Abundances of satellite lines relative to diagram lines in the $K$-Auger spectrum of neon and $L$-Auger spectrum of argon are measured as a function of the energy of impact electrons. The ratios of satellite to diagram lines are found to be independent of the energy except near the threshold for initial ionization, where the ratios decrease sharply. These ratios are taken to be evidence of the extent of initial double-to-single ionization, i.e., the $\mathrm{KL}$ to $K$ ionization in neon and $\mathrm{LM}$-to-$L$ ionization in argon; and the results are discussed in terms of electron shake-off and the sudden approximation.

Absolute cross sections for the electron-impact excitation of the ${\mathrm{O}}_2^{+}$ first negative bands were measured from threshold to 400 eV and extrapolated to 1000 eV by means of a Bethe-Oppenheimer relationship. The peak cross sections for the ($n+1, n$) and ($n+2, n$) sequences were found to be 5.30×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$±10% and 2.10×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$±10% at 100 eV, respectively. The cross sections for the (0,0) and (1,0) bands had a maximum value of 2.14×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$±15% and 4.33×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$±15%, respectively. The ratio of the total ionization cross section of ${\mathrm{O}}_2$ to the excitation cross sections of the first negative bands was nearly constant over the energy range 30-1000 eV; it had an average value of 64 for the (1,0) band. The lifetime of the ${\nu }^{\prime }=1\mathrm{}$ level of the $b^4{\Sigma }_g^{-}$ state was found to be 1.19 μsec±5%.

A classical-impulse binary-collision model is used to predict the laboratory angle and velocity distributions of protons resulting from the vibrational dissociation of ${\mathrm{H}}_2^{+}$ by He. The treatment is partly heuristic and is not a quantitative success, since the computed cross sections turn out to be roughly an order of magnitude too large compared to those for electronic excitation of the $2p{\sigma }_u$ state of ${\mathrm{H}}_2^{+}$. Nonetheless, the theory clearly identifies some major features of the experimental results of Gibson, Los, and Schopman as being due to vibrational dissociation.

Absolute cross sections for electron capture into the $3p$ and $3d$ states of hydrogen have been measured for 10- to 100-keV proton impact on He, Ne, Ar, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$. Improved $3s$ cross sections are presented for these gases from 10 to 120 keV. An apparent maximum in the $3p$ cross section occurs in this energy range for all gases. The $3d$ cross sections decrease monotonically with increasing impact energy according to an $\exp [-{\left(\frac{E}{K}\right)}^{\frac{1}{2}}]$ relationship, where $E$ is the impact energy and $K$ is a constant, with the exception of helium which shows a maximum in the $3d$ cross section between 15 and 20 keV. The value of $K$ is identical for all the diatomic gases. Balmer-$\alpha$ cross sections are synthesized from these results. Polarization of the $3d\to 2p$ radiation is reported.

The cross sections for formation of ${\mathrm{He}}^{+}$ and ${\mathrm{He}}^{++}$ ions have been measured over the energy range from 0.15 to 1.00 MeV for the case of protons incident on helium gas. The individual ions were detected with an electron multiplier that was operated at near 100% efficiency. An observation of the angular distribution of the slow ions in a "field-free" environment yielded essentially an isotropic distribution in the laboratory reference frame. It was also observed that much less than 1% of the ions had energies greater than 1 eV. It was concluded that, in order for the recoil ions to have an appreciable angular distribution, there must be a substantial energy transfer in the collision, such as would be the case for heavy projectile-target combinations.

The triple-valued structure in the inelastic energy loss in certain violent ${\mathrm{Ar}}^{+}$-on-Ar collisions is commonly thought to be due to the creation of $L$-shell vacancies. These should de-excite through an Auger process that results in the emission of fast electrons whose energy is of the order of 180 eV. The present experiment detects such electrons in coincidence with a scattered ion appearing at a known angle $\theta$ with a known final charge state $m$. Large-angle scattering in the reaction ${\mathrm{Ar}}^{+}+\mathrm{Ar}\to {\mathrm{Ar}}^{+m}+{\mathrm{Ar}}^{+n}+(m+n-1\mathrm{})\mathrm{}{e}^{-}$ is studied for incident energies between 10 and 30 keV, where the ${\mathrm{Ar}}^{+m}$ is scattered to $\theta =21\mathrm{}°$. The electron-energy spectrum measured in coincidence shows the expected peak, though its location in energy decreases as $m$ increases. The number of fast electrons agrees fairly well with the number expected according to a statistical model developed earlier.

