Slow collisions of different isotopes of the same species are considered. The adiabatic representation of wave functions is used. There is no restriction to inversion-symmetry-conserving collisions because of the isotopic difference. Such parity-changing collisions are considered and, since levels of different parity can cross, it is shown that the cross sections may be large. The "switching functions," previously used, are shown to play an important role in this reaction and their interpretation is discussed.

The problem of the threshold law for electron-atom impact ionization is reconsidered as an analytic continuation of inelastic-scattering cross sections through the ionization threshold. The cross sections are evaluated from a distorted-wave matrix element, the final state of which describes the scattering from the Nth excited state of the target atom. The actual calculation is carried out for the $e-\mathrm{H}$ system, and a model is introduced in which the $r_{12}^{-1\mathrm{}}$ repulsion is replaced by ${(r_1+r_2)}^{-1\mathrm{}}$. This model is shown to preserve the essential properties of the problem while at the same time reducing the dimensionality of the Schrödinger equation. Nevertheless, the scattering equation is still very complex. It is dominated by the optical potential which is expanded in terms of the eigenspectrum of $\mathrm{QHQ}$. It is shown by actual calculation that the lower eigenvalues of this spectrum descend below the relevant inelastic-scattering thresholds; it follows rigorously that the optical potential contains repulsive terms. Analytical solutions of the final-state wave function are obtained with several approximations of the optical potential: (i) omission of the optical potential, (ii) inclusion of the lowest term and dominant pole term, and (iii) a closure approximation which depends on an effective energy ${\overline{\mathcal{E}}}_N$ for each threshold energy $E_N$. The threshold law in all these cases is obtained. In the closure approximation the law depends on the sign and $N$ dependence of $E_N-{\overline{\mathcal{E}}}_N$. However, the above phenomenon of eigenvalues descending below threshold suggests that $E_N-{\overline{\mathcal{E}}}_N$ is an oscillating function of $N$. In that case the derivative of the yield curve is an oscillating (but non-negative) function of the available energy $E$. A form of such a threshold law is given.

Transition amplitudes corresponding to bound-bound and bound-free multiphoton transitions for an He atom in the presence of an intense laser beam have been evaluated. Results show that for multiphoton excitation the transition amplitude for small values of $N$ (the number of photons being absorbed) decreases with increasing intensity. However, for higher values of $N$ the amplitude continues to rise with increasing intensity. A particular feature of the present method of calculating multiphoton ionization is that the transition amplitude increases linearly for small values of the intensity, but for higher values, the slope of the curve decreases, showing an important nonlinear effect.

A coincidence measurement of the absolute cross section for electron-atomic-field bremsstrahlung, differential in photon energy, photon-emission angle, and electron scattering angle, is reported. The incident electron energy was 140 keV and the scattering materials were thin films of aluminum and gold. Measurements were made for the following cases of electron scattering angle (${\theta }_{\mathrm{ei}}$), photon-emission angle (${\theta }_{\gamma i}$), and photon energy ($k$): ${\theta }_{\mathrm{ei}}=15\mathrm{}°$, ${\theta }_{\gamma i}=270\mathrm{}°$, and $k=30\mathrm{} \mathrm{and} 70$ keV; ${\theta }_{\mathrm{ei}}=30\mathrm{}°$, ${\theta }_{\gamma i}=270\mathrm{}°$, and $k=20\mathrm{} \mathrm{and} 70$ keV; and ${\theta }_{\mathrm{ei}}=30\mathrm{}°$, ${\theta }_{\gamma i}=30\mathrm{}°$, and $k=20, 30, 50, \mathrm{and} 70$ keV. The data are compared to the theoretical calculations of Elwert and Haug and of Bethe and Heitler. Both theories give generally satisfactory agreement for aluminum. The Elwert-Haug theory is somewhat more accurate for gold, although neither theory agrees with the data at ${\theta }_{\gamma i}=270\mathrm{}°$ and $k=70\mathrm{}$ keV. A discrepancy between theory and experiment for both gold and aluminum also appears to exist for low photon energies ($k=20\mathrm{}$ keV) for the case of both the electron and photon being emitted at 30°.

The eikonal distorted-wave Born approximation (DWBA) developed recently by Chen, Joachain, and Watson is applied to atom-atom excitation in the intermediate energy range. In this paper the excitation of a hydrogen atom to the $2s$, $2p_{\pm }$, or $2p_0$ state by hydrogen impact is considered. Differential cross sections are presented. Total cross sections are presented and compared to previous calculations. It is shown that the eikonal DWBA results for the total cross section approach the two-state distortion-approximation results in the limit of high energy and very-small-angle scattering.

