The vibrational excitation by electron impact on C${\mathrm{O}}_2$ has been studied in the energy range 3-5 eV by observing scattered electrons at an angle of 90°. Such scattering is dominated by the ${}_{}{}^2{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ shape resonance. The energy-loss spectrum at 3.6 eV consists of about 30 peaks, which we associate with two progressions of vibrational excitation of the C${\mathrm{O}}_2$ molecule, namely, the $n00\mathrm{}$ and $n10\mathrm{}$ modes. This assignment is consistent with previously measured angular distributions of the inelastically scattered electrons. The energy dependence of the vibrational cross sections exhibits structure. The peaks and valleys of this structure shift to higher energies as the vibrational quantum number of the final state increases. The experimental observations are qualitatively consistent with an extension of the boomerang model which has been developed by Herzenberg for the compound state in ${\mathrm{N}}_2$.

Using the method of configuration interaction as applied to autoionization by Fano, expressions involving the reaction matrix K in the basis of the original configurations are given for the width and resonance energy. The expression obtained for the width is a Fermi "golden rule" type formula similar to that proposed by Miller. The expression for the resonance energy changes only slightly as the independent energy parameter varies, and therefore it is possible to consider a particular resonance among closely spaced resonances without elaborate search procedures. Application is made to the $\left(n{l}^2\right){}_{}{}^1{}_{}{}^{}S$ autoionizing states of He below the $n=4\mathrm{}$ threshold. No significant near-neighbor resonance interactions were found despite the small energy intervals between adjacent levels. The results indicate the $5s^2$ state falls below the $n=4\mathrm{}$ threshold, which is reflected in the small width given by our results. Widths, resonance energies, relative decay probabilities for each of the open channels, and Fano-Cooper cross-section parameters are given for all the states considered. Comparison is made with experiment and other theories where possible.

I present a perturbation theory of multiphoton ionization based on the resolvent operator. The theory is applied to a detailed study of two-photon ionization under near-resonance conditions. It is shown that a distinction must be made between linear level shifts and widths, and resonance shifts and widths which appear in the transition probability. The resonance shifts and widths exhibit saturation effects and their values tend to be much smaller than those of the linear level shifts and widths. Using numerical examples corresponding to tunable dye lasers and alkali-metal atoms, we show that the above shifts can have a dramatic effect on the ionization rate even when the laser is not in exact resonance with the intermediate level. The question of "one-step" vs "two-step" two-photon ionization is also discussed. It is shown that exact resonance does not necessarily imply a two-step process. In fact, in most cases it is quite the opposite. A quantitative criterion for this distinction is established. Finally, a distinction is made between instrumental saturation and saturation of the transition probability. The two are shown to be of different nature. Further extensions of the work are also discussed.

A simple set of coupled equations applicable for medium-energy scattering by composite systems is derived. The scattering function is expanded in the basis functions such that the average inelastic scattering channels simulate both adiabatic and impulse limits. Detailed discussions are given on the construction of the basis functions by the sum-rule technique. A procedure to solve the coupled set of equations by the Green's functions is presented, and the evaluation of the amplitude using the angle-averaging method is outlined.

The effective-channel approach to medium-energy scattering has been formulated previously by constructing a set of coupled equations for the elastic-scattering and average inelastic-scattering channels, with the evaluation of the average fluctuation potential and the average excitation energy to be carried out by a variational procedure. The formalism is applied here to the electron and positron scattering from atomic hydrogen in the energy range 50-500 eV. The various quantities which parametrize the effective channel are explicitly calculated. An approximate solution of the coupled equations is then obtained using a set of Green's functions in the semiclassical approximation. Contributions to the elasticscattering amplitude which arise from the static interaction and the coupling to the average inelastic-scattering channel are isolated for the purpose of ready comparison with previous calculations. The present calculation contains in effect no free adjustable parameters when the information from the total-cross-section data is incorporated into the theory through the use of the optical theorem.

Absolute cross sections for electron capture into the $n=3,4\mathrm{}$ states of H have been measured for 0.3-3.0-keV ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$ impact on ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, C${\mathrm{O}}_2$. This cross section decreases exponentially with decreasing impact velocity according to an $\sigma =A\exp \left(\frac{-B\left|\Delta E\right|}{v}\right)$ relationship, where $\left|\Delta E\right|$ is the internal energy of the reaction, $v$ is the ion velocity, and $A$ and $B$ are constant.

