The liquid structure factor of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured in the momentum transfer range from 0.133 to 1.125 ${\mathrm{\AA }}^{-1\mathrm{}}$ and a variety of temperatures from 0.38 to 4.6 K. At the lowest temperature, the structure factor demonstrates a gentle change of slope in the momentum transfer region near 0.4 ${\mathrm{\AA }}^{-1\mathrm{}}$. Values for the first and second moments of the pair correlation function are obtained at 1.45 and 3.30 K. We compare our results with recent neutron and x-ray work and also with recent theories.

A variational Monte Carlo calculation of the ground-state energy of liquid ${\mathrm{He}}^4$ has been performed with a product wave function of a flexible analytic form using several different proposed pair potentials. The calculated ground-state energy, particularly its density dependence, depends sensitively on the form of the pair interaction potential used. The variational nature of the calculations is used to set limits on the depth of some of the proposed forms of the pair potential.

The problem of the growth of the ${\mathrm{He}}^3$ phase from a free surface of a nearly saturated solution of ${\mathrm{He}}^3$ in superfluid ${\mathrm{He}}^4$ at zero temperature is considered. Using a Fermi-liquid theory modified to account for the finite thickness of the ${\mathrm{He}}^3$ phase by introducing a distortion of the Fermi surface, we find that the number of ${\mathrm{He}}^3$ layers $N_L$ in the ${\mathrm{He}}^3$ phase increases as the ${\mathrm{He}}^3$ chemical potential ${\mu }_3$ approaches its bulk value ${\mu }_0^3$ as $N_L\sim {({\mu }_3^0-{\mu }_3)}^{-\frac{1}{2}}$. This prediction is in agreement with recent experimental results of Guo, Edwards, Sarwinski, and Tough.

The experimentally observed spectrum for superfluid liquid helium has properties which are characteristic of a sound spectrum but in disagreement with the predictions of a naive use of the single-particle-Green's-function approach. It is argued that the dynamical origins of the spectrum are closely related to those which give rise to the sound propagation in normal liquids, and therefore that the helium spectrum should be sought in structures and formalisms that would be used to study sound in normal liquids.

The results of numerical calculations of the transient stimulated Raman scattering reported previously have been verified experimentally under conditions where both linear dispersion and self-focusing effects were negligible. The existence of a delay between maxima of the laser and Stokes pulses is experimentally demonstrated for the first time, while the pulse shortening in time via Raman scattering is established more firmly than in previous work. The incident-laser-pulse duration, generated-Stokes-pulse duration, and delay between intensity maxima for the laser and Stokes pulses were measured with the two-photon absorption-fluorescence technique. The effective phonon-dephasing time is determined via spontaneous Raman scattering. By using these measured quantities, inferences are made as to the magnitude of the transient gain and the shape of the exciting picosecond laser pulse.

We have investigated the self-induced transparency effect in ruby over a range of input energies which range from linear absorption to full transparency. The transmission, pulse delay, and pulse broadening were studied as a function of input energy. The transition region is narrower than that found in similar studies of the C${\mathrm{O}}_2$/S${\mathrm{F}}_6$ system; this is consistent with predictions based on ensembles of two-level systems. Included are the first pulse-delay and pulse-broadening curves to be obtained for the ruby system.

Intense laser light with frequency ${\omega }_0$ near the plasma frequency excites transverse waves with real frequency components 0 and $\pm 2{\omega }_0$ and longitudinal plasma oscillations at $\pm {\omega }_0$. The resonant coupling is due to the $\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}}$ forces and relativistic mass corrections. The maximum growth rate is $\frac{{\omega }_0{v}_0^2}{16c^2}$, where $v_0$ is the maximum electron velocity in the incident laser light.

The general motion of ions in He II is investigated assuming that nucleation of and escape from vortex rings is a random thermally activated process. The mean drift velocity $v_d$ is calculated as a function of temperature, applied field, and ionic species. It is shown that lowfield data up to and just beyond the giant discontinuity can be explained, provided careful attention is paid to the friction forces on small rings, by assuming that $v_d$ is the equilibrium drift velocity. The transition between bare-ion and vortex-ring behavior is discussed in some detail. At higher fields one must take into account vortex-ring dynamics and the possibility of escapes. In general $v_d$ is larger than the equilibrium velocity and, for very large fields, increases with field. Predictions of the theory are compared with experimental drift-velocity data. Also considered are the characteristics of ion currents in nonuniform fields. In particular, predictions are made for the "persistence current" observed when ions propagate first through a region of constant field, then through a region of zero or retarding field.

