Silicon and silicon dioxide $K$ x-ray spectra produced by 0.8-MeV hydrogen, 3.2-MeV helium, and 13.0- and 35.0-MeV oxygen bombardment were measured with a high-resolution crystal spectrometer. The resulting $K\alpha$ and $K\beta$, diagram and satellite, chemical energy shifts observed with these ions and those from electron excitation are compared and discussed. In general, the chemical shifts obtained from the different projectiles are similar and are dependent upon the amount of additional $L$-shell ionization. However, the oxygen-produced $K\beta$ satellite shifts are anomalously large. The spectra indicate that perhaps these shifts are due to transitions from the conduction band of silicon dioxide.

Studies have been conducted using the ion-beam-gas excitation method with a doubly differentially pumped gas target (with a pressure ratio of ${10}^4$ to 1 or more between gas target and observation chamber) to obtain the first known radiative-lifetime measurements for the $3p {}_{}{}^5{}_{}{}^{}P$ (3849 Å), $3p {}_{}{}^3{}_{}{}^{}P$ (4025 Å), $3d {}_{}{}^5{}_{}{}^{}D_{}^0{}_{}{}^{}$ (3504 Å), $3p^{\prime }{}_{}{}^3{}_{}{}^{}D$ (4114 Å), $3p^{\prime }{}_{}{}^1{}_{}{}^{}F$ (4299 Å), and $3p^{\prime }{}_{}{}^3{}_{}{}^{}F$ (3901 Å) levels of F II. The lifetimes of these levels were measured as 8.17±0.29, 8.18±0.24, 5.74±0.20, 10.62±0.08, 10.41±0.68, and 9.45±0.34 ns, respectively. In addition, the lifetime associated with 3602-Å F II transition was measured as 4.40±0.27 ns, the level ($s$) of origin being undetermined (either $3p^{\prime \prime }{}_{}{}^3{}_{}{}^{}P$ or $3d^{\prime }{}_{}{}^3{}_{}{}^{}G_{}^0{}_{}{}^{}$). The uncertainties given are two times the standard deviations of the means (∼95% confidence level). Absolute uncertainties are estimated to be less than 10%.

We consider the passage of initially unpolarized light through a medium possessing both birefringence and differential attenuation with respect to the same pair of perpendicular axes. Circular polarization is produced if the axes undergo rotation as the light path progresses. The twisting rate that maximizes $N_2$ (the circular Stokes parameter) is found to be an elliptic function with modulus depending on the path length. Various limits are discussed, and the maximized $N_2$ is tabulated and graphed against path length for several ratios of birefringence to differential attenuation. These results are pertinent to the polarization of hard x rays by a slightly tilted crystal.

A model kinetic equation is proposed for the interaction of thermal radiation with a rarefied diatomic gas when the inelastic molecule-molecule collisions permit the transfer of energy between translational and internal modes. The model term is obtained in a general noninertial frame of reference and satisfies the conservation laws as well as the Boltzmann $H$ theorem.

$L$-shell total ionization cross sections have been measured for targets of Sn, Ag, Tb, Bi, and Au from bombardment of 1-5-MeV $\alpha$ particles. Similar $M$-shell x-ray cross sections have been obtained for Tb, Bi, and Au. The $L$-shell cross sections have been compared with theoretical calculations from the plane-wave Born approximation, the semiclassical approximation, and the binary-encounter approximation. The latter theory best reproduces the experimental data. A comparison of $L$-subshell transitions was also made between experiment and the three theories.

Studies have been made of uv and metastable excitation functions for ${\mathrm{H}}_2$ near threshold. Within 2 eV of threshold the total cross sections appear to be dominated by two vibrational series of resonances. In the excitation function of $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ (uv emitting), one series (band "$a$") is ten times more intense than the other (band "$c$"), while for $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ excitation (metastable), the two series have approximately equal intensity. The measured energy positions of the resonant peaks agree well with results obtained by other experimental techniques and with theory. Energy calibration of the metastable excitation function has confirmed that the $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}\mathrm{}(v=0\mathrm{})\mathrm{}$ level is metastable, and there was no obvious threshold for a second metastable vibrational level, although the nature of the data does not preclude its existence.