The vibrational-state population of electronically excited, neutral molecules produced by ion impact at 2-7 × ${10}^7$ cm/sec has been determined by measuring the relative intensities of the vibrational components of electronic band systems observed in the energy-loss spectra of ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{N}}^{+}$ scattered from ${\mathrm{N}}_2$ and CO. The measured intensities agree with intensities which have been observed in optical and electron-impact spectra as well as with theoretical predictions based on the Franck-Condon principle. Previous reports of anomalous vibrational excitation of ${\mathrm{N}}_2\left(a{}_{}{}^1{}_{}{}^{}\Pi g\right)$ by proton impact are demonstrated to be the result of protonimpact excitation of ${\mathrm{N}}_2$ to both the $a{}_{}{}^1{}_{}{}^{}\Pi g$ and $w{}_{}{}^1{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$ states.

The current transients of prebreakdown electron avalanches in uniform electric fields in oxygen are studied with a bakable drift tube and a time resolution of about 1% of the ion transit time involved. At this low time resolution, electronic-current components are discovered which are attributed to detachment from the diatomic ion ${\mathrm{O}}_2^{-}$. Detachment rates of ${\mathrm{O}}_2^{-}$ in ${\mathrm{O}}_2$ are measured over a range of pressures from 1 to 32 Torr, and over a range of field strength to pressure ratios from 35 to 130 V/cm Torr, corresponding to mean ion swarm energies for ${\mathrm{O}}_2^{-}$ between about 0.2 and 1.5 eV. The detachment rates observed depend linearly on pressure, indicating a two-body detachment reaction, and are consistent with a detachment cross section near threshold (0.44 eV) of approximately 0.7 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. Also obtained are effective electron attachment rates for ${\mathrm{O}}_2^{-}$ and ${\mathrm{O}}_3^{-}$ in oxygen, which show a characteristic pressure dependence consistent with attributing the observed detachment to diatomic ${\mathrm{O}}_2^{-}$. These rates reflect the formation of the diatomic ion ${\mathrm{O}}_2^{-}$ by charge transfer from the primary atomic ion ${\mathrm{O}}^{-}$. The pressure dependence observed, however, is inconsistent with the trial assumptions that either the atomic ion ${\mathrm{O}}^{-}$, or the triatomic ion ${\mathrm{O}}_3^{-}$, detach their electrons at the rates reported here. The mass-spectrometric study undertaken supports these conclusions.

A quantum-statistical treatment of degenerate (single-mode) parametric amplification is given in which the pump is allowed to have time-dependent amplitude and phase. This relaxes earlier restrictions of a constant pump in exact resonance with the signal. Solutions are obtained for the case where the ratio of the time derivative of the pump phase to the coupling strength between pump and signal is constant. This includes the special case of simple offresonance, where the pump has a constant frequency differing from twice the signal frequency by a given amount (and has constant amplitude). The Wigner distribution for the signal mode is obtained (the $P$ distribution does not in general exist as a well-defined function beyond a finite time interval for this process) and is used to determine the time development of the expectation values of various field operators of interest, such as field strengths and fluctuations. A critical point exists in the solution for the photon annihilation operator such that the behavior of the solution and the resulting quantities which it determines is divided into an exponential region and an oscillatory region. The critical point defines, from the expectation value for the photon number, the condition for amplification. For the case of simple off-resonance, this gives the frequency range of amplification. A calculation without using the rotating-wave approximation is given in the Appendix which shows that, to first order, the same range is obtained as when the approximation is used. The effect of damping is given, showing, e.g., how it slows the growth rate of the signal (in the region of amplification) and how it narrows the frequency range of amplification. The effect of a time-dependent pump (and damping) on the breakdown of the $P$ distribution is also described.

