A general relation is derived, thus making possible calculations of the static permittivity of conductive components binary mixtures. This relation allows generalization of a result found already in some simple cases on the nonrelaxation condition. That relation is discussed within the framework of the Bergman general theory on the dielectric properties of dispersed systems, and is applied to the particular case where the two components have the same dc conductivity. The general equations of the field are exactly solved in that case.

A new integral equation in which the hypernetted-chain and Percus-Yevick approximations are "mixed" as a function of interparticle separation is described. An adjustable parameter $\alpha$ in the mixing function is used to enforce thermodynamic consistency. For simple $\frac{1}{r^n}$ potential fluids, $\alpha$ is constant for all densities, and the solutions of the integral equations are in very good agreement with Monte Carlo calculations. For the one-component plasma, $\alpha$ is a slowly varying function of density, but the agreement between calculated solutions and Monte Carlo is also good. This approach has definite advantages over previous thermodynamically consistent equations.

The computer-assisted $C$-matrix, Löwdin-alpha-function, single-center expansion method in spherical harmonics has been applied to the three-center nuclear-attraction integral (potential due to the product of separated Slater-type orbitals). Exact formulas are produced for 13 terms of an infinite series that permits evaluation to ten decimal digits of an example using $1s$ orbitals.

Effective collision strengths are presented for all 78 inelastic transitions, including the fine structure, involving the states $1s^2\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)$, $1s2s({}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{},{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{})$, $1s2p({}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{},{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{})$, $1s3s({}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{},{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{})$, and $1s3p({}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{},{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{})$ in ${\mathrm{Ca}}^{18+}$. Resonance effects due to autoionization and dielectronic recombination are considered as in earlier papers. Departure from $\mathrm{LS}$ coupling, due to relativistic effects, is included with use of the Breit-Pauli approximation. A nine-state distorted-wave approximation is employed for partial waves $l,l^{\prime }\le 15$; the contribution from $l>\mathrm{}15\mathrm{}$ to optically allowed transitions is treated by the Coulomb-Bethe method. Dipole oscillator strengths for 28 allowed transitions are also calculated. Resonance and relativistic effects are shown to be important for a number of transitions.

The $K$ Auger-electron production cross sections of fluorine produced in collisions with thin helium- and neon-gas targets were obtained for incident fluorine ions of charge states $q=2\mathrm{}$ to $q=8\mathrm{}$ and incident energies of 6, 9, 12, and 15 MeV. The cross sections were measured with an electrostatic cylindrical mirror electron analyzer. The Auger transitions for the lower-charge states $\left(q\le 5\right)$ are from fluorine states created by ionization and excitation, but, for $q=6\mathrm{}$, are from fluorine states created primarily by excitation. For the higher-charge states $(q=7\mathrm{}\mathrm{and}8)$, single and double electron capture to excited states lead to the creation of autoionizing fluorine states.

Cross sections for $7^{2}D$ and $8^{2}D$ fine-structure mixing in Rb, induced by collisions with various ground-state atoms and ${\mathrm{N}}_2$ molecules, have been determined using methods of atomic fluorescence. Rb vapor, pure or mixed with a buffer gas, was irradiated in a glass fluorescence cell with pulses of radiation from a ${\mathrm{N}}_2$ laser-pumped dye laser, populating a ${}_{}{}^2{}_{}{}^{}D$ fine-structure state by two-photon absorption. The resulting fluorescence included a direct component arising from the optically excited state and a sensitized component due to the collisionally populated fine-structure state. Measurements of relative intensities of the two components in relation to buffer-gas pressure yielded the following cross sections (in units of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$): $Q(7^2{D}_{\frac{3}{2}}\to 7^2{D}_{\frac{5}{2}})=14.1,15.5,\mathrm{and}10.0$; $Q(7^2{D}_{\frac{3}{2}}\leftarrow 7^2{D}_{\frac{5}{2}})=9.0,10.5,\mathrm{and}6.9$, for Kr, Xe, and ${\mathrm{N}}_2$, respectively; $Q(8^2{D}_{\frac{3}{2}}\to 8^2{D}_{\frac{5}{2}})=8.9,4.9,12.4,24.9,25.8,12.1,\mathrm{and}43.1$; $Q(8^2{D}_{\frac{3}{2}}\leftarrow 8^2{D}_{\frac{5}{2}})=5.8,3.2,9.4,15.1,17.6,8.3,\mathrm{and}28.5$, for He, Ne, Ar, Kr, Xe, ${\mathrm{N}}_2$, and Rb, respectively. Cross sections for the effective depopulation of the ${}_{}{}^2{}_{}{}^{}D$ states were also determined.

The Fermi approximation is fundamental in the use of thermal-neutron scattering to study solid-state and molecular physics. It is important to understand how accurate this approximation is. There have been a number of computations of corrections to the Fermi approximation for model systems. For some of these, however, the correction has been found to be divergent. This raises some questions about the validity of these calculations. Here we calculate the first-order correction to the Fermi approximation through an approach in which the scattering nucleus is replaced by a boundary condition. It is shown that the first-order correction to the Fermi approximation can always be made to converge and that the magnitude of the correction is small.

