An explicit form for the density matrix of a two-dimensional electron gas in a transverse magnetic field is obtained as a function of the Fermi energy and the field strength. The high- and low-field limits of this generalized expression lead to known results derived earlier. Expressions for the kinetic and exchange energies are derived from the density matrix and are recast as density functionals in terms of the density and the current density as basic variables. The scheme for a density-functional calculation using these energy functionals is outlined.

Our numerical analysis of thermal activation in a one-dimensional bistable potential driven by colored noise is updated for the sake of comparison with recent theoretical predictions.

Vacuum-ultraviolet continuous emission spectra have been acquired from dense, cold helium gas in the pressure of solid hydrogen during excitation by a 6.5-MeV proton beam. The emission has been identified as the $D^2$${\Sigma }^{+}$→X ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ radiative dissociation of HeH, based on theoretical potential curves and the qualitative similarities of the continuum to discrete bands previously observed with this experimental technique.

Dielectronic recombination cross sections for the metastable O vii and C v ions are calculated and found to be extremely large, of the order of ${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$ for the individual resonances. The rates are at the level of ${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$/sec. With some field enhancement and assuming that the initial ion beam is a mixture of metastable 1s2s${(}^1$S and ${}_{}{}^3{}_{}{}^{})$ states, the overall feature of the recent experimental data of Andersen et al. [Phys. Rev. Lett. 62, 2656 (1989)] is reproduced, including the broad peaks at the incident-electron kinetic energies of 4.7 and 12.5 eV, and partially also at 2.5 and 6.8 eV. With a slightly different mixture, the C C v data are well reproduced.

Along with two-photon excitation of ${\mathrm{H}}_2$ (X->EF) stimulated electronic hyper-Raman scattering (SEHRS) is observed on four of seven two-photon resonances. The tunable Stokes transitions to B-state levels are in the range 750–840 nm. This is, to our knowledge, the first observation of SEHRS with a molecule. In addition, an unassigned stimulated line, redshifted by 26.7 ${\mathrm{cm}}^{\mathrm{-}1}$ relative to the EF(v’=6)->B(v’’=1) P(2) line, is observed. This transition entails four additional vacuum ultraviolet lines, blueshifted by the same amount relative to tabulated B→X transitions.

The universality classes and critical exponents of the unbinding transition in a model of semiflexible membranes (or polymers) in (1+1) dimensions are determined for wall potentials that fall off with distance z as $z^{\mathrm{-}p}$. For p>(2/3 the unbinding transition is first order, and for attractive potentials with p<(2/3 the membrane is always bound. The marginal case p=(2/3 is quite similar to the intermediate-fluctuation regime in (1+1)-dimensional wetting.

Transmission electron microscopy studies have recently shown that low-energy cluster-beam deposition allows the formation of higher-quality films compared with the classical molecular-beam deposition. This work presents preliminary results obtained with antimony deposits.

Hamiltonian dynamical systems with many degrees of freedom are investigated using symplectic map lattices. It is shown that anomalous diffusion exists only up to some crossover time beyond which the diffusion is normal. A diffusion constant, which is inversely proportional to the crossover time, exhibits a faster than any power-law dependence on the nonintegrability parameter, strongly suggesting the relevance of a bound by Nekhoroshev for Arnold diffusion. The motion in the standard mapping is also reexamined to show that the flicker noise is seen only down to some crossover frequency.

Self-cohering, localized excitations of a DNA polymer chain are predicted using elastic parameter values that correspond well with established data. This ‘‘soliton’’ is constructed out of hydrogen-bond-stretching optical phonons and transverse-acoustic shearing waves. Numerical integration of model equations of motion shows a clear transformation from dispersive packets at low amplitude to solitonlike states at higher amplitude. Minimum excitation energies are estimated in the range of 0.1 eV.

The Thomas-Fermi (TF) atom in an external homogeneous electric field has been discussed. We introduce the appropriate TF equation and the boundary conditions. The TF equation for this problem has no spherical symmetry. We approximate the partial differential TF equation by the set of simple ordinary differential equations. Our approximation is valid for ‘‘very large’’ electric field values (much larger than those for which the perturbation theory is justified). We found the TF solutions for various values of the electric field and various numbers of bounded electrons. The external electric field ionizes and polarizes the atom. We have shown that ionization of a multielectron atom is substantial even when the external field is significantly smaller than the atomic one.

