Two terms of the large-collision-energy expansion of the first Born cross section, the Bethe-Born (BB) cross section, are presented for ionization and for the total inelastic scattering in electron-$\mathrm{H}_2^{}{}_{}{}^{+}$ collisions. An approximation made in an earlier calculation of the total inelastic BB cross section, which is known to produce an error in the second BB coefficient, is removed. Knowledge of these two theoretical cross sections makes possible a comparison of theory with the experimentally measured proton production, total dissociation, dissociative-excitation, and ionization cross sections for large collision energies. The theoretical dissociative-excitation cross section is calculated in the first Born approximation. Comparison between theory and experiment for all collision energies is accomplished by use of the Born dissociative-excitation cross section appropriately combined with the experimental ionization cross section. Experiment and theory agree within the expectations for first Born and BB theories. The measurements of the various cross sections from the different laboratories are shown to be mutually consistent.

The 200-500-nm radiation excited by collisions of beams of 1-25-keV ${\mathrm{H}}^{+}$, ${\mathrm{D}}^{+}$, H, and D with ${\mathrm{N}}_2$ has been studied under thin-target conditions with a viewing geometry chosen to minimize polarization effects. For both ion and neutral impact, the $\mathrm{N}_2^{}{}_{}{}^{+}$ ($B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}-X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$) first negative ($1n$) bands are the most intense spectral features in this wavelength range. As expected from consideration of electron-spin conservation, the probability of excitation of the ${\mathrm{N}}_{2}C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}-B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ second positive ($2p$) bands by H or D impact greatly exceeds that for ${\mathrm{H}}^{+}$ or ${\mathrm{D}}^{+}$ bombardment. Relative emission cross sections for the (0,0) bands of the $1n$ system at 391.4 nm and the $2p$ system at 337.1 nm were determined and made absolute via normalization to measurements reported at higher energies by previous workers. The relative vibrational population $P\left(v^{\prime }\right)$ for ${\mathrm{N}}_{2}C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ formed in 3-25-keV H and D impact is in good agreement with the prediction of a simple, Franck-Condon excitation mechanism; however, for $\mathrm{N}_2^{}{}_{}{}^{+}B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ formed in collisions with 4-25-keV H and D, a dramatic enhancement in $P\left(v^{\prime }\right)$ for $v^{\prime }>0\mathrm{}$ over the Franck-Condon values is observed at low projectile velocities. The higher-velocity onset and greater magnitude of this effect for H and D in comparison with that observed for ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ are in disagreement with the predictions of a modified Franck-Condon mechanism that allows for polarization of ${\mathrm{N}}_2$ by the incident projectile. The measured values of $P\left(v^{\prime }\right)$ were used in conjunction with the (0,0) band cross sections to derive total cross sections for formation of $\mathrm{N}_2^{}{}_{}{}^{+}B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and ${\mathrm{N}}_{2}C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$. A maximum in the cross section for formation of $\mathrm{N}_2^{}{}_{}{}^{+}B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ of 1.12×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 10 keV was found for ${\mathrm{H}}^{+}$ impact, while for H, the cross section for formation of this state rises steadily with increasing collision energy until reaching a nearly constant value of 3.4×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ in the 15-25-keV range. The fraction of the total $\mathrm{N}_2^{}{}_{}{}^{+}$ yield that is formed in the $B$ state increases from about 0.03 to 0.08 in the energy range studied. For formation of ${\mathrm{N}}_{2}C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ the cross section has a maximum value of 2.2×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 5 keV. At H-atom energies below 7 keV, exchange excitation of ${\mathrm{N}}_2$ to the $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state is more probable than ionization to yield $\mathrm{N}_2^{}{}_{}{}^{+}$ in the $B$ state while, at higher energies, ionization to yield the $B$ state is the more probable process. Comparison of our results with values calculated via the application of recently developed, semiempirical scaling relationships to electron impact cross-section data indicates that the latter approach yields a good prediction of the energy dependence and an acceptable prediction of the magnitude of the $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ cross section for 1-100-keV H impact. The semiempirical approach also makes a good prediction of the cross section for formation of $\mathrm{N}_2^{}{}_{}{}^{+}B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ in ${\mathrm{H}}^{+}$ or H impact above 10 keV; however, primarily because of the lack of experimental data at lower energies, previous semiempirical predictions have overestimated the ionization contribution to the over-all $\mathrm{N}_2^{}{}_{}{}^{+}B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ cross section.