A tractable form of the Glauber eikonal amplitude for electron-molecule scattering is obtained with an effective complex potential. We report calculations of differential and integral cross sections for elastic scattering and pure rotational excitations, and of absorption cross sections (for sum of all electronic excitations and ionization processes) for $e$-${\mathrm{H}}_2$ collisions at 40-100 eV. The absorption potential is modeled following Valone, Thirumalai, and Truhlar. It is found that rotationally summed elastic cross sections (integral) are reduced by about (3-5)% when absorption is considered and total cross sections (including absorption cross sections) agree well with available experimental measurements.

Charge-exchange processes in small-impact-parameter collisions have been studied for systems consisting of C, N, O, Ne, and Ar ions, in the 0.5—1.8-MeV range. A "compound atom" model based on an assumption of a randomization of the electrons' motion during the collision was developed. It successfully reproduces the experimental distributions of the charge-states.

A special type of atom-surface resonance is analyzed, called coalescent resonances, which display an unusual broadening effect in their width. It is shown that the Fermi golden rule does not apply for these resonances.

In atom-surface collisions, there are pairs of resonances which merge into a single resonance for special values of initial parameters of atomic beam. They display an unusual broadening effect when they are close to each other. In this paper we describe some of their properties based upon a model example.

Time delay in collisions is analyzed when zero-angular-momentum resonances are present. It is shown that very large delay comes from an orbiting wave. This is reflected in rapid change with energy of the phase of the $S$-matrix residue. In addition, we show the proper definition of time delay in terms of the scattering amplitude.

The Coster-Kronig probability $f_{23}$ for lead has been measured by a $K$-x-ray—$L$-x-ray coincidence technique. Analytic fitting of the $K\alpha$-x-ray triplet using nonlinear least-squares methodology was employed to determine the corrections necessitated by the overlap of the $K{\alpha }_2$ and $K{\alpha }_1$ peaks. The result, 0.112±0.002, is to be compared with the Dirac-Hartree-Slater prediction of 0.122 and a recently measured value of 0.130±0.002 obtained by a different approach to the overlap correction. The present result may provide an estimate of relaxation and many-body effects, which—if included—would lower the Dirac-Hartree-Slater single-particle-model prediction.

Radiative transition rates to $M$-shell vacancies have been calculated in Coulomb and length gauges for ten elements with atomic numbers $48\le Z\le 92$. The computations are relativistic, based on Dirac-Fock wave functions. As previously found for $K$ and $L$ shells, length-gauge results exceed rates computed in the Coulomb gauge by ~34%at $Z=48\mathrm{}$ to ~4% at $Z=92\mathrm{}$ for the $M_1$ shell and by ~44% at $Z=48\mathrm{}$ to ~3.5% at $Z=92\mathrm{}$ for the $M_3$ shell. Dirac-Fock rates calculated in the Coulomb gauge agree well with Dirac-Hartree-Slater results, to ~7% throughout. Contributions from higher multipoles are found to be small, the largest being ~1.5% $E2\mathrm{}$ for $3s$ and $3p$ and 0.07% $E2\mathrm{}$ for $3d$ initial vacancies. Relativistic effects are studied and analyzed in some detail.

A previous calculation of forces on atoms in external (dc) fields and in homogeneous traveling-wave laser fields is modified for the case of a standing-wave laser field. The case of intense laser fields, where the Rabi frequency is much greater than the natural decay rate of the atom, is described. A general result for any Doppler shift of the laser frequency due to the atomic motion is obtained. It is specialized to the two cases in which this shift is either much smaller or larger than the natural decay rate. In the first case, we get the same result as that of a previous calculation. The second case has not been discussed previously.

