The spin-optimized self-consistent-field (SOSCF) method, based on optimizing the spin function in the whole ($S, M_s$) space simultaneously with spatial orbital optimization, is applied to the ${}_{}{}^4{}_{}{}^{}S$ ground state of the nitrogen atom. The maximally paired Hartree-Fock (MPHF) function, where both $1s$ and $2s$ electron pairs are associated with the singlet factor $\alpha \beta -\beta \alpha$, is also calculated, as are functions in which either the $1s$ or the $2s$ electrons are thus paired. The SOSCF energy is -54.421 67 Hartree, compared with -54. 400 93 by the restricted Hartree-Fock (RHF) and -54. 417 22 by the MPHF methods. The net spin density at the nucleus, responsible for the hfs of nitrogen, is 0. 1200 a.u., compared with 0. 1853 a.u. by the spin-extended Hartree-Fock method and the experimental value of 0.0972 a.u. (the RHF and MPHF methods give 0). The contributions of the $1s$ and $2s$ pairs, obtained from two separate calculations employing two-dimensional subspaces of the six-dimensional spin-function space, add very nearly to the full SOSCF results for the energy and spin density. The SOSCF orbitals are also described. Their most interesting feature is the nonexistence of radial nodes in any of them.

The 2-eV shape resonance in ${\mathrm{N}}_2$-electron scattering is calculated by a self-consistent-field energy-variational procedure. The resonance state corresponds to the attachment of an incident $d$-wave electron to the $1{\pi }_g$ valence orbital of the metastable ${}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ state of ${\mathrm{N}}_2^{-}$. The resonant behavior is due to the tunnelling of the electron through a $\frac{2(2+1)\mathrm{}}{{\mathcal{r}}^2}$ centrifugal barrier and temporary trapping in an attractive field. This tunnelling is reflected in the bimodal behavior of the calculated $1{\pi }_g$ orbitals; the inner portion of the orbital defines the resonance state. The "potential" curve for ${\mathrm{N}}_2^{-}$ is calculated in the Hartree-Fock approximation; a resonance threshold of 2.5 eV is predicted, with $R_e=2.27\mathrm{}$ a.u. and ${\omega }_e\approx 2000$ ${\mathrm{cm}}^{-1\mathrm{}}$. Expected correlation-energy corrections would improve the agreement with experiment. A local potential for electron scattering is generated by inverting the $1{\pi }_g$ orbital, and resonance widths are calculated. The widths vary from 0.13 eV at the equilibrium distance of ${\mathrm{N}}_2^{-}$ to 0.8 eV at the ${\mathrm{N}}_2$ equilibrium distance.

The energy results of an accurate configuration-interaction calculation of the ground state of C are reported. Special emphasis is placed on the quantitative assessment of all sources of truncation errors. In this way, the nonrelativistic energy is estimated to be -37.8436 ± 0.0015 a.u. (C), in agreement with previous estimates obtained by different methods. Nesbet's calculation is interpreted in the light of the present results.

This article presents a study of the propagation of small-area pulses of coherent light through matter. It is found that the small-area pulses exactly obey an area theorem which, in the case of an attenuating medium, requires that the pulse area decay to zero exponentially with increasing distance of propagation. This, however, does not necessarily imply that the pulse energy decays exponentially. Instead, it is found that pulses of duration comparable to or shorter than the transverse relaxation time of the medium $T_2$ (including both homogeneous and inhomogeneous broadening) propagate with low energy loss. The results are explained in terms of simple physical arguments which indicate that the pulse envelope should oscillate between positive and negative values, causing the area to decrease without a comparable decrease in the pulse energy. Analytic solutions are presented for the case of a pulse whose envelope varies as $t^k{e}^{-t}$ for $t>\mathrm{}0\mathrm{}$, a rectangular pulse, an ultrashort pulse (i.e., pulse width much less than $T_2$), and the leading portion of a step-function pulse. The propagation of a small-area Gaussian pulse is studied numerically.

Experimental cross sections for the simultaneous excitation and ionization of argon to the $4p$ configuration of ${\mathrm{Ar}}^{+}$ are presented. The data are found to be in considerable disagreement with previous work. Optical excitation functions for the important argon-ion laser lines are given, and the results are compared with the observed relative gains of the lines in a pulsed laser. The cross sections for excitation to the $4p{}_{}{}^2{}_{}{}^{}P$ states of ${\mathrm{Ar}}^{+}$ are found to have an $E^{-1\mathrm{}}$ dependence with energy in the range 250-700 eV, in disagreement with the asymptotic behavior predicted from the sudden approximation.