We have measured the broadening of ${\mathrm{Rb}}^{87}$ level-crossing signals due to collisions with ${\mathrm{Rb}}^{85}$. The depolarization or broadening rates for the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state orientation, the $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state orientation and alignment, and the $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state 58-G crossing were measured. Theoretical resonance-broadening depolarization rates for the electronic angular momentum, due to Carrington, Stacey, and Cooper, have been incorporated into calculations of the Hanle-effect signals in the presence of nuclear-spin coupling. The experimental broadening rates are corrected for a minor amount of coherence narrowing. The measured broadening rate for the three $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state level-crossing signals are in 20% agreement with the theory. The measured $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state broadening rate exceeds the theoretical by about a factor of 2. This discrepancy may be due to the action of the hyperfine interaction during these unusually long duration collisions. The natural lifetimes of the $5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ and $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ states are determined from the low-density linewidth to be 27.0 ± 0.5 and 29.4 ± 0.7 nsec, respectively.

All aspects of photoionization in the soft-x-ray region are taken into account, and a complete partitioning of the photoionization cross section of neon is given in terms of single-electron processes in $2p$, $2s$, and $1s$ subshells and multiple-electron processes involving these subshells. The various processes, including their angular dependences, are identified and studied by the technique of photoelectron spectrometry. The partition relies solely on experimental evidence. Absolute subshell cross sections for the emission of a single electron are compared with current theoretical predictions: The single-particle, frozen-structure model (Cooper, 1962) that uses the Herman-Skillman potential overestimated ${\sigma }_{2p}$ by up to 15%, ${\sigma }_{2s}$ by (25-35)%, and ${\sigma }_{1s}$ by about 20%; the random-phase-approximation-with-exchange model (Amusia, 1972) that includes multielectron correlation and uses Hartree-Fock wave functions predictions correctly ${\sigma }_{2s}$ at $110<h\nu <220\mathrm{}$ eV, where comparative data exist. The absolute cross section for double ionization in the $L$ shell is 5 × ${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$ at $h\nu =278\mathrm{}$ eV as compared with the theoretical value of 4 × ${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$. The energy dependence of simultaneous excitation and ionization processes in the $L$ shell is reported. A finite threshold value is observed and a plateau at higher energy is indicated. For $h\nu >130\mathrm{}$ eV, $\epsilon l,n^{\prime }{l}^{\prime }$ transitions are found to be most probable in which the continuum electron changes its angular momentum, $\Delta l=\pm 1$, and the excited electron retains its momentum, $\Delta l=0\mathrm{}$, namely $2p^6\to 2p^4\epsilon d,np$. Anisotropy parameters $\beta$ for $2p$ electrons agree well with theoretical results; however an unexplained maximum near $\theta =0^{\circ }$ at $h\nu >1\mathrm{}$ keV is found for the angular distributions of $2p$ photoelectrons.

The statistics and autocorrelation function of the light scattered from polystyrene latex have been studied with a light-detecting system on-line with a small digital computer. The distributions of photoelectric counts have been measured during count intervals from 5 × ${10}^{-5\mathrm{}}$ to 5 × ${10}^{-3\mathrm{}}$ sec. The results were well accounted for by the approximate theory of Mandel. The factorial moments have been measured to sixth order and the results were in excellent agreement with theoretical calculations. For the first time, we have directly measured the autocorrelation function without using a clipping or scaling method. With this direct method, the comparison between the results of the composite measurements and the theoretical predictions can be quantitatively discussed.

The intensities and line profiles of several forbidden optical transitions, together with their companion allowed lines were measured in a helium plasma having densities $N$ ranging between ∼ 1 × ${10}^{16}$ and ∼ 5 × ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The plasma was produced by irradiating helium gas with light from a repetitively pulsed, high-power C${\mathrm{O}}_2$ laser. The time and space-resolved spectra of three forbidden lines of He 1 were examined: the $2{}_{}{}^1{}_{}{}^{}P-3{}_{}{}^1{}_{}{}^{}P$ transition at 6632 Å, the $2{}_{}{}^3{}_{}{}^{}P-4{}_{}{}^3{}_{}{}^{}F$ transition at 4470 Å, and the $2{}_{}{}^3{}_{}{}^{}P-4{}_{}{}^3{}_{}{}^{}P$ transition at 4517 Å. The Abel-transformed line shapes were compared with recent theories and, while some discrepancies exist, their magnitude is considerably less than has been reported hitherto. A series of tests was made from which it is concluded that the existing disagreements are not the result of measuring deficiencies or errors in data processing, and are probably due to some remaining inadequacies of the theoretical models.