The $L$-Auger spectra of ${}_{94}{}^{239}{}_{}{}^{}\mathrm{Pu}$ (64 lines), ${}_{100}{}^{254}{}_{}{}^{}\mathrm{Fm}$ (54 lines), ${}_{95}{}^{241}{}_{}{}^{}\mathrm{Am}$ (41 $\mathrm{LMM}$ lines only), and ${}_{98}{}^{250}{}_{}{}^{}\mathrm{Cf}$ (35 $\mathrm{LMM}$ lines only) were scanned over the range 6-19 keV at high resolution (${10}^{-3\mathrm{}}\le \frac{\Delta E}{E}\le 2\times {10}^{-3\mathrm{}}$) in the Argonne National Laboratory iron-free double toroidal spectrometer using thin (≤1 μg/${\mathrm{cm}}^2$) isotopically separated radioactive sources. The observed energies of lines or line complexes agreed with Larkins's semiempirical predictions within the combined (theoretical plus experimental) standard deviations $(1\mathrm{}\mathrm{s}.\mathrm{d}.\mathrm{}=10-20\mathrm{}$ eV in 10-20 keV) in 78% of the comparisons, and 19% were within 1-2 s.d. The measured intensities (relative to $L_3{M}_4{M}_5$) for Pu were compared to nonrelativistic predictions of McGuire for $Z=90\mathrm{}$, with the relativistic predictions of Chen et al. for $Z=94\mathrm{}$, and with a mixed system using Chen et al. for Coster-Kronig and McGuire for $L$-Auger transitions. Fm intensities (and Am and Cf qualitatively) could be compared only to relativistic theories. Relativistic predictions are clearly better for Pu, but are not, in general, satisfactory for either Pu or Fm; for all Pu and Fm lines, taken together, 58% are within 1 s.d., 30% in the range 1-2 s.d., and 12% greater than 2 s.d., with the relativistic predictions generally low except for the $L_3\mathrm{MM}$ band, which is in acceptable agreement. The ratio of the intense lines $\frac{I_{L_2{M}_4{M}_5}}{I_{L_3{M}_4{M}_5}}$ averaged for all four spectra is $(27\mathrm{}\pm 7)\%$ above the relativistic prediction. The first clearly resolved spectator vacancy satellites of Auger lines were seen in ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ and ${}_{}{}^{250}{}_{}{}^{}\mathrm{Cf}$, and Coster-Kronig coefficients were deduced from their intensities relative to the main line. Their displacements in ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$ agree with calculations of Shirley. Intermediate coupling components of some Auger lines were also first resolved and their relative intensities observed to fit the nonrelativistic calculations of Haynes. From the relative intensities of $M$- and $N$-shell internal conversion lines of the 18.249-keV transition in ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$, an $M1\mathrm{}$ multipolarity is assigned.

Constraints placed on a reduced density matrix or density by the requirement that it correspond to an eigenstate or ensemble of eigenstates of some operator are investigated. Linear conditions, including expectation value, commutator, hypervirial, and hierarchy equation conditions, may lead to linear constraints on lower-order reduced density matrices and densities or leave them unconstrained. A zero-dispersion condition for a $p$-electron operator defines a parabolic trough on which reduced density matrices of order $2p$ must lie, but usually does not restrict lower-order reduced density matrices or the density. Some properties of symmetrized and antisymmetrized matrix products, related to their reduction behavior, are also investigated.

We report an investigation of the role of molecular multiphoton ionization in the production of ${\mathrm{Na}}_2^{+}$ when sodium vapor is subjected to intense optical radiation. Previous authors attribute the source of much of the ion dimer signal to laser-induced associative ionization of atom sodium. In this experiment, we distinguish the molecular process from atomic collisional mechanisms by producing an intense molecular beam created through free-jet expansion of the metal vapor. The beam of nearly 50% dimers cooled to their low rotational and vibrational states allow us to obtain a simplified three-photon ionization spectrum. We find that the spectrum displays two-photon resonances corresponding to known Rydberg level transitions and that the $A$ state, acting as virtual intermediate, plays a crucial role in the large peak-to-peak intensity variations. We employ a simple model of multiphoton ionization which uses a rate-equation approach to generate a calculated spectrum. Based on the experimental results and the success of the model in reflecting them, we conclude that much of the highly structured component of the dimer ion signal reported previously under different experimental conditions is probably due to molecular multiphoton ionization but that this structure rides on a slowly varying broad signal envelope due to laser-induced associative ionization.

We obtain an upper limit on the electron vector—proton axial vector weak-coupling constant, $C_{2p}$, of 620, using the parity-odd signature of weak-induced interferences in a microwave transition rate in $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$. Several powerful techniques, based on the analysis of resonance line shapes, allow us to detect the presence of interference processes and understand their nature. They permit us to sort out and accurately eliminate systematic effects and to extract residual parity-nonconserving contributions to the transition rate. We extend the well-known method of invariant analysis to time-dependent situations and relate it to line-shape theory. Because of their analytical nature, the results obtained lend themselves well to the precise description of experimental line shapes and should have application in other research areas.

The first photoemission measurements of the I $4d$ and I " $4p$ " subshells in methyl iodide are presented. Cross sections and angular-distribution asymmetry parameters were measured from threshold to 300 eV photon energy for the I $4d$ level (to 440 eV for the asymmetry parameter), and from 175 to 300 eV for the I " $4p$ " level. The I $4d$ results exhibited atomiclike behavior throughout this energy range, mimicking the behavior of the Xe $4d$ subshell. Theoretical calculations for the Xe $4d$ subshell agree very well with the I $4d$ asymmetry-parameter results, indicating that the I $4d$ subshell is localized on the iodine atom in ${\mathrm{CH}}_3$I. Nearer to threshold, the spin-orbit final states, ${4d}_{\frac{5}{2}}$ and ${4d}_{\frac{3}{2}}$, were resolved and exhibited nonstatistical intensity ratios mainly due to a kinetic energy effect. The I " $4p$ " asymmetry-parameter results were found to be essentially identical to the asymmetry-parameter results for the I $4d$ subshell at the same photon energies, suggesting strong interchannel coupling. This result is discussed with respect to collective effects in the iodine $N$ shell.