factor (C). This CPSS theory is developed further to include relativistic effects (R) of the target wave function through a procedure that reproduces the results of numerical calculations for heavy target atoms. With electron capture by the projectiles as an additional channel of ionization, the CPSSR theory is compared with experiment.

Energy spectra of certain randomly-stirred fluids

Abstract: The velocity correlations of an incompressible fluid governed by the Navier-Stokes equations are studied in steady states maintained by random-white-noise stirring forces with varying spatial correlations. The asymptotic properties of the long-wavelength fluctuations are deduced by field-renormalization-group techniques. The results of Forster, Nelson, and Stephen are recovered for the random-force spectra these authors discuss, and a Kolmogorov spectrum is obtained when the force correlations have equal strength at all wave numbers, that is, when the force correlations behave as ${k}^{\ensuremath{-}d}$ in $d$ dimensions and $dg2$. Although the derivation is valid to all orders in the anomalous dimension, it implicitly assumes that there is no crossover in operator dimensionality.

Local-density theory of multiplet structure

Abstract: In order to obtain multiplet energies and therefore energies of excited states of atoms and molecules, the local-density theory of Hohenberg, Kohn, and Sham has recently been extended to give the lowest energy of a specified angular momentum and spin symmetry. It is explained why this method does not work if the exchange correlation functional is taken to be symmetry independent. Instead it is shown how the local-density theory can be used to estimate the energies of states of mixed symmetry and how the multiplet splittings are obtained from these estimates. The new method is tested on light atoms and the local-density theory with exchange only reproduces the Hartree-Fock results within 0.1 eV. With correlation included, the error in the local-density approach is typically a factor of 3 less than in the Hartree-Fock approach.

Optimal configuration of a class of irreversible heat engines. I

Abstract: In a previous paper we analyzed a class of irreversible cyclic heat engines to find their optimal operating configuration for specific performance goals. In that paper the thermodynamic variables of the working fluid were not treated as dynamical variables, instead the dynamics was replaced by an integral constraint. In this paper we reanalyze the same class of heat engines treating the thermodynamic variables of the working fluid as dynamical variables, and we obtain the optimal configuration of the engine when the performance goal is to maximize the average power output per cycle or, alternatively, to maximize the efficiency of the engine. To carry through this program it is necessary to use mathematical techniques from optimal-control theory. Since this subject is unfamiliar to most physicists and chemists, we briefly introduce some of the central ideas of the theory.

Variational calculations of accurate e − -He cross sections below 19 eV

Abstract: Variational calculations of $s$- and $p$-wave phase shifts for ${e}^{\ensuremath{-}}$-He scattering have been carried out for energies less than 19 eV. The variational wave function represents target-atom electronic correlation, electric dipole and quadrupole polarizability response, and short-range electron-atom correlation at a level of accuracy sufficient for 1% accuracy in the differential cross section. The partial-wave Born approximation is used for phase shifts $lg1$. Calculated phase shifts are corrected for estimated systematic errors, and these estimated phase shifts are interpolated as smooth functions of energy by cubic spline fits to auxiliary interpolating functions. Comparison with recent experimental and theoretical cross section data indicates compatibility with the present error estimate of no more than 1%. Data given here make it possible to compute the differential cross section from simple formulas over the energy range considered. The present value of the scattering length is $1.1835{a}_{0}$ with 0.5% error.

