An integral equation for the static structure function has been obtained for a two-dimensional classical electron liquid from the second Bogoliubov-Born-Green-Kirkwood-Yvon equation using the Totsuji-Ichimaru scheme, originally due to O'Neil and Rostoker. The results of the various static properties of two-dimensional classical electron liquid obtained from the self-consistent solution of the integral equation have been compared with the other approximation schemes and the computer results of Totsuji. It is found that the quality of our results is as good as in other approximations except that in the present approach the compressibility sum rule is better satisfied.

Besides second-harmonic generation by coupling of the incident wave with the directly driven plasma wave in resonance absorption, the incident wave can couple to a wave scattered from the critical surface which is rippled by ion-acoustic waves resulting from an instability of resonance absorption. This results in additional red shift corresponding to the frequency of the ion-acoustic waves, which, being sensitive to the plasma density-gradient scale length, has been evaluated for a self-consistent modified plasma-density profile.

This paper presents a rigorous theoretical investigation of the filamentation and modulational instabilities of an upper hybrid laser radiation in a hot, collisionless and homogeneous plasma in the presence of the self-generated dc magnetic field of the order of a few megagauss. Fluid equations have been employed to find the nonlinear response of electrons. The low-frequency nonlinearity arises through the ponderomotive force on electrons, whereas the high-frequency nonlinearity arises through the current densities associated with the scattered sidebands. It is observed that the growth rate of the filamentation instability decreases with increasing magnetic field, while the growth rate of the modulational instability increases with increasing magnetic field. Furthermore, the growth rate of the filamentation instability is higher by about one order of magnitude than that of the modulational instability for the same set of plasma parameters.

The Hamiltonian of a translationally invariant $n$-body system is reduced to that of $n-1\mathrm{}$ bodies in the field of a fixed force center by a canonical transformation. This may be interpreted as a transformation to an accelerated coordinate system with origin on one of the particles. All recoil effects are contained in effective masses and additional momentum-dependent interactions. This representation is expected to be useful in scattering and reaction calculations. Its application to the reaction ${\mathrm{D}}^{+}$ + H → D + ${\mathrm{H}}^{+}$ is discussed as an example.

The local-density approximation of the density-functional theory is applied to calculate the ground-state properties of ${\mathrm{Ag}}_2$, within the framework of the pseudopotential method. The calculated values of the bond length and the harmonic vibrational frequency are in good agreement with experiment. The bonding properties are found to be influenced by the $d$-electron states in a significant way. The results are compared with those of configuration-interaction calculations.

This paper reports the results of experiments designed to study simple collisional excitation in ionmolecule collisions. Comparison of the data with the predictions of both the semiclassical treatment of inelastic scattering and the Bethe approximation indicates that optical selection rules strongly influence the excitation process; hence the excitation probably occurs in a long-range collsiion.

A projectile-dependent isotope effect was found for the elastic-scattering differential cross sections in the hydrogen-isotope collision systems. All four differential cross sections lie on a common curve if they are divided by the square of the reduced mass and plotted against momentum transfer. The experimental results are in satisfactory agreement with a simple Glauber-approximation calculation.

A Monte Carlo method to integrate the Lippmann-Schwinger equation for elastic scattering is presented. Advantages and limitations of this algorithm are compared with traditional methods of computation.

The effects of collisional broadening and radiative recombination on the temporal behavior of the initial-state population $P_0\mathrm{}\left(t\right)\mathrm{}$ are examined for a photoexcited autoionized atom. The results show the existence of coherent or dissipative regimes whenever the Rabi oscillations or relaxation rates dominate, respectively. Radiative recombination tends to increase the lifetime of $P_0\mathrm{}\left(t\right)\mathrm{}$ while collisional broadening has the reverse effect. A simple approximation for $P_0\mathrm{}\left(t\right)\mathrm{}$ is suggested and demonstrated to be excellent in the dissipative regime.

Autoionization widths and energies of the lowest-lying Landau excited states of a hydrogen atom in strong magnetic fields are calculated for azimuthal quantum numbers $\mathrm{}\left|m\right|=0,1\mathrm{}$, and $2$. For fields ranging from below ${10}^9$ G, where these states lie close to the ionization threshold, up to 4.7 × ${10}^{12}$ G, the width of the lowest autoionizing state in each $m$ subspace is, to within the accuracy of the calculation, inversely proportional to the fourth root of the field strength. A comparison with radiative widths is made.

A novel pulsed ion source suitable for laser spectroscopy on any metallic element is described. The source is based on a large-bore low-pressure hollow-cathode discharge. The first direct radiative lifetime measurements in Nb II are reported. Radiative lifetimes for $z^{5}G$ and $z^{3}D$ levels of Nb II are determined using time-resolved laser-induced fluorescence on a Nb II ion beam.

Differential cross sections for Rayleigh and Compton scattering of 145-keV $\gamma$ rays by Cu, Cd, and Pb have been measured from 25° and 80°. The ratio of these cross sections, which can be determined with higher precision than absolute values, is given. The experimental cross sections, which complement earlier results, are compared with the theories of the relativistic and modified form factor and the incoherent scattering function. Agreement exists for the Compton cross section and scattering function theory showing the influence of the binding energy of the electrons. The Rayleigh differential cross sections are found to be lower than the results of the relativistic form-factor theory. Better agreement is found with the modified form-factor theory.

The quadratic Zeeman effect of Rydberg atoms is treated with the help of first-order perturbation theory and a special WKB approximation. The Bohr-Sommerfeld quantization leads to complete elliptic integrals. As a result we found that the spectrum is doubly degenerate if $\frac{n^2}{m^2>5\mathrm{}}$, this part exhibiting a linear Stark effect in an additional weak electric field; the rest of the spectrum ($\frac{n^2}{m^2<5\mathrm{}}$) is nondegenerate, exhibiting a quadratic Stark effect in an additional weak electric field.

The determination from ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ NMR data of the relevant order parameters that describe the chain ordering of potassium palmitate in a liquid-crystalline lamellar phase is reviewed in order to establish the conditions for its agreement with recent results obtained by Post, James, and Berendsen for a similar lyotropic mixture and via ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ NMR. The sign of one of these order parameters is then compared with that which has been predicted theoretically.

A general formulation is made on the Bayesian estimation of the nonlinear Markovian variables, $x$ and $y$ being subject to the master equation. It is assumed that only the variable $y$ can be observed. The evolution equation of the conditional probability density $p(x,t|\mathrm{}{y}_{t^{\prime }},t_i\le t^{\prime }\le t)$ of $x$ is derived, which forcasts the value of $x$ at the time $t$ upon knowing the observations $y_{t^{\prime }}$ performed on the variable $y$ in the time interval from the initial time $t_i$ to the present time $t$. The formulation is applied to nonlinear diffusion processes.

We show that some of the deterministic one-dimensional cellular automata studied recently by Wolfram exhibit a kind of spontaneous symmetry breaking. The associated kinks (Bloch walls) perform annihilating diffusive walks for large times.

It is shown that the "new class of coherent states" defined by Rajagopal and Marshall is equivalent to the well-known two-photon coherent states.