The emission spectrum of electron-bombarded superfluid helium has been measured as a function of wavelength between 600 and 1100 Å. The spectrum is characterized by a very intense band of continuous emission peaking at approximately 800 Å, along with a series of less intense bands between the wavelengths of 600 and 710 Å. This continuum is interpreted in terms of the radiative dissociation of neutral helium molecules in the reaction $A{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$. The over-all intensity corresponds to about 5×${10}^{15}$ (photons/sec)/μA of 160-keV electron beam excitation. The uv fluorescence of electron-bombarded superfluid helium is by far the most intense emission of the excited liquid and may represent a useful source of uv light.

In this paper we describe a precision measurement of the $g$ factor of the free positron. The basic experimental technique is that developed by Rich and Crane in an earlier positron experiment: A group of positrons from a ${\mathrm{Co}}^{58}$ source is confined in a magnetic mirror trap. On emission from the source, the positron beam is polarized parallel to its average velocity $〈\overrightarrow{\mathrm{v}}〉$, with polarization $\overrightarrow{\mathrm{P}}=\frac{〈\overrightarrow{\mathrm{v}}〉}{c}$. While in the field the beam undergoes cyclotron orbital motion at an angular frequency ${\omega }_c$. Simultaneously $\overrightarrow{\mathrm{P}}$ precesses at an angular frequency ${\omega }_s$, i.e., $\overrightarrow{\mathrm{P}}$ rotates about $\overrightarrow{\mathrm{v}}$ at the difference frequency ${\omega }_D={\omega }_s-{\omega }_c$. After a controlled length of time, the particles are ejected from the trap and sent into a polarimeter, this being a device whose response is proportional to the helicity, $\frac{\overrightarrow{\mathrm{v}}·\overrightarrow{\mathrm{P}}}{\left|\overrightarrow{\mathrm{v}}\parallel \overrightarrow{\mathrm{P}}\right|}$. The recorded polarimeter output vs trapping time is fitted to a cosine curve and the best-fit frequency is taken as ${\omega }_D$. This measurement of ${\omega }_D$, when combined with a measurement of the time-averaged field $B$ experienced by the positrons in the trap, is the basis of the experiment. More explicitly, if the $g$ factor is written as $g=2\mathrm{}(1+a)\mathrm{}$, where $a$ is the $g$ factor anomaly, then $a=\left(\frac{m_{0}c}{\mathrm{eB}}\right){\omega }_D$. The principal difference between the present experiment and previous work is the use of a pulsed coil instead of a dc magnet to generate a 10-kG magnetic field used in the polarimeter. Fringe fields from the dc magnet caused severe drifting of the trapped beam, a problem which has been overcome by use of the coil. The longer trapping times now obtained account for a factor of 5 improvement in measurement accuracy. The result of our experiment may be written as $a=(11\mathrm{}603\pm 12)\times {10}^{-7\mathrm{}}$. Invariance under $\mathrm{TCP}$ requires equality of the electron and positron $g$ factors. Our results, when compared with previous electron measurements, serve to confirm this prediction at the 1-ppm level in the $g$ factor. Furthermore, since the ${\mu }^{+}$ and ${\mu }^{-}$ $g$ factors are equal to within 0.7 ppm, any violation of $\mathrm{TCP}$ which manifests itself in a lepton-antilepton $g$ factor asymmetry is ruled out at the 1-ppm level.

We report some numerical results for a lattice gas of hard-core molecules on the plane square lattice, occupancy of first, second, and fourth nearest neighbors to an occupied site being forbidden (1-2-4 model). Periodic lattices of even width up to 14 sites have been studied by the matrix method; the results indicate that any transition occurs at an activity $z_t=3.315\mathrm{}\pm 0.005$. However, there is evidence that the transition is not first order; indeed it is likely that no Ehrenfest phase transition (EPT) occurs in the model.