Statistics of lattice animals and dilute branched polymers

Abstract: A field theory, recently introduced by the authors, whose partition function yields the generating function for the number of configurations of ${N}_{p}$ branched polymers containing ${N}_{b}$ monomers, ${N}_{f}f$-functional units, and ${N}_{L}$ loops, is used to study the statistics of animals (clusters on a lattice) and the intimately related problem of the statistics of branched polymers in the dilute limit. The number $A({N}_{b})$ of animals per site containing ${N}_{b}$ bonds grows as ${{N}_{b}}^{\ensuremath{-}\ensuremath{\theta}}{\ensuremath{\lambda}}^{N\mathrm{b}}$ as ${N}_{b}$ tends to infinity, leading to a singularity in the generating function $\ensuremath{\Xi}(K){\ensuremath{\Sigma}}_{\mathrm{Nb}}{K}^{\mathrm{Nb}}A({N}_{b})$ of the form $\ensuremath{\Xi}(K)\ensuremath{\sim}{|K\ensuremath{-}{K}_{c}|}^{\ensuremath{\theta}\ensuremath{-}1}$, where ${K}_{c}={\ensuremath{\lambda}}^{\ensuremath{-}1}$. Mean-field theory for this and other animal functions is valid above an upper critical dimension ${d}_{c}$ of 8. For the related polymer problem, ${d}_{c}$ is 8 in good solvents and 6 in $\ensuremath{\theta}$ solvents. In both cases, the critical behavior of generating and correlation functions depends on the nature of applied constraints. If a special combination of fields corresponding to the natural order parameter of the field theory is held constant, the susceptibility and correlation-length exponents $\ensuremath{\gamma}$ and $\ensuremath{ u}$ obtain their usual mean-field values of 1 and \textonehalf{} for $dg{d}_{c}$. First-order corrections in ${d}_{c}\ensuremath{-}d$ are calculated for these and other exponents. If fugacities are held constant, there is a Fisher-like renormalization of critical exponents leading to animal's exponents $\ensuremath{\theta}=\frac{5}{2}$, ${\ensuremath{\gamma}}_{a}=\frac{1}{2}$, and ${\ensuremath{ u}}_{a}=\frac{1}{4}$ for $dg{d}_{c}$; $\ensuremath{\theta}=\frac{5}{2}$ agrees with exact calculations on a Cayley tree and ${\ensuremath{ u}}_{a}=\frac{1}{4}$ with calculations by Zimm and Stackmayer of the radius of gyration of a branched polymer. For $dl{d}_{c}$, $\ensuremath{\theta}\ensuremath{-}1=\frac{(3\ensuremath{\gamma}\ensuremath{-}2{\ensuremath{\mu}}_{3})}{(2\ensuremath{\gamma}\ensuremath{-}{\ensuremath{\mu}}_{3})}$, ${\ensuremath{\gamma}}_{a}=\frac{\ensuremath{\gamma}}{(2\ensuremath{\gamma}\ensuremath{-}{\ensuremath{\mu}}_{3})}$, and ${\ensuremath{ u}}_{a}=\frac{\ensuremath{ u}}{(2\ensuremath{\gamma}\ensuremath{-}{\ensuremath{\mu}}_{3})}$, where ${\ensuremath{\mu}}_{3}$ is a critical exponent controlling the critical behavior of an irrelevant three-point vertex that is of order $d\ensuremath{-}{d}_{c}$ for $d$ near ${d}_{c}$. Both the constant-order-parameter and constant-fugacity theories violate the hyperscaling $d\ensuremath{ u}=2\ensuremath{-}\ensuremath{\alpha}$, where $\ensuremath{\alpha}$ is the specific-heat exponent.

Coherent states and the resonance of a quantum damped oscillator

Abstract: A quantum-mechanical model of a damped harmonic oscillator (both with time-independent and time-dependent parameters) is studied in the framework of the linear Schr\"odinger equation with a Hermitian nonstationary Hamiltonian. Integrals of the motion of this equation and their eigenstates, including coherent states, are constructed. The influence of an external harmonic force to the time evolution of various average values calculated over coherent states is considered, including the resonance case. The specific symmetry of the Hamiltonian leading to the new concept of loss-energy states is discussed.

Variance of the distributions of energy levels and of the transition arrays in atomic spectra

Abstract: Formulas are derived for the mean values and variances of the energy distributions of the levels of an atomic configuration and of the radiative transitions between the levels of two configurations (in intermediate coupling). The variance ${\ensuremath{\sigma}}^{2}$ of the distribution of the eigenstate energies belonging to a given configuration is considered first: ${\ensuremath{\sigma}}^{2}$ is expressed as a linear combination of squares and cross products of the usual Slater electrostatic and spin-orbit radial integrals. It is shown how this expression can be used to check the numerical matrices of energy-integral coefficients. Then expressions are derived for the mean value and for the variance of the weighted distribution of the transition energies between two configurations (the weight of each transition being its strength) in the $n{l}^{N+1}\ensuremath{-}n{l}^{N}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ and $n{l}^{N}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}\ensuremath{-}n{l}^{N}{n}^{\ensuremath{'}\ensuremath{'}}{l}^{\ensuremath{'}\ensuremath{'}}$ cases. This derivation is based on the second-quantization formalism. An extension is made to the case of complementary configurations. For transitions $n{l}^{N+1}\ensuremath{-}n{l}^{N}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$, an explicit formula is obtained for the shift between the mean energy of the transition array and the difference of the mean energies of the configurations. Numerical tables of the angular coefficients appearing in ${\ensuremath{\sigma}}^{2}$ are given for most cases where $l$, ${l}^{\ensuremath{'}}$, ${l}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\le}3$. The main application presented here concerns highly ionized spectra of molybdenum, with transitions between $3{d}^{N+1}$ and $3{d}^{N}4p$, $3{d}^{N}4f$, $3{d}^{N}5p$, and $3{d}^{N}5f$. The agreement between experimental and theoretical (ab initio) mean wave numbers and variances is good. A discussion of the physical conditions of applicability of the results to experimental situations is given.