The absolute fluorescence intensity of the first negative (0, 0) band of ${\mathrm{N}}_2^{+}$ at 3914 Å excited by bombardment of ${\mathrm{N}}_2$ and ${\mathrm{N}}_2$: ${\mathrm{O}}_2$ mixtures with electrons in the previously unstudied energy range 0.65 to 1.6 MeV has been measured at gas pressures of 0.05 to 8 Torr. An effective cross section for the production of these photons by 1.5-MeV primary electrons and all secondary electrons resulting from the ionization events is found to be (1.6 ± 0.4) × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$. The measurements indicate that 10% of the ${\mathrm{N}}_2^{+}$ ions are formed in the $B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}(v^{\prime }=0)$ state and that the fluorescence efficiency for the 3914-Å band is (6.0 ± 1.9) × ${10}^{-3\mathrm{}}$ for ${\mathrm{N}}_2$ and (4.8 ± 1.5) × ${10}^{-3\mathrm{}}$ for air, in agreement with modern results at lower energies. From comparison with recent published results of primary excitation at lower energies, it appears that $\frac{2}{3}$ of the observed photons are produced by secondary electrons. Quenching cross sections for the $B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}(v^{\prime }=0)$ state of ${\mathrm{N}}_2^{+}$ in collisions with ground-state neutral molecules of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ have been found to be (6.5 ± 0.4) × ${10}^{-15\mathrm{}}$ and (10.9 ± 4.5) × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$, respectively.

A more detailed measurement and calculation are reported for the ${\mathrm{Cs}}^{+}$ + Cs charge-transfer cross section which contains continuous uniform oscillatory structure. Ten oscillation maxima are experimentally observed in the energy range from 0.6 to 21 keV. The oscillations are regular with inverse velocity and appear to show two superimposed oscillation frequencies. Calculations suggest that this may be due to the combined effect of a maximum in the interaction potential difference and of a large repulsive electron core, each generating a separate oscillation. It is shown that there is a very wide range of different potentials which could explain the oscillations.

The cross section $Q\left(U\right)\mathrm{}$ for energy transfer of at least $U$ is given for the case where the incident particle is lighter than the target particle. Complete results for $Q\left(U\right)\mathrm{}$ are represented with the aid of a diagram, the coordinates of which are nondimensionalized mass and nondimensionalized energy of the target particle. Some remarks are made about scaling laws for direct excitation.

A stationary afterglow system has been utilized to determine rate constants for thermalenergy negative-ion-molecule reactions in photoionized NO-${\mathrm{H}}_2$O mixtures. When the decay of the plasma is controlled by ambipolar diffusion of positive and negative ions, quantitative determination of rate constants is shown to be feasible. The plasma transition from electron-positive-ion ambipolar diffusive domination of the transport loss processes to domination by positive-ion-negative-ion ambipolar diffusion is explained by a model which includes the effects of negative-ion trapping. Prominant negative ions in the afterglow include N${\mathrm{O}}_2^{-}$, its hydrates, and clusters involving HN${\mathrm{O}}_2$. Reaction-rate constants for the processes N${\mathrm{O}}_2^{-}$+${\mathrm{H}}_2$O+NO → N${\mathrm{O}}_2^{-}$ · ${\mathrm{H}}_2$O + NO and ${\mathrm{Cl}}^{-}$ + ${\mathrm{H}}_2$O + N${\mathrm{O}}^{\to }$ ${\mathrm{Cl}}^{-}$ · ${\mathrm{H}}_2$O + NO are found to be 1.3±0.3×${10}^{-28\mathrm{}}$ ${\mathrm{cm}}^6$/sec and 3.4±1.3 × ${10}^{-29\mathrm{}}$ ${\mathrm{cm}}^6$/sec at 293 K, respectively. Steady glows in NO-${\mathrm{H}}_2$O-${\mathrm{O}}_2$ mixtures revealed that N${\mathrm{O}}_2^{-}$ and the impurity HC${\mathrm{O}}_3^{-}$ also formed multiple hydrates and clustered with HN${\mathrm{O}}_2$. These results indicate that the terminal negative ions in the D-region of the ionosphere will likely be hydrated.

