We consider the self-generated dc magnetic fields due to resonant excitation of plasma waves by intense laser light. From Ampere's law we show that the time scale associated with the growth of the magnetic field is essentially the same as the time scale for the growth of the plasma wave. Further, we obtain a simple expression for the steady-state magnetic fields arising from a steady-state current derived in terms of the high-frequency excited fields. Computer simulations verify the theoretical conclusions on both the time variation and the steady-state value of the magnetic field. Difficulties of earlier calculations based on the so-called stress-tensor approach are discussed, and it is shown that the proper use of this method requires the use of a self-consistent kinetic theory for the plasma which takes into account the convection of momentum out of the resonance region.

The Thomas-Fermi-Dirac statistical model and one that adds a Debye-Hückel interaction between particles is used to compute the Gibbs potential for mixtures. It is found that, in certain cases, the two models have different predictions with respect to phase separation. Calculations are presented for the mixtures of iron and hydrogen under astrophysical conditions.

A knowledge of the dynamics of nonlinear systems with multiple excitations is important for calculation of the continuum density of states and for one method of calculation of the classical statistical mechanics of the sine-Gordon Hamiltonian. Hirota's $N$-soliton construction for the sine-Gordon equation is extended by analytic continuation to incorporate usefully breather and continuum solutions as well. The significance of these classical solutions is illustrated in the context of the propagation and excitations of domain walls in a classical uniaxial ferromagnet of infinite extent. From these solutions, formulas for the relative phase shifts in the scattering of a soliton, breather, or continuum solution from any one of these, acting as scatterer, are derived. Following Hirota, it is shown that under certain assumptions about the asymptotic properties of the solution the relative phase shifts of solutions corresponding to many soliton, breather, and continuum states may be found by adding the derived pairwise phase shifts.

When the interaction potential of a ferromagnet decreases like $r^{-s}$, we prove that two-point correlations (i) do not decay faster than $r^{-s}$ and (ii) decay at least like $r^{-s}$ at large magnetic field and, moreover, at least like $r^{-(s-2\mathrm{}\nu )}$ where $\nu$ is the space dimension, for any nonzero magnetic field and arbitrary temperature. Extensions of the latter result to $n$-point correlations and to other systems are indicated, and a central-limit theorem, or Gaussian limit of block-spin distribution, is mentioned for slowly decreasing ferromagnetic interactions at any nonzero magnetic field.

The time-integrated spectrum from a plasma of beryllium produced by a 1-GW ruby laser has been observed in the soft-x-ray region with spectral and spatial resolution. The lines of Beiv are broadened near the target. Stark broadening and a Doppler shift due to the expansion of the plasma towards the vacuum combine with the opacity of the plasma itself to give an apparent profile with asymmetrical shift reversal. The equation of radiative transfer is solved in this case with a computed plasma model. Parameters like electron temperature, and density and plasma dimensions have been spectroscopically measured, while Stark parameters have been adopted from the theory. The profiles predicted by the model are in good agreement with the observed ones, especially if time-dependent ionization equilibria are considered. Electron densities inferred from Stark-broadened lines can be estimated up to densities of ${10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$.

A comparison is made of the recent systematic solution of the mean-field equations for liquid crystals by Shen et al. with that of McMillan. It is shown that the discrepancies in McMillan's phase diagram are due to an undesirable chain-length factor in his potential and not due to the truncation of his Fourier expansion of the spatial potential function. The rectified phase diagram is shown to be identical to that of Lee et al.

The $p$-wave contribution to the positron-hydrogen annihilation rate, in terms of $Z_{\mathrm{eff}}$, is corrected from a previous calculation of the authors, thereby removing the discrepancy with later calculations of Chan and McEachran. The present results should be the most accurate available. This opportunity is taken to give thermally averaged positron-hydrogen annihilation coefficients $\overline{Z}\mathrm{}\left(T\right)\mathrm{}$, which are of use in the analysis of solar-flare observations of the positron-electron annihilation line. For reference and experimental purposes we also present curves of the integrated elastic and momentum-transfer (i.e., diffusion) cross sections, as well as effective cross sections which account for the finite acceptance angle of the detector.

Experimental evidence is presented for emission of $K\alpha \alpha$ radiation from both Na and Ne atoms in ${\mathrm{Na}}^{+}$-Ne single collisions. We suggest that there will always be a sharing of $\mathrm{KK}$ vacancies between asymmetric collision partners but that the $K\alpha \alpha$ x ray from the heavier atom/ion is frequently obscured.

We show that the Hartree or Hartree-Fock momentum-space wave function for a self-interacting bound state decreases faster than any power of the momentum for large momentum so long as the underlying two-body force is local.

Padé approximants are examined as a means for approximately summing the power-series expansions for inelastic Born cross sections developed in recent work. The advantages of the Padé cross section over the two-term series expansion in ${\left(\frac{v}{c}\right)}^{-2\mathrm{}}$ are indicated. Explicit calculations for the total electron-loss cross section for ${\mathrm{H}}^{-}$ ions incident on ${\mathrm{H}}_2$, He, and Ar are carried out. The results are compared with the available experimental data in the 10-keV to 1-MeV energy range and with the quasiclassical impulse approximation of Bates and Walker.

