The Blankenbecler-Goldberger approximation to the scattering amplitude is applied to the inelastic $e-\mathrm{H} (1s\to 2s)$ and $e-\mathrm{He} [{\mathrm{}\left(1s\right)\mathrm{}}^2\to \mathrm{}(1s\left)\mathrm{}\right(2s\left)\right]$ scattering. The results for the differential cross section indicate a very good agreement with the Glauber approximation, but the Blankenbecler-Goldberger method is more difficult to evaluate than the Glauber approximation.

Differential cross sections for excitation to the $n=2\mathrm{}$ states of He are studied with an electron-impact spectrometer from threshold to 4 eV above. We observe pronounced angle-dependent structures in threshold excitation to the $2{}_{}{}^3{}_{}{}^{}P$ state and in near-threshold excitation in the $2{}_{}{}^3{}_{}{}^{}S$ state. Together, these experimental findings and recent theoretical considerations suggest the existence of a new ${}_{}{}^2{}_{}{}^{}P$ resonance near 20.8 eV.

A recent paper by Eichinger solved for the radial distribution function $g\left(r\right)\mathrm{}$ and the osmotic pressure for polymer solutions, starting from a linearized hypernetted chain (HNC) equation with the assumption that the force between pairs of molecules is governed by the Flory-Krigbaum potential. It is pointed out here that some of these results can be extended by treating the full HNC equation. Simple analytical expressions for $g\left(r\right)\mathrm{}$ and for the virial coefficients which are of a much broader range of applicability are derived.

The use of multiple-frequency illumination is shown to be capable of reducing the energy of suprathermal electrons produced in the laser-plasma interaction. The range of the suprathermal electrons is shown to vary inversely with the number of spectral components.

A new calculational ansatz for the quantum problem of a hydrogenlike atom in a nonresonant superintense laser field is presented. It is shown that the ground-state energy scales down from the field-free value by the ratio of the Bohr radius to the electron oscillation amplitude in the laser field.

Recently, electron-loss cross sections were presented by Kim and Meyer [Phys. Rev. Lett. 44, 1047 (1980)] for 40 keV/amu ${\mathrm{N}}^{3+}$ + ${\mathrm{H}}^{**}\mathrm{}\left(n\right)\mathrm{}$ collisions which scaled as $n^{3.12}$, where $n$ is the principal quantum number of the excited ${\mathrm{H}}^0$. Such results are in contrast to an $n^2$ scaling predicted by classical and first Born theoretical methods. Our calculations indicate that a major component of the experimentally observed ion signal was due to Stark ionization by deflector grids of highly excited ${\mathrm{H}}^0$ produced in excitation-transfer collisions. Inclusion of the excitation process in a theoretical interpretation reveals qualitative agreement between theory and experiment and stresses the importance of excitation transfer in ion-Rydberg-atom collisions.

It has long been known that the cross section for the inelastic scattering of relativistic charged particles by atoms rises logarithmically with increasing energy. I rederive this result without introducing the current-current interaction (and hence without quantizing the electromagnetic field). This is done by working in the projectile frame in which the projectile current vanishes. The advantage of using the projectile frame is emphasized. A rough heuristic derivation of the logarithmic divergence is also given with the collision viewed in the projectile frame.

We report here a simple and direct observation that the molecular long axis is not, on the average, a rotation axis for the entire molecule in the smectic $C$ phase (rotational freeze-out). This observation is made in the compound 4-$n$-heptyl-$d_{15}$-oxybenzoic acid-$d_1$ where experiment clearly shows that the principal axes of the time-averaged deuterium quadrupole interactions at specific sites of the hydrocarbon chain are not all parallel, demonstrating that they do not share a common axis of rotation.

Scattering of electrons, atoms, and ions by linear, symmetric-top, and asymmetric-top molecules is considered in the adiabatic-rotation approximation. The energy-loss rate or the stopping cross section, defined by multiplying the cross section by the excitation energy and by summing over final states, is independent of the initial rotational state. Thus, an average over the rotational distribution is independent of the rotational temperature of the gas.

The wavelength of the transition $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1s2p{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ of heliumlike Fe xxv has been measured in beam-foil-excited spectra at 7 MeV/nucleon. The result is $\lambda (2\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})=271.02\mathrm{}\mp 0.09$ Å. The present wavelength measurement is sensitive to Lamb-shift contributions alone to a precision of ∓ 3%.