The time-dependent equation $\frac{i\hslash v\partial \varphi (\mathcal{r}, R)}{\partial Z}=\exp \left(\frac{i{H}_{e}Z}{\hslash v}\right)V(\mathcal{r}, R)\exp (-\frac{i{H}_{e}Z}{\hslash v})\varphi (v, R), t=\frac{Z}{v}$ describing a fast particle perturbing a bound system was solved by Glauber in the diabatic approximation of setting $H_e$ equal to zero. The nonlocal potential $\exp \left(\frac{i{H}_{e}Z}{\hslash v}\right)V(\mathcal{r}, R)\times \exp (-\frac{i{H}_{e}Z}{\hslash v})$ is thus approximated by a local or diagonal form $V(\mathcal{r}, R)$. In this paper the local approximation is retained. The bound system is assumed to consist of a single electron attached to a fixed point with wave function $\exp (-\frac{\mathcal{r}}{a_0})$. It is then shown how the diabatic approximation can be relaxed by modifying $V$ to include the effect of $H_e$ to order $v^{-1\mathrm{}}$. In particular in the impulse approximation, scattering is described by a static local potential $V_L(\mathcal{r}, R)=\frac{1}{R}-\frac{\left[\mathrm{erf}\right(i^{\frac{1}{2}}\alpha +\epsilon \left)\right]}{|\overrightarrow{\mathrm{R}}-\overrightarrow{\mathrm{r}}|}$, where ${\alpha }^2=\frac{{|\overrightarrow{\mathrm{R}}-\overrightarrow{\mathrm{r}}|}^2}{\mathrm{}\left(2cZ\right)\mathrm{}}$, and $c=\frac{\hslash }{\left(mv{a}_0\right)}$. An analytic form is given for $\varphi (\mathcal{r} ;\overrightarrow{\mathrm{B}}, \infty )$. The binding of the electron neglected in the impulse approximation can be taken into account by changing $V_L$ to $V_L(\mathcal{r}+x, R)$, where $x=e^{\mathrm{icZ}}-1\mathrm{}$. The scattering problem is thus reduced to quadratures.

A general method for calculating the cross sections for single-quantum annihilation (SQA) of positrons in various atomic shells, valid to second order in the $\alpha Z$ expansion (one order beyond the leading term), is presented with the help of the modified Sommerfeld-Maue wave function for incoming positrons and the relativistic wave functions for the bound electrons in any atomic shells. It is shown in this approximation that the differential cross sections are of the form ${\sigma }_{\mathrm{njl}}(k, q)=C_{\mathrm{nl}}{\sigma }_{n_0\mathrm{jl}}(k, q)$, where $n_0=l+1\mathrm{}$, and $k$ and $q$ are the photon energy and the magnitude of momentum transfer to a nucleus, respectively. The factor $C_{\mathrm{nl}}$ is evaluated in general. The SQA cross sections are calculated for the $1s_{\frac{1}{2}}$, $2p_{\frac{1}{2}}$, and $2p_{\frac{3}{2}}$ states to 2nd order in the $\alpha Z$ expansion and for the $3d_{\frac{3}{2}}$ and $3d_{\frac{5}{2}}$ states to lowest order in the $\alpha Z$ expansion, and are in closed form. The relationship between the SQA cross section for any state and the corresponding cross section for the atomic photoeffect is discussed. The leading term for the SQA cross section is closely related to that for the photoeffect, but there is a distinct difference between the correction terms for the former and the latter. The comparison of the results of the present work for the $K$ and $L_{\mathrm{I}}$ shells with a recent numerical calculation done by others shows that for low and intermediate energies, the above factorization rule is valid within 1.4% for $Z=47\mathrm{}$ and 3.8% for $Z=90\mathrm{}$. However, the $1s_{\frac{1}{2}}$ cross section for $Z\geqq 82$ is negative for any energy below 2.264 Mev.

$\gamma -\gamma$ directional -correlation experiments performed on low-density gaseous sources of xenon isotopes are described. The angular correlations corresponding to the cascade transitions of 172-203 keV in ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ and 55-188 keV in ${}_{}{}^{125}{}_{}{}^{}\mathrm{I}$ have been measured and found to be strongly perturbed. The effect is ascribed to the hyperfine interaction of the iodine ions that are formed following $K$ capture of xenon isotopes. An interference phenomenon that results in the appearance of a resonance in the coincidence counting rate has been observed for the $\gamma -\gamma$ cascade of 172-203 keV. The effect is interpreted as being due to the crossing of hyperfine energy levels at zero magnetic field.