A simpler, more general version of a formula given by Sharma for the expansion of functions of the form, $F\left(\overrightarrow{\mathrm{r}}\right)=f\left(r\right)\mathrm{}{Y}_l^m(\theta , \phi )$, in terms of spherical harmonics and radial functions at a new origin, is derived from an earlier treatment of the expansion problem based on Fourier transforms.

Much understanding of the bremsstrahlung spectrum can be obtained from the behavior at its two end points. The low-energy theorem can be used to obtain the soft-photon end point from elastic scattering; this may be combined with data from the hard-photon portion of the spectrum to interpolate through the soft-photon region, which is difficult to calculate directly because partial-wave series converge slowly. The low-energy theorem may also be used to show that, contrary to statements in the literature, the ratio of the Born approximation to the exact cross section approaches unity at the soft-photon end point for the Coulomb potential but not for a screened potential.

The differential and integrated cross sections of elastic scattering of positrons by hydrogen atoms in the ground state are calculated with the modified Glauber amplitude recently proposed for atomic scatterings. While experimental data of this positron process are still not available for comparison, our results show a drastic difference from those obtained in the full-eikonal calculations by Foster and Williamson, as well as in other theoretical models. Thus the results of the analysis shown here can serve in the role of making the distinction between our Glauber model and others.

Several comments are made on Radi's computation of standard Hylleraas-type wave functions for the ground state of the helium atom. It is shown that the 125-term wave function yields a variational energy of -2.903 724 343 a.u. and not -2.903 724 371 a.u.

The $R$-matrix formulation of electron-molecule collision theory is applied to low-energy $e$-${\mathrm{N}}_2$ scattering in the static-exchange approximation. Particular attention is given to the determination of basis sets for such $L^2$-variational calculations, and a study of important basis-set characteristics in the context of this collision problem is presented. Results for elastic $e$-${\mathrm{N}}_2$ collisions for scattering energies in the range from about 0.01 to 13.0 eV are reported. The importance of including long-range interactions is briefly discussed.

Normalized differential cross sections (DCS's) for the electron impact excitation of the lowest three singlet ($a^{\prime }, a, \omega$), and lowest five triplet ($A, B, W, {\mathrm{B}}^{\prime }, C$) valence electronic states of ${\mathrm{N}}_2$, and of the two ($3s{\sigma }_g$) Rydberg states ($E, a^{\prime \prime }$) have been determined at seven incident electron energies ranging from 10 to 50 eV. These DCS's were obtained for the scattering-angle range 5° to 138° by analyzing electron energy-loss spectra in ${\mathrm{N}}_2$ at a number of fixed scattering angles within that range. These data, which are the first that cover such a large incident energy and scattering-angle range for such a wide variety of final target states, show that each of the DCS's for the ten final target states falls into one of four classes. Since the initial molecular target state is a singlet, and none of the final states studied here is dipole allowed, these four classes are determined according to whether the final target state is triplet, singlet, parity-unfavored, or Rydberg in character. The DCS's for all the final target states change rapidly in shape as the incident electron energy is varied. Theoretical DCS's obtained from first-order perturbation models (Born-Ochkur and Ochkur-Rudge) agree poorly with the measured DCS's.

Normalized integral cross-sections for the electron impact excitation of the lowest three singlet ($a^{\prime }, a, w$) and lowest five triplet ($A, B, W, B^{\prime }, C$) valence electronic states of ${\mathrm{N}}_2$, and of the two ($3s{\sigma }_g$) Rydberg states ($E, a^{\prime }$), have been determined at seven incident electron energies ranging from 10 to 50 eV. These cross sections were obtained by integrating the differential cross section reported in the preceding paper, over all scattering angles. The cross sections for excitation of the $W$, $B^{\prime }$, and $a^{\prime }$ states are considerably larger than previously estimated, that for excitation of the $C$ state is in excellent agreement with previously reported values, while those for the $A$, $B$, and $a$ states are smaller than previous results. Theoretical cross sections obtained with Born-type theories give integral cross sections that are in surprisingly good agreement for many of the excited states, but in a few cases ($A, W, B^{\prime }, a^{\prime }$) the theoretical cross sections are in poor agreement.

Normalized absolute differential and integral cross sections for electron-impact excitation of five optically-allowed singlet states, two known triplet states, and two unknown triplet-like states of ${\mathrm{N}}_2$, lying in the energy-loss range 12.5-14.2 eV, have been determined by analysis of electron energy-loss data at incident electron energies of 40 and 60 eV. The range of scattering angles considered in this work was 5° to 138°. The optically allowed transitions are to the $b{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $c{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $c^{\prime }{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$, $o{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and $b^{\prime }{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$, states and the known triplet excitations are to the $F{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ and $G{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ states. Cross sections for excitation to two unidentified triplet-like states at 13.155 and 13.395 eV were also obtained from the data analysis. The relationship of the generalized oscillator strength for the dipole-allowed states obtained from the present measurements to known optical oscillator strengths is discussed.