Atomic-field pair-production polarization correlations between incident photon and emitted positron are discussed for incident photon energies in the range 1.073-2.615 MeV. Results are reported from an exact numerical calculation in partial-wave formulation using screened potentials. It is shown that pair production can be used as a polarizer of positrons, or transmitter of polarization from photons to positrons, or an analyzer of polarized photons. In heavy elements at suitable positron angles all these correlations can be large. It is shown that the polarization correlations are practically independent of atomic-electron screening, which is a consequence of the normalization screening theory discussed in our previous work.

We have observed the energy shifts and intensity ratios of the $K$ x rays of titanium and copper excited by bombarding foils of these materials with fission fragments from the spontaneous fission of ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$. A lithium-drifted-silicon detector was employed to make the measurements. For both metals studied, larger shifts in the x-ray energies were observed than were recorded for nickel by Watson and Li in their investigation using only the light fission fragments as projectiles. In addition, the $\frac{K\beta }{K\alpha }$ intensity ratio for titanium, after correcting for $K$-edge absorption in the foil, was found to be very small. We interpret this last result as being due to very high stripping of the $M$ shell of the recoiling titanium atom in collisions with other titanium atoms.

High pressure Xe and Ar were excited by high-current relativistic-electron bursts. The spectral and temporal characteristics of the uv continua, centered near 1700 Å in Xe and 1260 Å in Ar, were measured. The maximum of the Xe spectral distribution shifted from 1690 ± 9 to 1710 ± 9 Å, and the spectral width decreased from 150 ± 3 to 110 ± 3 Å when the pressure was raised from 2 to 34 atm. The shift of the Ar continuum centered at 1260 ± 9 Å was negligible and the spectral width decreased from 130 ± 3 to 90 ± 3 Å when the pressure was raised from 2 to 61 atm. Exponential time constants for the buildup and decay of the Xe and Ar continua were obtained. They are characterized by a $p^{-1.5\mathrm{}}$ pressure dependence below 3 atm. Pressure-independent decay time constants of 4 ± 1, 16 ± 2.5, and about 280 nsec were obtained for Xe at high pressure. For Ar the pressure-independent decay time constants were 6 ± 1.5, 30 ± 5, and about 230 nsec. The efficiency for conversion of electron kinetic energy to uv energy was 10 ± 4% in Xe and 15 ± 7% in Ar.

Electron transport is considered in high-density fully ionized liquid metals. Ionic structure is described in terms of hard-sphere-correlation functions and the scattering is determined from self-consistently screened point ions. Applications to the physical properties of the deep interior of Jupiter are briefly considered.

Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.

A simple phenomenological model of the structure of an inhomogeneous quantum fluid is proposed. As examples of the application of the model the structure of the free surface of He II and the structure of the negative-ion bubble in He II are investigated. The free-surface structure compares well with the results of a more elaborate microscopic calculation. Questions concerning the effect of surface curvature and "tightening" of the bubble surface are examined.

It is the purpose of this paper to report a noniterative calculation of the classical electron-gas radial distribution function, for $\Gamma$ values up to 10.0, that is both accurate and relatively inexpensive. The theoretical method uses collective coordinates in conjunction with a rapidly convergent perturbation expansion. Numerical results are presented in both tabular and graphical form. Systematic corrections are discussed.

Capillary waves in a superfluid are shown to propagate with the classical form of the dispersion, ${\omega }^2\sim k^3$, but the coefficient in the model is not given by the surface tension.

Stimulated Raman scattering in the backward direction is observed in organic liquids under 5300-Å picosecond excitation. The spectrum and intensity of the backward-directed light is measured and compared with the emission in the forward direction. The Stokes spectrum of the light emitted in backward direction consists of stimulated Raman light, while in the forward direction both stimulated Raman and self-phase-modulated light is detected. No stimulated Brillouin or Rayleigh light is detected in the backward direction. The experimental results are in qualitative agreement with transient Raman theory.

Modified moments provide coefficients in expansions for time-autocorrelation functions (TAF's) and for their spectral densities. The expansions for TAF's are very generally convergent; the expansions for their spectral densities converge when these densities satisfy sufficient continuity or smoothness conditions. Whenever a partial sum to the density is non-negative, the corresponding partial sum to the TAF necessarily lies between the rigorous bounds recently obtained by Platz and Gordon. The accuracy of these expansions is illustrated by an application to the harmonic solid model considered by Platz and Gordon. The expansion for the TAF is consistently one or two orders of magnitude more accurate than the bounds obtained from the same number of moments and accurately represents the TAF to substantially longer times than do the bounds.