A simple model is developed that describes certain properties of the iodine ions formed after electron capture of xenon isotopes. Semiempirical energy-level diagrams for the most abundant ions are constructed and the following properties are derived therefrom: (i) The ionic states reached after the Auger cascade consist of the configurations with vacancies above the $4p$ shell and also of some configurations with holes in the $4p$ and $4s$ shell. (ii) The magnetic hfs constant appropriate to the 203-keV level in ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ is calculated for some representative Auger-stable states. The results of $\gamma -\gamma$ directional-correlation experiments (preceding paper) are interpreted in terms of the properties of the ionic states. The strong hyperfine interactions found experimentally are in accord with the predictions of the model. In addition, time-dependent effects due to the lifetimes of the ionic states are observed for the 203-keV state in ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$. They are interpreted as arising from fast electronic dipole transitions. It is suggested that the strong hyperfine fields induced by electron capture may be used for measuring electromagnetic moments of extremely short-lived nuclear states.

Recent developments in the theory of fluids have produced an analytical expression for the $\mathrm{PVT}$ behavior of rigid-sphere fluids. The equation ${\left(\frac{\mathrm{PV}}{\mathrm{NkT}}\right)}^0=\frac{(1+y+y^2-y^3)}{{\mathrm{}(1-y)\mathrm{}}^3}$, where $y=\frac{b}{4V}=\frac{\sqrt{2}\pi N{\sigma }^3}{6V}$, has been shown to be the best analytical equation for rigid-sphere fluids presently known. Incorporation of the expression into the model of Longuet-Higgins and Widom for argon near its triple point, in a manner used by Guggenheim, demonstrates the sensitivity of predicted liquid behavior to the mathematical expression for rigid-sphere $\mathrm{PVT}$ behavior.

This paper reports the determination of the loss factor of electron energy lost per collision moving in a cesium discharge. Measurements of the electric field $E$ and the electron temperature $U_e$ are used to determine the energy-loss factor of the electron. Those values are measured using Langmuir probes. The energy-loss factor of the electron in a cesium discharge has been obtained for $\frac{E}{n_a}$ (V ${\mathrm{cm}}^2$) values between 8×${10}^{-17\mathrm{}}$ and 6.2×${10}^{-15\mathrm{}}$.

This paper presents a theory of the coupling between electron-acoustic, ion-acoustic, and electromagnetic plane waves at an idealized shock front in a two-fluid, fully ionized viscous plasma. The viscous-fluid equations and Maxwell's equations are used to derive the dispersion equation relating the frequency and propagation constant of possible modes of propagation in a viscous plasma. Boundary conditions which must hold at the shock front in the presence of an incoming perturbation are then derived, and the amplitudes and energies of predicted wave modes generated at the boundary are calculated. In the limit of small viscosity, the energy-coupling ratios reduce to the values found previously in the inviscid problem, and for all values of viscosity we find enhanced wave transmission as previously found in the inviscid problem. Additionally, maxima in the energy-coupling ratios are found to exist, depending upon the viscosity of the medium.

Upper and lower bounds are derived for the average potential energy and Helmholtz free energy of an electron gas with uniform positive background. In the ground-state limit, upper and lower bounds are given for the average kinetic energy, average potential energy, and total ground-state energy. Inequalities are derived for the static form factor $S\left(k\right)\mathrm{}$ and wave-number-dependent dielectric function $\epsilon (k, 0)$, making use of exact sum rules for the Fourier-transformed density-density commutator and of the assumption that $S\left(k\right)\mathrm{}\le 1$. Comparison is made with the exact behavior of these quantities for small $k$. The sum rules are used to construct an approximate nonlinear integral equation for the ground-state static form factor of the electron gas.

The density matrix in the $P$ representation of a beam of radiation amplified by a two-photon amplifier has been derived up to the lowest order in the time-dependent perturbation theory without placing any restriction on the population of the state of the atom. It is shown that a laser beam containing noise in addition to the harmonic signal exhibits anticorrelation after being passed through such an amplifier, if less than one-sixth of the total number of atoms are maintained in the excited state.

The scattering of high-energy neutrons from liquid ${\mathrm{He}}^4$ was discussed in an earlier article on the basis of the Gram-Charlier series expansion of the incoherent scattering function. In the present paper, interference effects ignored previously are taken into account approximately and are shown to give rise to an oscillation in the half-width of the scattering function as a function of the momentum transfer. The temperature dependence of the scattering is investigated by deriving approximate expressions for the parameters in the Gram-Charlier expansion in terms of their values at $T=0\mathrm{}$, together with the observed thermodynamic properties of liquid ${\mathrm{He}}^4$. Reasonable agreement with the neutron-scattering data of Cowley and Woods is obtained.

Elastic and inelastic scattering of charged particles by helium atoms is analyzed in the Glauber approximation. Applications are made to the differential cross sections for electronhelium elastic scattering, and the predictions are compared with the first Born approximation and with measurements between 100 and 500 eV. At small momentum transfers the calculated intensities for elastic scattering are significantly greater than those obtained from the Born approximation.