The Atkins theory of the temperature dependence of the surface tension $\alpha$ in superfluid ${\mathrm{He}}^4$ has been improved by including the effects of compressibility, phonon dispersion, and Gibb's "surface adsorption" or "surface mass" in the calculation of the spectrum of the surface excitations or "ripplons." The theoretical ripplon spectrum is found to have a minimum close to the roton minimum in the empirical phonon spectrum. The results of the theory, which should be accurate up to a temperature of ∼1.3 K, are presented in terms of the ripplon and phonon contributions to the surface entropy ($-\frac{d\alpha }{dT}$). The ripplon spectrum and the surface entropy are found to depend on two phenomenological parameters: a length $\delta$ which is the surface mass per unit area divided by the density, and an area $a$ which is the derivative of $\delta$ with respect to the curvature of the surface. In principle, both $\delta$ and $a$ can be obtained from static measurements on curved surfaces. The theory is compared to new measurements of the surface entropy near 1 K and, assuming that $\delta$ is small, $a$ is found to be about 1.5${\mathrm{\AA }}^2$.

It is pointed out that symmetries of Maxwell's equations under interchange of electric and magnetic fields can be exploited to convert calculations of van der Waals forces between electrically polarizable particles and dielectric materials into results for magnetically polarizable particles and permeable materials. In particular, the forces between perfectly conducting materials calculated from ideas of zero-point radiation are the same as the forces between infinitely permeable materials. Combinations of dielectric materials and permeable materials can lead to repulsive van der Waals forces. For example, two infinitely permeable parallel plates are attracted together with exactly the same force as obtained by Casimir for the van der Waals attraction between two perfectly conducting plates. On the other hand, two parallel plates of area $A$ and separation $d$, one of which is a perfect conductor and one of which is infinitely permeable, are repelled by a force $F=\frac{7}{8}\frac{{\pi }^2\hslash cA}{240d^4}$, differing in magnitude by a factor of $\frac{7}{8}$ from Casimir's attractive force. A calculation of the repulsive force is given based on ideas of classical electromagnetic zero-point radiation.

In previous work an expression was developed which partially incorporates the effect of final-state interactions on thermal-neutron scattering from a many-body system. This expression is evaluated for a liquid ${\mathrm{He}}^4$ target at momentum transfers of 14.3 and 28.6 ${\mathrm{\AA }}^{-1\mathrm{}}$. The experimental results of Mook, Scherm, and Wilkinson for the scattering of neutrons from liquid helium are analyzed in terms of (a) a modified impulse approximation which includes final-state corrections only in the condensate contribution to the scattering and (b) an approximation which includes final-state effects on both condendate and noncondensate contributions to the scattering. These calculations substantiate a previous empirical assessment of the condensate portion of the scattering [(2.4 ± 1)%] and suggest that certain barely discernible features of the experimental scattering are real structures in the condensate contribution attributable to the structure of the liquid and the interaction potential of the helium atoms. Other helium properties deduced from the data at 1.2 and 4.2 $\stackrel{\mathrm{̊}}{\mathrm{K}}$ are single-particle momentum distribution, one-particle density matrix, and mean kinetic energy of the helium atoms. These quantities are compared with predictions from existing Monte Carlo numerical studies of the ground state of ${\mathrm{He}}^4$.

Paramagnetic resonance observations indicate that $p-\mathrm{azoxyanisole}$ (PAA) is in cellular or vortex flow when a dc electric field is applied perpendicular to the magnetic field. We observe partial realignment of the PAA molecules when the fields are parallel. These results qualitatively agree with the literature. Similar experiments on the nematic phase of 4-butyloxy-benzylidene-′4-acetoaniline yielded results which are not as easily understood. This technique permits observations of dynamic instabilities on a molecular level.

We have carried out a rigorous asymptotic analysis of the thermodynamic behavior of an ideal Bose gas confined to an arbitrary, finite cuboidal geometry under periodic boundary conditions. Our investigation, which is based on the grand canonical ensemble, leads to the construction of an abstract, thermogeometric space in which the process of Bose-Einstein condensation appears as a "collapse" of the lattice points of the space towards its origin. In an infinite geometry, the collapse is accomplished in an infinitesimally small interval of temperature; this results in the appearance of mathematical singularities in the thermodynamic functions of the system. In a finite geometry, the "collapse" proceeds gradually and is spread over a temperature range $\Delta T$ such that $\frac{\Delta T}{T_0}=O\left(\frac{\overline{l}}{L_{<}}\right)$, where $\overline{l}$ is the mean interatomic distance while $L_{<}$ is the length of the shortest side of the assembly; accordingly, the thermodynamic functions of the system remain smooth throughout. Special events, such as the specific-heat maximum, occur when the "lattice parameters" of our thermogeometric space acquire certain characteristic values which depend only on the shape of the system and not on its actual size. This leads to a new law of corresponding states for Bose-Einstein systems of finite size.