The coupled-cluster method (CCM) of quantum many-body theory has been widely and very successfully applied to a broad spectrum of condensed-matter systems. At a given level of approximation in a hierarchy of truncations which are necessary to implement the method in practice, the many-body Schrödinger equation is decomposed into a finite set of coupled nonlinear equations for the various amplitudes that otherwise exactly describe the correlated clusters or subsystems within the interacting many-body medium. The properties of the multiple solutions to these equations and their implications for the method itself are the primary concern here. We perform a detailed investigation for the simple but illustrative one-body problem of a quartic anharmonic oscillator, which provides a very stringent test of the convergence properties of any method rooted in perturbation theory. The problem is treated as a model field theory in 0+1 dimensions in order to illuminate general properties of the CCM. The various supercoherent states generated by the CCM at other than the lowest levels of truncation are unnormalizable but yield finite and well-defined estimates for quantities of physical interest. Their possible use as multiphoton generalizations of the two-photon squeezed coherent states is pointed out.

The path-integral formulation of quantum mechanics has promoted the study of classical periodic trajectories. In this spirit, the three-body Coulomb problem with a nucleus of infinite mass is considered in the special case of a rigid rotation. Using only Newton’s fundamental law for a classical atomic system, one can show that both electrons must be equidistant from the nucleus, and one obtains the solutions previously derived by Klar [Phys. Rev. Lett. 57, 66 (1986); Z. Phys. D 3, 353 (1986); J. Opt. Soc. Am. B 4, 788 (1987)]. Nevertheless, if one allows the charge at rest to be arbitrary, one finds that for Z less than unity unsymmetrical solutions may exist. The stability of each of these configurations is considered. In each case an exponentially increasing solution is present, but the unstable character is less marked in the unsymmetrical configuration. Possible consequences for atomic systems are discussed.

The magnetic interaction has been shown to produce inversion of 1s2p ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ and 1s2p ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ for Z≤3 and Z≥46. In this paper we have used the multiconfiguration Dirac-Fock method to compute with high precision the 2 ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$–2 ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ separation energy, including relativistic contributions to electron-electron correlations and radiative corrections. This energy happens to be very small around the crossing, so that the hyperfine interaction can mix both levels significantly. We have then computed the effect of this mixing on both the energy and lifetime of those levels. This calculation shows that a precise measurement of the $2^3$${\mathit{P}}_{0,\mathit{F}=\mathit{I}\mathrm{-}1}$–1${\mathit{S}}_0$F=I lifetime will enable us to measure the $2^3$${\mathrm{P}}_1$–2 ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ separation energy accurately even though the radiative width of the 2 ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ level is actually larger than the level separation.

For neutral molecules in a homogeneous magnetic field there exists a constant of motion, the pseudomomentum, which allows a complete pseudoseparation of the center-of-mass motion. For molecular ions a complete set of constants of motion is not known, neither exactly nor approximately. In this paper we investigate the structure an approximate constant of motion for a molecular ion can have in general and arrive at an interesting formula. An explicit approximate constant of motion that obeys this structure formula is derived from a physically intuitive picture that says that an approximately conserved quantity can be obtained as the pseudomomentum relative to the instantaneously fixed-nuclei center of charge of the system. Some special examples are discussed in detail.

We have studied in a crossed-beam experiment the electron-impact-induced fluorescence spectrum of ${\mathrm{N}}_2$ in the extreme ultraviolet (euv) at a spectral resolution of up to 0.03 nm. The optically thin experiment allowed us to obtain the highest-resolution electron-impact emission spectrum of the Rydberg and valence states of ${\mathrm{N}}_2$. The spectral measurements provide the emission cross sections of each of the vibrational transitions of the $c_4^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$→X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ Carroll-Yoshino band system and the b’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$→X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ Birge-Hopfield-II band system. The $c_4^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ and b’ ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ states strongly perturb one another by homogeneous configuration interactions. This perturbation leads to vibrational-excitation cross sections whose dependence on v’ is quite different from the variation of the unperturbed Franck-Condon factors.