Spin-density gradient expansion for the kinetic energy

Abstract: Expressions for the kinetic energy $T$ (and incidentally also for the exchange energy ${E}_{x}$) of a ground-state inhomogeneous electron gas as a functional of the electron density $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, and for $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ as a functional of the one-electron potential $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, are readily generalized to the case of two unequal spin densities ${n}_{\ensuremath{\uparrow}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ and ${n}_{\ensuremath{\downarrow}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$. As an example the authors consider the expansions of $T$ up to fourth order in the gradients of $n$, and of $n$ up to fourth order in the gradients of $V$. These expansions are tested for the extreme case of one- and two-electron atoms. It is found that (i) The $n[V]$ expansion contains serious pathologies, while the $T[n]$ expansion leads to much more reasonable results when applied to either the exact density $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ or to an $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ obtained by minimization of the approximate total-energy functional $E[n]$. (ii) Good approximations to $E$ and $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ in one-electron atoms are obtained only when the complete spin polarization of a single electron is taken into account via $T[{n}_{\ensuremath{\uparrow}}, {n}_{\ensuremath{\downarrow}}]$. (iii) Within a variational calculation, the inclusion of second- and fourth-order gradient corrections to the zeroth-order (Thomas-Fermi) approximation for $T$ leads to systematic improvements in the analytic behavior of $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ near the nucleus. The authors also compare the local-exchange approximation with the local-exchange-correlation approximation in one- and two-electron atoms, and find that correlation should not be neglected.

Electroclinic effect at the A-C phase change in a chiral smectic liquid crystal

Abstract: 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.

Dissociative attachment and vibrational excitation in low-energy collisions of electrons with H 2 and D 2

Abstract: Bardsley JN, Wadehra JM. Dissociative attachment and vibrational excitation in low-energy collisions of electrons with H2 and D2.

The Non-Linear Theory of Free Electron Lasers and Efficiency Enhancement

Abstract: The development of lasers in which the active medium is a relativistic stream of free electrons has recently evoked much interest. The potential advantages of such free-electron lasers include, among other things, continuous frequency tunability, very high operating power, and high efficiency. The free-electron laser (FEL) is characterized by a pump field, for example, a spatially periodic magnetic field which scatters from a relativistic-electron beam. The scattered radiation has a wavelength much smaller than the pump wavelength, depending on the electron-beam energy. The authors present a general self-consistent nonlinear theory of the FEL process. The nonlinear formulation of the temporal steady-state FEL problem results in a set of coupled differential equations governing the spatial evolution of the amplitudes and wavelength of the radiation and space-charge fields. These equations are readily solved numerically since the amplitude and wavelength vary on a spatial scale which is comparable to a growth length of the output radiation. A number of numerical and analytical illustrations are presented, ranging from the optical to the submillimeter-wavelength regime. Our nonlinear formulation in the linear regime is compared with linear theory, and agreement is found to be excellent. Analytical expressions for the saturated efficiency and radiation amplitude are alsomore » shown to be in very good agreement with our nonlinear numerical solutions. Efficiency curves are obtained for both the optical and submillimeter FEL examples with fixed magnetic-pump parameters. It is shown that these intrinsic efficiencies can be greatly enhanced by appropriately contouring the magnetic-pump period. In the case of the optical FEL, the theoretical single-pass efficiency can be made greater than 20% by appropriately decreasing the pump period and increasing the pump magnetic field.« less

General form of the quantum-defect theory

Abstract: The quantum-defect-theory (QDT) treatment of an electron in the Coulomb field surrounding an ionic core is recast in a form largely independent of field characteristics and thus applicable, e.g., to square wells or to the Morse fields of diatomic molecules. The reformulation parallels Seaton's classification of alternative Coulomb-field wave functions, and makes it applicable to other fields. Wronskians of alternative pairs of base functions have an important role in the theory. For electron energies $\ensuremath{\epsilon}l0$ in a Coulomb field these Wronskians reduce to trigonometric functions of $\ensuremath{ u}={(\ensuremath{-}2\ensuremath{\epsilon})}^{\ensuremath{-}\frac{1}{2}}$, familiar in the QDT; other fields lead to trigonometric functions of different arguments. Quantum defects are generalized to eigenvalues of a reaction matrix, as in Seaton's work, but this matrix can now be calculated even below threshold energies with the introduction of a "smooth" Green's function appropriate to QDT applications.