During the last five years, several different neutron scattering experiments have been carried out in search of direct evidence for Bose-Einstein condensation in superfluid ${\mathrm{He}}^4$. Although the structure in the scattering line that was expected if a condensate were present has never been distinctly visible, various methods of analyzing the data have led to estimates for the condensate contribution that range between 2.4 and 17%. The reeexamination begins with a review of this previous work. The next step is a calculation of the line shape using the impulse approximation (IA) and the momentum distribution function determined by McMillan by a Monte Carlo technique. The possibility of simple line broadening due to final-state interactions (FSI) is also considered. This initial treatment is essentially a repetition of one first carried out by Gersch and Smith, except that our work conforms to the conditions of the Mook, Scherm, and Wilkinson (MSW) experiment, which provides the most accurate data presently available for comparison purposes. Direct comparison suggests that the condensate fraction is no greater than about 4%, and that it may be vanishingly small. Observing that a more precise estimate would be possible if one could assess more accurately the FSI effects, particularly with respect to broadening, we then present evidence based on sum rules and other theoretical considerations which supports the idea that corrections to the IA may indeed be negligible under the conditions of the MSW experiment. With this as a basis, it is postulated that the IA is strictly applicable to the MSW data and the consequences are studied. First, it is found that the shape of the peak of the line observed by MSW would be consistent with no condensate at all; but if any were present, it would have to be less than 1%. A discussion of the conflict between this estimate and the (2.4 ± 1)% deduced by MSW is then given. Also a method of checking on the validity of the postulate concerning the applicability of the IA to the MSW conditions is described. Next, neglecting whatever condensate that is possibly present, the IA formula for $S(Q,\omega )$ is inverted and the experimental data of MSW is used to compute $n\left(k\right)\mathrm{}$, the momentum distribution of atoms in liquid ${\mathrm{He}}^4$. This, together with the kinetic energy per particle and the one-particle density matrix in the space-coordinate representation are reported for ${\mathrm{He}}^4$ at 1.2°K and 4.2°K.

A theory of the thermomagnetic force in dilute polyatomic gases is presented which, like that for the thermomagnetic torque (Scott effect), depends on a Burnett transport coefficient. The theory is shown to be in good agreement with experiments in NO and ${\mathrm{N}}_2$.

The small relativistic (magnetic) interactions in a plasma are investigated and are shown to be equivalent to a "dipole-dipole" interaction. Comparison with the results of Trubnikov and Kosachev is made with equivalent results if it is assumed that oscillatory sum functions vanish. However, the oscillatory part may lead to significant collective behavior involving many weak long-range pairwise effective interactions.

A quantum hard-sphere system bounded by two parallel rigid walls is studied at absolute zero by numerically integrating the Schrödinger equation for the system. A very pronounced layered structure in the density profile across the channel is observed. The numerical calculations are performed on fairly small systems of about 64 hard spheres. It is also found that the layered structure is very sensitive to the distance between the walls. A comparison is made with the results of variational calculations which also show definite but less striking layered structures. A classical hard-sphere fluid in a similar geometry again shows a layered structure which is also sensitive to the distance between the walls. We suggest that the occurrence of the layers can be semiquantitatively related to the oscillations exhibited by the radial distribution function at the same density.

Expressions for the asymptotic behavior of the angular-velocity and orientation correlation functions for a fluid of linear molecules are derived by a microscopic calculation based on the generalized Langevin equation. The previously obtained $t^{\frac{-5\mathrm{}}{2}}$ decay of the angular-velocity autocorrelation function is confirmed, but a somewhat more general expression for the coefficient of this decay is obtained. The vector-orientation autocorrelation function, on the other hand, is found to decay as $t^{\frac{-7\mathrm{}}{2}}$ for long times. This result, which is based on a direct calculation of the correlation function, is in disagreement with hydrodynamic results which conjecture a $t^{\frac{-5\mathrm{}}{2}}$ decay.