The super-radiant master equation (SME) of Bonifacio et al. is analyzed using the coherent-atomic-state representation. We have succeeded in deriving an exact Fokker-Planck equation for the density function corresponding to the reduced atomic density operator in the diagonal atomic-state representation. A solution to the Fokker-Planck equation has been provided in an elementary fashion for arbitrary atomic states which are sufficiently removed from the state of complete inversion at time zero. The general solution for arbitrary initial conditions (including the initial state of complete inversion) has been obtained using the method of eigen-function expansions and the final result expressed in terms of an integral over the initial density function. The moments of the collective atomic operators are also discussed.

The free-energy density of a one-dimensional Ginzburg-Landau field with $n$ components ${\phi }_3$ is identified with the quantum-mechanical ground-state energy of an $n$-dimensional anharmonic oscillator. Normalizing the anharmonic term by ${\mathrm{}\left(4n\right)\mathrm{}}^{-1\mathrm{}}$ and expanding in powers of $n^{-1\mathrm{}}$, we find for the ground-state energy, $n{E}_{\infty }+E^{\mathrm{}\left(1\right)\mathrm{}}+n^{-1\mathrm{}}{E}^{\mathrm{}\left(2\right)\mathrm{}}$, where $E_{\infty }=\frac{\kappa }{2}-\frac{1}{16{\kappa }^2}$, and $E^{\mathrm{}\left(1\right)\mathrm{}}=\frac{({\kappa }_2-2\mathrm{}\kappa )}{2}$ and $E^{\mathrm{}\left(2\right)\mathrm{}}=3\mathrm{}{\kappa }_2^{-2\mathrm{}}-6\mathrm{}\kappa {\kappa }_2^{-3\mathrm{}}-\left(\frac{11}{4}\right){\kappa }^{-1\mathrm{}}{\kappa }_2^{-4\mathrm{}}$ are the Hartree and first and second screening approximations, respectively. $\kappa$ and ${\kappa }_2={(4\mathrm{}{\kappa }^2+{\kappa }^{-1\mathrm{}})}^{\frac{1}{2}}$ are the inverse correlation lengths for ${\phi }_i$ and $\Sigma {\phi }_i^2$ respectively. The temperature is linearly related to the spring constant $\tau$, which in turn is connected with the correlation lengths by $\tau ={\kappa }^2-\frac{1}{2\kappa }$. The analytic results are compared with exact numerical computations for $n=1, 2, 3, \mathrm{and} 4$. The second screening correction modestly improves the accuracy of the approximation.

The problem of minimizing the general fourth-order Ginzburg-Landau free energy for $d$-wave pairing in a homogeneous system is solved. The highly degenerate family of solutions arising when the fourth-order term has the elementary BCS form, is found to be associated with a point lying on the boundary of two regimes in the general parameter space. On either side of the boundary the degeneracy is reduced to the minimum required by gauge and rotational invariance, but in very different ways: on one side pairing is in a state with $L_z=2\mathrm{}$, on the other, pairing is in a state with $〈\overrightarrow{\mathrm{L}}〉=0\mathrm{}$. It is therefore essential to know the form of the corrections to the elementary BCS theory, whether or not they prove to be large.

The problem of superradiant emission from a small atomic system is treated under conditions in which the effects of inhomogeneous broadening are important, as in a solid. The treatment is semiclassical, with the assumption that all atoms see the same electromagnetic field. A set of coupled integrodifferential equations is obtained characterizing the state of each atom of resonant frequency ω at time $t$. It is found that, in general, atoms of different frequencies evolve differently in time, whether or not they start from the same initial state. The effect of the inhomogeneous broadening is generally to delay the onset and to reduce the amplitude of the superradiant pulse. Some effects of inhomogeneous broadening are manifest even when the inhomogeneous lifetime is much longer than the usual superradiance time. When the atomic system starts in the ground state and is then exposed to a coherent excitation pulse, superradiant effects can appear even when the inhomogeneous lifetime is very short compared with the usual superradiance time.

An experimental study of the flow of superfluid helium through a small hole (6-10 μ diameter) between 0.3 and 1.7 °K is reported. The hole is inside a small volume protected by a porous filter. Two distinct stable-flow regimes are observed: a fast velocity (up to 1000 cm/sec) which decreases as ${\left(\frac{{\rho }_s}{\rho T}\right)}^{\frac{1}{2}}$ between 0.5 and 1.7 °K (in this case the dissipation mechanism is probaby the thermal excitation of vortex rings), and a slow temperature-independent velocity which increases as the square root of the chemical-potential difference, for which vortex emission from a source filament pinned in the flow is given as a model.