The laboratory cross sections were measured from 10 to 400 eV. A modified Born approximation analytic model is given for the $c_4^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and b’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ vibrational-excitation cross sections. The modified Born approximation analysis leads to accurate band-system oscillator strengths. The emission cross section for the $c_4^{\mathcal{’}}$(0) level is found to be the same to within 10% by the relative flow technique and the theoretical excitation cross section using the modified Born approximation and the published $c_4^{\mathcal{’}}$(0,0) oscillator strength. The relative emission cross section for each of the vibrational levels (v’=0–4,6) of the $c_4^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state closely agrees with the relative excitation cross section from electron-energy-loss experiments. Predissociation for the vibrational levels of the $c_4^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state is estimated to be less than 10%. On the other hand, a comparison of emission and excitation cross sections shows that the b’ ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state is 84% predissociated and that the predissociation yield generally increases with vibrational quantum number.

In addition, we have measured at low resolution (0.5 nm) the cross section of the atomic dissociation fragments (N ,N II,N III) from 40 to 102 nm, and we have measured at medium resolution (0.05 nm) the emission cross section of the $c_4$ ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $c_5^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$, $c_5$ ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and $c_6^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$→X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$(0,0) transitions. The emission and excitation cross sections represent a substantial improvement in the available data base. Previous electron-impact measurements were hampered by an incorrect value of the Lyman-α standard cross section, uncertain band-system oscillator strengths, incorrect identification of strongest spectral features, and unresolved structure. This problem has led aeronomers of the Earth’s upper atmosphere to overestimate the euv photon flux and predissociation yields from Rydberg and valence states of ${\mathrm{N}}_2$ in the photoelectron-excited dayglow and aurora by a factor of 2.

Equilibrium charge distributions have been measured for 18 kinds of ions passing through a carbon foil in the energy region of 1–6 MeV/u for light ions and of 0.2–1 MeV/u for heavy ions. By combining the data obtained at present with those reported for other energies or ion species, an attempt is made to find the systematics for charge fraction F(q), mean charge q¯, and distribution width d over the wide range of ion species Z and energy E. Strong correlation has been found between the shell structure of ions and the variation of q¯ or d with Z or E. The analysis for this correlation enables the evaluation of rather reliable values of q¯, d, or F(q) for ion species 4≤Z≤92 in carbon foils from 0.02 to 6 MeV/u.

Within the arrangement channel-coupling array for treating exchange collisions one solves for the amplitude density functions. The usual procedure is to expand these functions in a square inte- grable $L^2$ basis set so that the final equations to be solved are algebraic equations. In this work the rate of convergence of the various reactive probabilities with respect to the choice of the different basis sets is studied (seven different basis sets were considered). The recommended basis sets for further numerical treatments are the sine functions.

We have calculated configuration-mixing LS-coupling and intermediate-coupling cross sections for the process of resonant transfer excitation followed by x-ray stabilization in collisions of the Li-like ions ${\mathrm{S}}^{13+}$, ${\mathrm{Ca}}^{17+}$, ${\mathrm{Ti}}^{19+}$, ${\mathrm{V}}^{20+}$, ${\mathrm{Ni}}^{25+}$, and ${\mathrm{Ge}}^{29+}$ with ${\mathrm{H}}_2$ and He. Fine-structure interactions preferentially enhance the KLL peak (by up to 35% for ${\mathrm{S}}^{13+}$) over the KLn (n>L) peak (+5%), and this largely resolves the discrepancy that exists between theoretical LS-coupling calculations and experiment over the relative height of the two peaks for the case of ${\mathrm{Ca}}^{17+}$+${\mathrm{H}}_2$.

Experimental cross sections for single ionization of ${\mathrm{La}}^{+}$, ${\mathrm{La}}^{2+}$, and ${\mathrm{La}}^{3+}$ ions as well as for double ionization of ${\mathrm{La}}^{+}$ and ${\mathrm{La}}^{2+}$ ions and for triple ionization of ${\mathrm{La}}^{2+}$ ions are presented in an electron-impact energy range from threshold up to 1000 eV. By using a fast energy-scanning technique with step widths of about 40 meV and an energy resolution of 0.4 eV, fine details in the cross sections and especially resonant contributions could be observed. Resonant excitation of ${\mathrm{La}}^{2+}$ at 95 eV with subsequent emission of three electrons appears in our interpretation to account for 30% of the total measured double-ionization cross section. The data are interpreted on the basis of calculations of energy levels and distorted-wave calculations of direct ionization from various electron subshells and of excitation-autoionization processes. A detailed analysis of the ${\mathrm{La}}^{3+}$ single ionization both for ground-state and 5$p^5$4f metastable ions is presented.