The dependence of the multiphoton absorption probability for an atomic system on the statistical properties of the incident light is investigated. It is shown, by means of $n\mathrm{th}$-order time-dependent perturbation theory, that the multiphoton absorption probability depends on the $(n, n)\mathrm{th}$ normally ordered correlation functions of the electromagnetic field. For stationary fields, the transition probability per unit time is constant and is directly related to the reduced cross-spectral correlation function of the electromagnetic field. This expression for the transition probability is then analyzed under various conditions of coherence. Explicit calculations are carried out for thermal light and for laser light, and the transition rates are compared when each has a Lorentzian spectrum. In particular, when the width of the final atomic level is much larger than the bandwidth of the field, the transition rate for thermal light is $n$! times higher than with laser light of the same mean intensity. The other extreme case, i.e., when the width of the final atomic level is much smaller than the bandwidth of the field, is also considered in detail. An equation for the density operator of the field is derived; this equation governs the change in the statistical properties of the photon system in $n$-photon absorption processes. On the basis of this equation, the time-dependent properties of the photon system are then studied and some physical consequences of these equations are discussed. Some numerical solutions relating to the time dependence of the factorial moments in two-photon absorption processes are presented.

Thermal-conductivity measurements made on hexagonal-close-packed helium-4 at 15.2-${\mathrm{cm}}^3$ molar volume are reported for specimens whose quality and orientation were determined directly by an x-ray method. The highest thermal conductivity in the umklapp region occurred for a single crystal oriented in the basal plane. Specimens of inferior quality exhibited lower conductivities.

The colliding-pole criterion for determining instability types from dispersion relations calls for a process of conformal mapping from the frequency plane into the wave-number plane. It is shown that this process can be inverted by mapping lines, parallel to the imaginary axis, from the wave-number plane into the frequency plane. Lines mapping into a cusp locate the frequencies at which the group velocity vanishes. These frequencies determine the instability character of the system.

A theoretical model for superradiant damping effect in inhomogeneously broadened media and its application to photon-echo problems are discussed. Only optically thin systems are considered, and all nonradiative relaxation mechanisms are neglected. Numerical calculations are performed for a very wide square inhomogeneous line shape and square applied pulses. It is shown that excitation of the system becomes increasingly difficult as the superradiant lifetime ${\tau }_s$ becomes comparable with $T_2^{*}$. The energy reradiated after the end of the exciting pulse is considerable for ${\tau }_s\approx T_2^{*}$ and for some applied pulse areas. Two-pulse sequences produce multiple echoes as the microscopic polarizations spontaneously rephase. The first-echo amplitude maximum is found to occur for first-applied-pulse areas increasingly above $\frac{1}{2}\pi$ as ${\tau }_s$ decreases. For a given first-pulse area, the echo intensities increase initially as ${\tau }_s$ decreases (negligible damping) and finally decrease and vanish (important damping). The ratio of the second- to first-echo amplitudes is found to be proportional to $\frac{T_2^{*}}{{\tau }_s}$ for small superradiance levels and to decrease when ${\tau }_s$ approaches $T_2^{*}$. An approximate estimate of this ratio is derived for the region of linearity in $\frac{T_2^{*}}{{\tau }_s}$.

It is shown that it is possible to determine the form of the repulsive part of the pair potential in liquids from the temperature dependence of the related hard-core potential as defined by Barker and Henderson. An application to recent molecular dynamics results on argon is discussed. Further application to liquid metals is suggested.

The elastic scattering of fast charged particles in a background plasma is considered. Investigation is limited to scattering by Maxwellian particles whose most probable speed is much less than the velocity of the fast test particle. A shielded-potential elastic-scattering cross section is used to formulate the scattering kernel. By taking the moments of the kernel, it is possible to obtain expressions for the rate of energy transfer, the slowing-down time, the rate of the mean-square energy transfer, and the dispersion of the initial energy distribution of the fast particles released to the background.

The traveling-wave interaction between an electron beam in vacuum and an $m=0\mathrm{}$ whistler (helicon) mode propagating in a cylinder of $n$-type InSb at 84 °K has been observed. A small hole through the center of the crystal, parallel to the cylinder axis and magnetic field, allows the electron beam to interact with the fringing fields associated with the whistler. The interaction is observed by (1) measuring the change in the whistler wave power transmitted through the crystal due to the presence of the electron beam, and (2) measuring the perturbation of the electron beam resulting from the interaction with the wave. The wave-phase velocity is varied by changing the magnetic field, the wave frequency, and the plasma density. In all cases, we find a resonant interaction between beam and wave when the beam velocity is nearly equal to the whistler phase velocity. The parametric dependence of this resonance, as well as the width and amplitude of the resonance, is found to be in good quantitative agreement with theory. The data demonstrate conclusively that the lattice dielectric constant is important in describing the whistler fields near a vacuum-plasma interface. The good agreement between theory and experiment demonstrates the use of the interaction as a diagnostic tool.