The partition function for an exponential potential in $s$ states, including the effect of phase shifts, is computed using an approximate Jost function. Based on this result, an expression for the partition function for a shielded Coulomb potential is proposed and compared to an exact calculation. This estimate of the partition function is a convergent sum, has the correct limits, and is reasonably accurate for unit charge, temperatures of 1 and 5 eV, and a variety of densities and angular momentum states.

A modified two-state model has been assumed in order to investigate the pressure dependence of the adiabatic volume viscosities ${\eta }_{\nu }$ and ${\eta }_{\nu }^{\prime }$, and mole fraction ${\mathit{x}}_2$ in the antiparalleldipole state, and the molal volume difference $\Delta V$ in methanol and ethanol. Anomalous behavior is observed for $\Delta V$, which has a minimum value at $P\approx 1000$ kg/${\mathrm{cm}}^2$ for both liquids.

We prove a simple combinatorial theorem regarding the cancellation between direct and exchange many-body clusters in liquid ${\mathrm{He}}^3$. Under certain simplifying assumptions, our result would mean that all $n$-body clusters cancel each other for $n>~3$. Deviations of the real ${\mathrm{He}}^3$ system from these simplifying assumptions are also discussed. Corresponding statements are made throughout for the nuclear-matter system as well.

The aim of this paper is to show the way the intensity fluctuations of an optical beam are modified after propagation in a nonlinear medium. In particular, a possible method for intensity stabilization of laser light is examined.

It has recently been proposed that several anomalous features in Raman and neutron scattering experiments on superfluid helium can be explained by the formation of two-roton bound states. In the present paper we analyze in detail the structure in the superfluid helium excitation spectrum associated with bound roton pairs and propose further experiments to examine the nature of the bound states. The two-roton spectrum is calculated including roton-roton interactions over a wide momentum range, and exhibits structure due to bound states which is in remarkable agreement with experiment. Interaction of the two-roton bound state with the single-particle excitations results in a hybridization of these states and a consequent splitting of the single-particle spectrum into two branches; the calculated momentum dependence of these branches is consistent with the neutron data. Inclusion of a finite roton lifetime is shown to be essential to the interpretation of the experimentally observed excitation spectrum in the vicinity of the bound-state energy. Possible physical mechanisms for the roton-roton interaction are considered, and the angular momentum character of the bound states is briefly discussed.

Recently, a self-consistent scheme for the mode-mode coupling theory of critical fluctuations was developed by Kawasaki in which the decay rate of concentration fluctuations for a binary critical mixture was obtained in the simplest approximation of ignoring all the vertex corrections. In this paper we calculate the contribution of the simplest vertex corrections. We find that the corrections are 2.44% for $q\ll \kappa$, and 0.40% for $q\gg \kappa$, where $q$ and $\kappa$ are the wave number and the inverse correlation range of concentration fluctuations, respectively.

Gyroscopic measurements of superfluid persistent currents in liquid helium below and near the $\lambda$ transition are presented here. Measurements were conducted in a variety of sizes of porous material from 0.05- to 150-μaverage size. Near the $\lambda$ transition, both the superfluid density $\frac{{\rho }_s}{\rho }$ and the critical velocity ${\omega }_c$ exhibit a $\frac{2}{3}$-power dependence on the temperature difference from the transition. A depression of the $\lambda$ transition is observed for both $\frac{{\rho }_s}{\rho }$ and ${\omega }_c$ in the smallest pores. Data for $\frac{{\rho }_s}{\rho }$ and ${\omega }_c$ away from the transition and down to about 1.25°K are given and are in agreement with measurements made by other methods.

A momentum-transfer theory is used to obtain an expression for the drift velocity of an ion in a multicomponent gas mixture. This is combined with an approximate calculation of the partition of the ion energy in the mixture to yield a formula for the drift velocity in terms of the drift velocities in the pure component gases. Positive deviations from Blanc's law at high fields are predicted, of magnitudes that should be easily measured experimentally.

The many-time Green's-function theory for a damped boson system subjected to an external time-dependent excitation is presented. The damping is properly taken into account by means of a generalized form of the Senitzky-Haken theory of a boson system interacting with a heat bath. The theory leads to a hierarchy of equations for the Green's functions of the system, which are averaged over the heat-bath variables and which take into account the damping of the various boson modes. Two examples for a ferromagnetic magnon system coupled by an anharmonic interaction are given.