The relaxation of vibrationally excited diatomic molecules of one kind is studied by second-quantization methods. The relaxation processes are described by interactions of the vibrational degree of freedom with translational and radiational heat baths. General quantummechanical expressions are developed for transition rates in vibration-translation, vibration-vibration, and vibration-radiation processes. These expressions include the broadening of spectral lines in a nonequilibrium gas. The line broadening is affected by the correlation function of both the dipole moment and the density matrix. In the interaction of the vibrational degree of freedom with a radiational heat bath, cooperative effects are studied. Cooperative molecular effects do not influence the induced emission and absorption, but lead to changes in the process of spontaneous emission.

The theory of Singwi and Sjölander for atomic motion in classical fluids is used to study the self-correlations in liquid sodium. The detailed numerical calculations have been done for the velocity-autocorrelation function and its frequency spectrum using two recently developed interatomic potentials. The results are compared with those obtained by Schiff and Rahman from molecular-dynamics experiments. The recent experimental results of Cocking for quasielastic scattering in liquid sodium at 388 °K are also analyzed using the results obtained from the above two model potentials.

A theory is proposed to explain the effects of the rotation-vibration coupling in the ir and Raman spectra of inert solutions of diatomic molecules. This theory is a stochastic-type theory related to similar theories of NMR spectra. Spectral manifestations of the rotation-vibration interaction are found to depend very strongly on whether an ir, isotropic, or anisotropic Raman spectrum is concerned, on the nature of molecular rotations in the liquid, and on the properties of the solvent-solute interaction forces. Explicit expressions are given for a number of profiles which are perturbed by this interaction.

Measurements are reported of the mobilities of helium ions in superfluid helium very close to the $\lambda$ transition. The mobilities of both positive and negative ions appear to be singular in the sense of having infinite slope at the transition. The measurements are made by a new differential technique, based on the space-charge-limited method, which makes possible a sensitivity to changes in mobility of the order of parts in ${10}^4$. This allows mobility measurements into the range $\left|\epsilon \right|<\mathrm{}{10}^{-4\mathrm{}}$, where $\epsilon =\left(\frac{T}{T_{\lambda }}\right)-1\mathrm{}$. Most of the reported measurements are taken along isotherms which cross the $\lambda$ line at elevated pressures, although a series at saturated vapor pressure is also reported. Means of transforming the data between various thermodynamic paths are discussed. Uncertainty as to which thermodynamic path should be considered fundamental together with experimental problems in the technique at this stage in its development make quantitative assessment of the singularity difficult. However, if we assume a limiting form $\frac{(\mu -{\mu }_{\lambda })}{{\mu }_{\lambda }}\sim {(-\epsilon )}^{{\rho }^{\prime }}$, where $\mu$ is the mobility and ${\mu }_{\lambda }$ its value at the transition, we find for the exponent ${\rho }^{\prime }=0.94\mathrm{}\pm 0.02$.

It is shown that light having completely random phase can be converted into phase-coherent light (having fixed values of phase) by parametric amplification with an intense coherent second-harmonic pump mode. Explicit results for a chaotic signal and experimental detection of interference between phase-coherent beams obtained from independent random-phase light beams is discussed.

A comparison is made between the Fokker-Planck equation (FPE) and the transport equation (TE) solutions of the problem of the collisional relaxation of an atomic or molecular system undergoing Brownian motion. It is shown that, for times ≲ (inverse collision rate), the FPE does not provide an appropriate approximation to the TE if the velocity bandwidth of the initially prepared sample is less than the root-mean-square change in velocity per collision. Possible experimental verification of the theory using laser-pump sources to provide narrow initial-velocity distributions is discussed.