Differential cross sections for electron capture in collisions between protons and hydrogen atoms have been experimentally determined for incident proton energies of 25, 60, and 125 keV in the center-of-mass scattering-angle range of 0-3 mrad. The experimental results compare more favorably with the results of both a multistate and a two-state calculation than with the results of a continuum distorted-wave-approximation calculation. There is no evidence of a Jackson-Schiff-type minimum.

The lowest inelastic (${}_{}{}^2{}_{}{}^{}P_{}^{\circ }{}_{}{}^{}$) resonance in the scattering of electrons from helium is recalculated using the quasiprojection formalism. An eigenvalue has been found at 20.52 eV using a closed-shell target ground-state quasiprojector, and is confirmed by using an open-shell target projector (yielding $\mathcal{E}=20.56\mathrm{}$ eV). The width is also calculated and is very large: $\Gamma =0.44\mathrm{}$ eV, thus unambiguously showing that the well-known experimental structure at ∼20.3 eV is a Feshbach and not a shape resonance. The associated nonresonant continuum phase shift reveals a pronounced enhancement beyond the $2{}_{}{}^1{}_{}{}^{}S$ threshold. This finding supports the observational inference of a second ${}_{}{}^2{}_{}{}^{}P_{}^{\circ }{}_{}{}^{}$ (shape) resonance at 20.8 eV by Phillips and Wong.

Variational solutions to the Dirac equation in a discrete $L^2$ basis set are investigated. Numerical calculations indicate that for a Coulomb potential, the basis set can be chosen in such a way that the variational eigenvalues satisfy a generalized Hylleraas-Undheim theorem. A number of relativistic sum rules are calculated to demonstrate that the variational solutions form a discrete representation of the complete Dirac spectrum including both positive-and negative-energy states. The results suggest that widely used methods for constructing $L^2$ representations of the nonrelativistic electron Green's function can be extended to the Dirac equation. As an example, the relativistic basis sets are used to calculate electric dipole oscillator strength sums from the ground state, and dipole polarizabilities.

The perpendicular component of the magnetic susceptibility of the hydrogen molecule is calculated in a gauge-invariant manner. This is accomplished by implementing the approximation in which the induced current density is taken perpendicular to the uniform magnetic field when this field is along a principal axis of ${\chi }_{\alpha \beta }$. A variational calculation using a zero-field orbital of Coulson then yields ${\chi }_{\perp }=-4.107\mathrm{}\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/mole. This value falls within the theoretical bounds determined by Rebane with a maximum error of less than one percent. The Coulson orbital gives results for ${\chi }_{\mathrm{av}}$ and ${\chi }_{\perp }-{\chi }_{\parallel }$ that compare well with experiment.

Differential inequality techniques are applied in the derivation of the following upper bound for the one-electron density $\rho \mathrm{}\left(x\right)\mathrm{}$ of atomic or molecular systems: $\sqrt{\rho \mathrm{}\left(x\right)\mathrm{}}\le C{\mathrm{}(1+r)\mathrm{}}^{\frac{\mathrm{}(Z-n+1\mathrm{})\mathrm{}}{\sqrt{2\epsilon }-1\mathrm{}}}{e}^{-\sqrt{2\epsilon }r}$ where $r=\left|x\right|\mathrm{}$, $\epsilon$ is the first ionization potential, $n$ the number of electrons, and $Z$ the nuclear charge (or the sum of nuclear charges in the molecular case). Related bounds on the decay of the $k$-electron density and the wave function itself are also given. These bounds improve upon previous results [TH-O, MH-O, RA Phys. Rev. A 18, 328 (1978)]. For the ground state of a two-electron atom (ion) we report a lower bound to $\rho \mathrm{}\left(x\right)\mathrm{}$ which exhibits the same functional form as the upper bound. Finally, for this case we give a lower bound to the wave function itself which shows essentially the same decay as the corresponding upper bound.