The properties of ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}_2^{+}$ were studied in helium-argon mixtures by means of the afterglow method. The time dependence of the number density of these ions was measured by massspectrometric techniques. The temporal behavior of the intensity of various spectral lines was also determined. The studies established the occurrence of the collisional recombination process ${\mathrm{Ar}}^{+}+2e\to \mathrm{Ar}+e+h\nu$, while they confirmed the importance of the dissociative recombination process ${\mathrm{Ar}}_2^{+}+e\to \mathrm{Ar}+\mathrm{Ar}+h\nu$. The collisional process appeared to populate all levels studied, while the dissociative process selectively populated the $2p$ and $3p$ energy levels. The only ion-molecule—association reaction observed for argon concentrations between 0.01 and 5% was ${\mathrm{Ar}}^{+}$+Ar+He→${\mathrm{Ar}}_2^{+}$+He. The rate constant was found to be 8.0×${10}^{-32\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$. The value of the mobility of ${\mathrm{Ar}}^{+}$ in the helium-argon mixtures obeyed Blanc's Law.

A high-resolution study of the He II $\lambda 4686$ Å ($n=3-4\mathrm{}$) line complex emitted from a cooled hollow cathode has been made using a double-etalon spectrometer with photoelectric detection. Computer analysis of the digitally recorded spectra of this line yields fine-structure and isotope-shift measurements for the isotopes ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ which agree with quantum electrodynamic theory to within ±0.0005 ${\mathrm{cm}}^{-1\mathrm{}}$ for the best measured components. The excitation and deexcitation processes for this transition, which are active in the hollow-cathode, have been analyzed. The results show that the anomalously large widths observed in ionized helium lines which have been electronically excited arise from large momentum transfers in the excitation process. Calculation of the momentum-transfer line profile in the process $\mathrm{He}+e\to {{\mathrm{He}}^{+}}^{*}+e+e$ gives reasonable agreement with the observed profiles when the instrumental profile and neutral He Doppler profile are included. Measurements further confirm that the origin of the small anode-drift shift is a residual electric field within the discharge.

Recent low-temperature measurements of the mobility of negative ions in dilute ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures are explained. A new method based on the Boltzmann equation is used to derive the general formula for the drag force of a heavy impurity in an arbitrary gas. It is shown that the structure of the negative ion (electron bubble) depends on the ${\mathrm{He}}^3$ concentration $C_3$ and temperature. Also, for $C_3$ above about 1% the distortion of the ${\mathrm{He}}^3$ distribution by the moving ion becomes important. The application of our theory to pure, highly degenerate ${\mathrm{He}}^3$ shows that the mobility remains finite at $T=0\mathrm{}$ and rises with temperature. Both results agree with experiment.

The description of the steady state by means of a minimum principle is given. Previous attempts to use the entropy production were successful only if the deviations from equilibrium were small. We show how entropy production can be defined so that the principle will hold for arbitrary deviations. The choice is further corroborated by a physical picture: That part of the entropy production which is due to the heat flow to the bath should be divided, not by the temperature of the bath, but by a different temperature. This temperature is determined as a function of the occupation probabilities. Unfortunately, this temperature cannot be defined in an invariant way. The definition is microscopic and holds only for systems that can be described by a linearized master equation. A proof is given that the generalized temperature used in the new entropy-production definition is higher than the equilibrium temperature, but less than or equal to the steady-state temperature. This proof is limited to a two-level system, for which a steady-state temperature can be defined, interacting with a heat reservoir and external radiation, as discussed in the text.

The long-wavelength dispersion of the phonon spectrum in liquid ${\mathrm{He}}^4$ can be computed from first principles. Part of the dispersion coefficient enters through the Feynman spectrum ${\epsilon }_0\mathrm{}\left(k\right)\mathrm{}$, and the other part enters through corrections to ${\epsilon }_0\mathrm{}\left(k\right)\mathrm{}$. The latter has been investigated by Jackson, Feenberg, and Lee using a perturbation expansion in the free-phonon basis. We define here a more plausible ordering scheme for the expansion and carry out the computation to second order.

A liquid cluster of identical molecules is considered, and it is concluded that in the case of classical systems: (i) The macroscopic rotation can be defined irrespective of the molecular mobility. (ii) The canonical partition function is approximately separable into translational, rotational, and internal partition functions, and the numerical value of the rotational partition function is approximately the same as that of a rigid system with the same density and shape. (iii) The rotational symmetry number need not be considered when dealing with the usual phase integral of nonrigid systems, such as that used in this paper. (iv) These considerations lead to a value of about ${10}^9$ for the rotational partition function of a cluster of about 100 water molecules.

A comparison is made of the predictions of three different theories of quantized vortex rings and the experimental data on the deflection of such rings, containing trapped ions, by magnetic fields.