Total photon interaction cross sections at 22 energies in the region between 3.3 and 165.8 keV are determined in the elements Al, V, Cu, Mo, Sn, Ta, Au, and Pb, using high-energy resolution Si(Li) and Ge(Li) detectors on a "good geometry" setup. An analysis of the experimental data in terms of total photoelectric cross sections is presented.

Angular distributions of protons resulting from stripping collisions of neutral hydrogen atoms in the ground state with He, Ar, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{H}}_2$O, C${\mathrm{O}}_2$, and ${\mathrm{C}}_6$${\mathrm{H}}_6$ have been measured for beam energies $E$ between 1-10 keV and angles of up to 7°. They are found to be strongly peaked in forward direction. Where known, total stripping cross sections were used to derive absolute differential cross sections $\frac{d\sigma }{d\Omega }$. For a given gas, the distribution widths vary roughly proportional to $\frac{1}{E}$. The product of beam energy and the half-cone angle ${\theta }_{50}$ into which 50% of all protons are scattered varies from approximately 0.5 keV deg for ${\mathrm{H}}_2$ to approximately 1.7 keV deg for Kr and ${\mathrm{C}}_6$${\mathrm{H}}_6$. For the atomic target gases, deduced normalized differential cross sections $\rho =\theta sin\theta \frac{d\sigma }{d\Omega }$ as functions of $E\theta$ agree in shape roughly with those derived for elastic scattering of hydrogen atoms. The impact parameters corresponding to ${\theta }_{50}$ are estimated. The significance of the peaking in forward direction is investigated.

Previous papers have expressed various experimental spectral data in terms of a single set of parameters (eigen-quantum-defects, transformation matrix, and excitation dipole moments). The parameters pertain to eigenstates of an electron-ion scattering matrix which represents only the effect of short-range interactions. This paper presents a method for calculating the same parameters by solving the many-electron Schrödinger equation for an atom within a limited spherical volume. Quantitative results, for Ar states with $J=1\mathrm{}$ and odd parity, are compared with data extracted earlier from an analysis of spectral data, and are also used to reproduce the first 65 discrete line positions and their intensities, the positions and profiles of autoionization lines, and the branching ratio of the photoionization.

The force terms in the wave equation for second sound which arise from the interaction of rotons and vortex lines are recalculated. When the phase of the perturbation in the roton drift velocity owing to dragging of the rotons by the vortex lines is taken into account, new force terms are found. One of these terms predicts a decrease of the second-sound velocity proportional to the vortex density, in agreement with recent experiments on rotating helium and heat currents. The other term predicts a new contribution to the attenuation of second sound in rotating helium which may be observable.

An Ising model with spin $S=1\mathrm{}$ at each lattice point which exhibits multiple tricritical points is presented. This is a generalization of the Blume-Emery-Griffiths model which was used for describing the tricritical point in ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures. The model is solved in the molecular-field approximation. It is found that its thermodynamic behavior near the tricritical point is in qualitative agreement with the thermodynamic behavior of ternary fluids near their tricritical points.

The specific heat of an ideal semi-infinite ($\infty \times \infty \times D$) Bose gas is calculated numerically using a number of boundary conditions. The results provide a suitable comparison with the analytical calculations of Fisher and Barber and of Pathria. The agreement is very good except for the Neumann boundary condition where the numerical result shows deviation from that of Pathria. However, the earlier assumption of the existence of a "correlation length" appears to have little physical basis. For the hard-wall case, the anomaly in the specific heat is probably due to constraint on particle density. The distinctive effect of such a boundary condition (${\Psi }_s=0\mathrm{}$) is explored more thoroughly in maximal assemblies ($L\times L\times D$) where its effect on specific heat shows up prominently.