It is known that the nonrelativistic ground-state energy $E$ of a neutral atom composed of $Z$ electrons can be rather well represented, especially for large $Z$, by $E\approx -(c_7{Z}^{\frac{7}{3}}+c_6{Z}^{\frac{6}{3}}+c_5{Z}^{\frac{5}{3}})$ Ry, where $c_7$ and $c_6$, the Thomas-Fermi and Scott coefficients, can be determined theoretically. (Recently $c_5$ was also determined theoretically.) We argue that $E$ or its derivative is a discontinuous function of $Z$—a reflection of the shell structure of atoms—so that $E$ cannot be expanded as an infinite power series in $Z^{-\frac{1}{3}}$, though it may well have an expansion through the three terms noted above, or possibly even a fourth. We also provide some insight into the remarkable accuracy of the above three-term expansion for all $Z$ down to $Z=1\mathrm{}$. We do this by examining three models [($a$), ($b$), and ($c$)] of an atom. In model ($a$) electron screening is neglected, in model ($b$) an electron is screened by electrons in lower shells but not by electrons in its own shell, and in model ($c$) there is also screening by some electrons in the same shell. We show that if $E^{\alpha }$ is the ground-state energy of the atom in model ($\alpha$), we can write $E^{\alpha }=E_{\mathrm{smth}}^{\alpha }+\Delta E^{\alpha }$, where $E_{\mathrm{smth}}^{\alpha }$ is a smooth continuous function of $Z$ which can be expanded as a convergent power series in $Z^{-\frac{1}{3}}$ for $Z>\mathrm{}{\left(18\mathrm{}\sqrt{3}\right)}^{-1\mathrm{}}$, rapidly convergent for $Z\ge 1$, and where $\Delta E^{\alpha }$ or its derivative is a discontinuous function which cannot be so expanded. We have $\frac{\Delta E^{\alpha }}{E_{\mathrm{smth}}^{\alpha }}=O\left(Z^{-\frac{p}{3}}\right)$, where $p=2, 3, 4$ in models ($a$), ($b$), ($c$), respectively. $E^c$ can be accurately approximated by the first few terms of the power series for $E_{\mathrm{smth}}^c$ even for $Z$ of order unity. We also show that the exact ground-state energy of an "atom" composed of $Z$ "electrons" which interact with each other and with a massive "nucleus" via harmonic oscillator forces is discontinuous; this increases our faith in the conjecture that $E$ is discontinuous owing to shell structure.

Using recent modifications of the original Hohenberg-Kohn theorem due to Levy [Proc. Natl. Acad. Sci. USA 76, 6062 (1979)] and Valone [J. Chem. Phys. 73, 1344 (1980)] and the modified Ritz variational principles [J.K.L. MacDonald, Phys. Rev. 46, 828 (1934)] alternative density functionals are exhibited which respect the bounds of the modified principles. Excited-state energies and electron densities may be calculated by direct minimization of the new functionals. The density functional $R_2[\rho ,U]$ obeys the bound $R_2[\rho ,U]\ge {(E_b-U)}^2$, where $U$ is a fixed constant energy and $E_b$ is the bound-state energy of the system closest to $U$. At present, it appears that the functional depends nontrivially on the external potential. Some properties of reduced density-matrix functionals are presented. The nature of the 2 matrix functional, $R_2[\rho ,U]$, provides clues to the nature of the density functional. The evident dependence of $R_2[\rho ,U]$ on the external potential indicates that the presence of excited states in the Levy density functional is very unlikely. The point of view in this paper is found to complement the recently proposed Theophilou density functional for excited states.

A diamagnetic inequality is used to extend beyond the dipole approximation an earlier result concerning the nonexistence of the superradiant phase transition.

Doubly excited states of helium sequence ($Z=1-10\mathrm{}$) are investigated by a complex-coordinate method. Some lower-lying ${}_{}{}^1{}_{}{}^{}S_{}^e{}_{}{}^{}$ and ${}_{}{}^{1,3}{}_{}{}^{}P_{}^o{}_{}{}^{}$ states below the $N=2\mathrm{}$ hydrogenic thresholds are calculated by the use of Hylleraas-type wave functions. Results are compared with recent calculations and experiments.

A method to calculate $\alpha$ values, ${\alpha }^{\mathrm{Cou}}$ for the Coulomb hole is presented. A shape for the Coulomb hole is developed, to yield theoretical ${\alpha }^{\mathrm{Cou}}$ values varying with atomic number. The trend of these ${\alpha }^{\mathrm{Cou}}$ values is the reverse of that for the theoretical Fermi hole $\alpha$, ${\alpha }^{\mathrm{Fer}}$ values. The Coulomb-hole effect is more long ranged than the Fermi-hole effect, and the Coulomb ${\alpha }^{\mathrm{Cou}}$ are smaller than the corresponding Fermi ${\alpha }^{\mathrm{Fer}}$, implying that the Coulomb-hole effect is weaker than the Fermi-hole effect.