A new theory of self-diffusion in simple liquids is outlined. Dynamical superposition is assumed and then it is shown that with no further approximations the self-diffusion coefficient can be computed if the functional form of the equilibrium pair correlation function $g\left(r\right)\mathrm{}$ is known. The result is formally equivalent to that found in the theory of dilute gases with the potential of mean force, $\omega \mathrm{}\left(r\right)=-\ln g\left(r\right)\mathrm{}$, taking the place of the intermolecular potential.

The Auger-transition rate is determined for multiplets formed by coupling $s$ or $p$ holes to partially filled $d$ shells. The Auger transitions considered are $s-pd$, $s-d^2$, $p-sd$, and $p-d^2$. A sum rule for Auger transitions involving two electrons from a partially filled shell is obtained. Transition rates are evaluated for atoms with ${\mathrm{}\left(3d\right)\mathrm{}}^n$ and ${\mathrm{}\left(4d\right)\mathrm{}}^n$ configurations. It is shown for elements with almost filled $4d$ shells that the $N_1$ and $N_{2,3}$ decay rates are large, leading to widths on the order of 10 eV. For the ${}_{}{}^5{}_{}{}^{}S$ and ${}_{}{}^7{}_{}{}^{}S$ multiplets created by adding a $3s$ hole to an ion with a ${\mathrm{}\left(d\right)\mathrm{}}^5{}_{}{}^6{}_{}{}^{}S$ ground-state configuration the calculated widths are significantly different, in contrast to the experimental observation of approximately equality of widths. It is shown that inclusion of configuration interaction with the continuum enhances the disagreement between calculation and experiment. However, including configuration interaction with discrete states removes the disagreement between calculation and experiment.

We present a formalism for the description of many-particle systems when the particles are themselves composites of several elementary constituents. We investigate specifically the case of composites made up of two fermions, the method being easily extended to more general composites. The formalism, although its development is guided by the knowledge that there are fermion constituents in the composites, is given entirely in the composite language and requires no reference to these underlying fermions. Thus, the procedure maintains all required symmetries at every step. Composite field operators satisfying all symmetries are defined, these fields obeying neither Bose nor Fermi commutation rules, but more complicated ones. The many-composite dynamics is studied via the Green's functions formed from composite operator products. A Hartree-Fock-like approximation is introduced and leads to the generation of composite wave functions describing the distortion of the composite internal states by the presence of other composites in the system.

We calculate variationally the coefficients of thermal conductivity $K_s$, spin diffusion $D_s$, and transverse viscosity ${\eta }_s$ in a two-dimensional Fermi liquid by using the Landau Fermi-liquid theory. The leading temperature dependence at small $T$ is $K_s^{{}^{-1\mathrm{}}}\propto T\ln T$, $D_s^{-1\mathrm{}}\propto T^2\ln T$, and ${\eta }_s^{-1\mathrm{}}\propto T^2$, in contrast with the behavior of a three-dimensional Fermi liquid, $K^{-1\mathrm{}}\propto T$, $D^{-1\mathrm{}}\propto T^2$, and ${\eta }^{-1\mathrm{}}\propto T^2$. The resulting formulas are used to predict $K_s$, $D_s$, and ${\eta }_s$ for the liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ monolayer or partial monolayer which can form on a free surface of superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

In this paper, we examine the theory of the rate at which spin-spin interactions produce energy transfer across an interface between a degenerate Fermi gas (liquid ${\mathrm{He}}^3$) and a system of electron spins. We consider first the case where the electron spins are conduction-electron spins in a metal, and examine the rate of energy transfer produced by spin-spin interactions of dipolar form, and also by a short-range exchange interaction. In the former case (dipolar coupling), the Kapitza conductance exhibits a $T^3\ln T$ dependence on temperature, but is very small in magnitude. In the second case (short-range interaction), the Kapitza conductance varies as $T^3$, with a magnitude that is also small. We conclude that neither dipolar interactions nor short-ranged interactions of the exchange type can produce a significant transfer of energy from the ${\mathrm{He}}^3$ spins to conduction-electron spins in metals. We also calculate the rate at which the ${\mathrm{He}}^3$ spins transfer energy to an array of paramagnetic local moments. We recover a result similar to that obtained earlier by Leggett and Vuorio. In contrast to Leggett and Vuorio, we use the full form of the dipolar interaction to couple the ${\mathrm{He}}^3$ spins to the local moments, and in all the calculations reported here, the effect of the surface on the single-particle wave functions is included by treating the surface as a barrier of infinite height.