A scaled particle theory is developed for a fluid of hard spherocylindrical rods with fixed orientations. Unlike earlier scaled particle treatments of this system, it maintains thermo-dynamic consistency in that the Maxwell relation $\frac{{\partial \mu }_i}{{\partial \rho }_j}=\frac{{\partial \mu }_j}{{\partial \rho }_i}$, where $\mu$ is the chemical potential and $\rho$ is the number density, is satisfied for all orientations $i$ and $j$ without sacrificing the internal logic or consistency of the scaled particle approach. The resulting expression for the Helmholtz free energy is used to derive the equilibrium thermodynamics of hard spherocylinders that are free to rotate among an arbitrary set of allowed orientations. Numerical results are presented for two special cases: (i) rods with a continuous distribution of orientations and (ii) rods permitted to adopt only three mutually perpendicular orientations. In both instances, the properties of the nematiclike ordered phase and of the anisotropic → isotropic phase transition are determined and compared with experimental data for nematic liquids, as well as with the predictions of other theories of the hard-rod fluid. This theory is shown to reduce to the Reiss, Frisch, and Lebowitz (or Percus-Yevick) theory of hard spheres when the length-to-breadth ratio of the spherocylinders decreases to unity.

We study the interaction between a homogeneous, imperfect Lorentzian plasma and two superposed electric fields, one of these being modulated in frequency. In the calculation of the electronic distribution function $f(\overrightarrow{\mathrm{v}}, t)$ by the Boltzmann equation, we only consider the first two anisotropies $f^0(v, t)$ and ${\overrightarrow{\mathrm{f}}}^1(v, t)$. For those, we try to find solutions in the form of an expansion in triple Fourier series. The knowledge of ${\overrightarrow{\mathrm{f}}}^1(v, t)$ allows us to calculate the electronic conductivity which shows the existence of various nonlinear effects which we analyze.

A general form of the scattering distribution function is obtained through the use of the Schrödinger equation. The formulation is quite adequate in the study of particle-wave interactions, plasma radiation, fusion reactions, and nonelastic scattering as well as elastic scattering. The distribution function is obtained from a first Born approximation and is separated into two independent functions: a space-time-correlation function and a potential function. The former is of great interest in simulation of the dynamics of many-body systems and in the interpretation of scattering experiments. The potential function allows the use of different interaction potentials without the labor of repeating the calculations and with considerable reduction in the computation time. Analytic expressions for the rate of energy transfer from test particles to background plasmas are obtained together with the proper thermalization time. The dynamic behavior of the plasma is taken into consideration. The present formulation is compared with other different approaches. Results which are available in the literature lack the mathematical rigor of the treatment given here and are bound to stringent physical limitations. Consequently, the behavior of a test particle thermalizing in a background plasma is different from that anticipated in several studies, especially in the area of high-temperature plasmas.

A general theory is described for nuclear quadrupolar spin-lattice relaxation in monatomic liquids. The theory is valid for either liquid rare gases or liquid metals when appropriate forms are taken for the local electric field gradient (EFG). It is shown that the relaxation rate may be approximated in terms of an integral over the "elastic" limit $S(k,0\mathrm{})\mathrm{}$ of the dynamic liquid structure factor multiplied by a weighting factor $I\left(k\right)\mathrm{}$ determined by the spatial variation of the EFG. Calculations of $I\left(k\right)\mathrm{}$ for Ne and Ga identify the ranges of $k$ values responsible for quadrupolar relaxation in these liquids. For Ne, the dominant modes fall in the range $K_0\lesssim k\lesssim 2K_0$, where $K_0$ is the position of the main peak in the static liquid structure factor. For Ga, and for metals in general, $I\left(k\right)\mathrm{}$ is largest near twice the Fermi wave vector ($2k_F$) if the EFG is determined from the asymptotic form of a screened ionic potential. For both liquid rare gases and liquid metals, these relatively high $k$ values indicate that collective motions play an important role in the nuclear relaxation process. As a corollary it is shown that magnetic dipolar relaxation in monatomic liquids can be described as a special case of the general theory with appropriate changes of the coupling constants. Numerical calculations of the relaxation rate for ${\mathrm{Ne}}^{21}$ and ${\mathrm{Ga}}^{69}$ near their respective melting points and the temperature dependence of the ${\mathrm{Ne}}^{21}$ rate are in good agreement with experiment.