Molecular hyperpolarizabilities. I. Theoretical calculations including correlation

Abstract: Static polarizabilities and hyperpolarizabilities for molecules are investigated at the correlated level. The finite-field, coupled Hartree-Fock theory is used as a zeroth-order approximation, with correlation included by using the linked-diagram expansion and many-body perturbation theory, that includes single, double, and quadruple excitation diagrams. The theory is illustrated by studying the hydrogen fluoride molecule. It is demonstrated that the correlation effect for the hyperpolarizabilities $\stackrel{\ensuremath{\leftrightarrow}}{\ensuremath{\beta}}$ and $\stackrel{\ensuremath{\leftrightarrow}}{\ensuremath{\gamma}}$ can be quite large. The average polarizability and dipole moment of HF are in excellent agreement with experiment. The relative importance of the various types of diagrams contributing to electric field properties are discussed. The dependence of the computed hyperpolarizability on basis sets is also investigated.

Absolute cross sections from the "boomerang model" for resonant electron-molecule scattering

Abstract: The boomerang model is used to calculate absolute cross sections near the $^{2}\ensuremath{\Pi}_{g}$ shape resonance in $e$-${\mathrm{N}}_{2}$ scattering. The calculated cross sections are shown to satisfy detailed balancing. The exchange of electrons is taken into account. A parametrized complex-potential curve for the intermediate ${\mathrm{N}}_{2}^{\ensuremath{-}}$ ion is determined from a small part of the experimental data, and then used to calculate other properties. The calculations are in good agreement with the absolute cross sections for vibrational excitation from the ground state, the absolute cross section $v=1\ensuremath{\rightarrow}2$, and the absolute total cross section.

Production of highly charged low-velocity recoil ions by heavy-ion bombardment of rare-gas targets

Abstract: The author has measured charge-state ($q$) spectra of recoil ions generated in single collisions of 25-45-MeV chlorine ions with targets of helium, neon, and argon. A high-efficiency time-of-flight spectrometer was used to identify the charge-to-mass ratio of the slowly moving recoils. Recoil $q$ up to + 8 (neon) and + 11 (argon) were observed. Cross sections for recoil production were measured as a function of projectile energy and incident charge state. The energy dependence of the cross sections is quite weak, while the recoil-$q$ dependences show clear shell effects in argon. For the lower-$q$ recoils, the cross sections are reasonably well described by the model of Olson, which treats the target electrons as moving independently. For higher $q$, a model based on energy deposition by the projectile with the target electrons, followed by statistically weighted electron emission, gives a better description of the data.

Multichannel relativistic random-phase approximation for the photoionization of atoms

Abstract: A multichannel relativistic random-phase approximation (RRPA) for the photoionization of atoms is presented. The RRPA equations are obtained by generalizing the nonrelativistic time-dependent Hartree-Fock equations using the Dirac-Breit Hamiltonian to describe the atomic electrons. The angular decomposition of the RRPA equations to a set of coupled equations for the radial wave functions is given, and the radiative-transition operators are developed for arbitrary electric and magnetic multipoles. Formulas are obtained for the total photoionization cross sections and angular distributions, including all multipoles. The method of constructing multichannel solutions from the RRPA radial wave functions is described and various ways of choosing approximate potentials for the photoelectron are given.

Measurements of nonlinear optical polarizabilities for twelve small molecules

Abstract: Second- and third-order nonlinear optical polarizabilities for a number of small molecules---${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, ${\mathrm{O}}_{2}$, CO, NO, C${\mathrm{O}}_{2}$, ${\mathrm{H}}_{2}$O, ${\mathrm{H}}_{2}$S, N${\mathrm{H}}_{3}$, S${\mathrm{F}}_{6}$, (C${\mathrm{H}}_{3}$)$_{2}\mathrm{O}$, and C${\mathrm{H}}_{3}$OH---are derived from measurements of the temperature dependence of dc-electric-field-induced optical second-harmonic generation in the gas phase. Agreement with related measurements (where available) is generally adequate, but the results of theoretical calculations taken from the literature are in poor agreement with the experimental data. Consideration of the present results for ${\mathrm{H}}_{2}$O together with liquid-phase measurements by Levine and Bethea offers a means of investigating intermolecular interactions in liquid water. The bond-additivity approximation applied to ${\mathrm{H}}_{2}$O, (C${\mathrm{H}}_{3}$)$_{2}\mathrm{O}$, and C${\mathrm{H}}_{3}$OH yields surprisingly good fits of the dipole moment, linear polarizabilities, and second- and third-order nonlinear polarizabilities to experimental data.