The Debye temperatures for two- and three-dimensional systems are compared using an isotropic elastic model that includes the effect of finite initial stress and assumes the Cauchy conditions. It is shown that the effect of initial pressure on sound speeds, Debye temperatures, and selected elastic properties is determined in both dimensions by the dimensionless product of pressure and compressibility. The model is applied to the observed similarity in Debye temperatures for monolayer and hcp bulk ${\mathrm{He}}^4$. Using 0 °K compressibility and pressure data, there is essential agreement between the elastic model and the experimental bulk Debye temperatures. The agreement results from the effect of initial pressure, which softens the bulk Debye temperatures by as much as 20% relative to the zero-pressure values for the same compressibility. A large softening also occurs in the two-dimensional extension when applied to the ${\mathrm{He}}^4$-graphite adsorption system but, in contrast to the bulk, the two-dimensional spreading pressures are insufficient to produce comparable quantitative agreement with the experimental film Debye temperatures. The idealized model is extended to include a specific substrate effect by separating the total film elastic constants into two parts: An intrinsic (Cauchy) contribution associated with the two-dimensional adsorbate lattice and a secondary contribution identified with the substrate, which lifts the Cauchy conditions on the total elastic constants for the film. The required fractional substrate contribution to the bulk and shear moduli yielding agreement with the experimental film Debye temperatures is examined.

The effect of a strong perturbing radiation field on spectral lines is studied using an extension of the Kubo-Zwanzig-Fano relaxation formalism. The problem of a dilute gas interacting with a strong perturbing field and a weak probe field is solved, assuming a separation of collisional and radiative processes, by introducing a classical-field renormalization technique. The solution is formulated entirely in terms of linear-response functions. This method is applied to the problem of the three-level absorber perturbed by a strong field and probed by a weak field. Multiphoton transitions, double resonance, and dynamic Stark effects can be treated as manifestations of this three-level problem.

Frequency broadening generated by picosecond laser pulses is investigated experimentally and theoretically near the electronic levels of a Pr${\mathrm{F}}_3$ crystal. Information is obtained on the role played by the electronic levels on self-phase-modulation and four-photon parametric emission, and on how the self-phase-modulation spectrum evolves through and beyond the electronic absorption levels.

Measurements of two-photon coincidences in single-mode light from a He-Ne 633 nm gain tube in which each spontaneously emitted photon has an average probability of 12% of inducing a second photon, show no time correlation between inducing and induced photons in the range from zero to 3.4 nsec.

Bloch has suggested that minima in the free energy as a function of angular momentum are responsible for the superfluidity of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in a ring. It is shown in this paper that at finite temperatures, the critical velocity is much too small, and hence minima in the free energy are not the cause of superfluidity in a ring.

It has been correctly stated by Blood that a previous interpretation of superfluidity in a ring, based on the existence of minima of the free energy, is valid only in the immediate vicinity of the absolute zero. Elaborating on a footnote, it is pointed out that the argument can be extended to higher temperatures if one considers different branches of the free energy and that it is plausible to assume transitions between them to be practically excluded.

Several aspects of the inseparable connection between the radiation-reaction field and the free field are discussed. The importance of the free-field terms in the calculation of two-time-correlation functions is pointed out.

We discuss a recent information-theoretic description of heat transport in an ideal gas and show that if the local-equilibrium and near-equilibrium assumptions are valid, the Boltzmann-equation and information-theory approaches yield formally identical expressions for the distribution function. We discuss the differences in the interpretation of the two expressions.