We report the observation of forced rotational autoionization of Rydberg states lying below the lowest ionization threshold of ${\mathrm{H}}_2^{+}$, when a small external electric field is applied. Our observations are accounted for by an intuitive classical ionization model which relates the autoionization process to the lowering of the ionization threshold with the applied field.

A trail is a lattice chain model which is allowed to self-intersect while an overlap of two bonds is forbidden. With each intersection is associated an attractive interaction energy, which gives rise to a transition from swollen to collapsed structures at a certain tricritical temperature. We study the tricritical behavior of trails on a square lattice using the scanning simulation method, which is especially efficient for this problem. The interesting question is whether trails and self-avoiding walks (SAW's) belong to the same universality class. In the present calculation, the shape exponent $v_t$ and the free-energy exponent ${\gamma }_t$ for trails at the tricritical point are found to be equal (within the statistical error) to the corresponding values derived analytically (and conjectured to be exact) for self-attracting SAW's. However, our value for the crossover exponent ${\phi }_t$ is significantly larger than the exact value of self-attracting SAW's.

Measurement of the molecular correlation length of the ferroelectric liquid crystal $S-2\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{y}\mathrm{l}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{y}\mathrm{l}-4-n-\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{x}\mathrm{y}\mathrm{b}\mathrm{i}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{y}\mathrm{l}-4^{\prime }-\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{b}\mathrm{o}\mathrm{x}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}$ (2M4DBC) has been obtained from field-dependent pyroelectric studies. The liquid-crystal behavior can be described in terms of a dynamically fluctuating mixture of two conformers having polarizations of opposite sense. The relative density of these species can be altered with an electric field, thereby allowing measurement of the effective dipole moment and correlation volume of the molecular clusters.

In the framework of the recently proposed supersymmetric WKB (SWKB) approximation scheme, we obtain an explicit expression for the quantization condition which contains all terms up to order ${ħ}^6$. For spherically symmetric potentials, we find that the SWKB approach automatically yields wave functions with the correct threshold behavior. This is in contrast to the usual WKB scheme, where proper r→0 behavior necessitates the use of cumbersome ‘‘Langer corrections.’’ Previous authors have shown that the leading-order (${ħ}^0$) SWKB quantization integral gives exact bound-state spectra for analytically solvable shape-invariant potentials. For these cases, we show that the higher-order correction terms vanish identically. Finally, for nonanalytically solvable potentials, a comparison of our results (comprising of higher-order corrections) with numerically determined eigenvalues reveals very good accuracy.

The detailed transition from classical mechanics to quantum mechanics, particularly in regard to the question of quantum corrections to the semiclassical quantization, can be completely understood for the $x^4$ perturbed harmonic oscillator. This is a consequence of five facts: (i) The quantum perturbation series for the energy can be solved order by order in closed form. (ii) The quantum series rearranges directly into the classical canonical perturbation series plus quantum corrections proportional to successively higher powers of ${ħ}^2$. (iii) The classical series and the subseries for the quantum corrections converge (subseries by subseries) to the terms of the Jeffreys-Wentzel-Kramers-Brillouin (JWKB) expansion for the energy (to all orders of ħ). (iv) The (all-order) JWKB expansion, conversely, yields the quantum perturbation series and consequently uniquely determines the exact eigenvalue. (v) The ratio of the quantum energy to the classical energy at action (n+1/2)ħ differs from 1 asymptotically by 1/[9π(n${+1/2)}^2$], independent of both ħ and the perturbation coupling constant, as the harmonic-oscillator quantum number n approaches ∞. An interesting additional feature is the mechanism by which the convergence of the classical perturbation series and of the series for the quantum corrections gets turned into the divergence of the quantum perturbation series.

A completely new nonlocal exchange-energy functional in terms of a $P_4$,3(x) Padé approximant is derived from its kinetic-energy-functional counterpart. The new formula exhibits correct asymptotic behavior for large and small density gradients. It can be written in the form of an exchange functional recently proposed by Becke. Furthermore, our exchange functional yields very good exchange energies when evaluated with Hartree-Fock–quality densities. Its functional derivative does not diverge for atomic systems, allowing one to obtain fairly good variational densities and exchange energies.

The configuration interaction in the odd states of the copper atom and its effects on energy levels and transition probabilities have been studied with the multiconfiguration Hartree-Fock method. Relativistic effects have been included to first order. Good agreement is found between the results of the present work and available experimental data. The origins of observed irregularities in the energy-level structure and lifetime trends are explained. Properties of importance for the possible generation of additional lines in the copper-vapor laser are discussed.

We study the scattering of a charged structureless particle by a nucleus, described by means of its electric multipole moments, projectile and target being immersed in a homogeneous and constant magnetic field. We present an analytical expression and a recurrence rule for the matrix elements of any multipole operator. The multipoles higher than zero induce reorientations of the target. The Coulomb excitation rates we obtained coincide in the zero-field limit with the well-known field-free result.

Lyapunov characteristic exponents are calculated for classical trajectories of the Hamiltonian describing a hydrogen atom in a uniform magnetic field, and particular attention is given to periodic orbits. As the magnetic field is turned on, instability grows around the almost circular orbit which is a precise circle in the integrable limit ɛ=-∞, ɛ being the scaled energy of the system. The Lyapunov exponent of the almost circular orbit is proportional to ‖ɛ${\Vert }^{\mathrm{-}3/2}$ near the integrable limit, and this is consistent with a square-root law found by G. Benettin [Physica D 13, 211 (1984)] for the onset of instability in certain billiards.

A phase-operator formalism is constructed for the Lie algebra of SU(1,1). Uncertainty relations, analogous to the usual number-phase relations, are also constructed. These relations are then evaluated for SU(1,1) coherent states, of which the squeezed-vacuum state of the electromagnetic field is an example. We argue that the new phase, in the case of single-mode fields, may be interpreted as the phase associated with the square of the field amplitude.

A quantum system driven by a high-frequency periodic perturbation is studied. By using the asymptotic expansions in terms of inverse powers of the driving frequency, a class of unitary time-dependent canonical transformations is defined which renders the transformed Hamiltonians time independent. One representative of those Hamiltonians is the quasienergy operator, which is explicitly derived up to the fourth order. The classical limit of the theory and the possibility of separating the mean-motion Hamiltonian is discussed. It is shown that this separation can consistently be carried out to higher orders only in the case of a uniform external force. The application of the method to unperturbed systems with regular confining and singular potentials is discussed by considering the examples of harmonic oscillator, particle in the double-well potential, and particle in the Coulomb potential.

We consider a tunneling problem as the decay of a prepared state using a modified two-potential approach. This method enables us to obtain a perturbative expansion for the decay width and the energy shift of an isolated quasistationary state. The first term is very simple and the correction terms are found to be small. Some examples for application of our result are presented. The quasi- classical limit of the width Γ has the form of the Gamow formula, but with a well-defined prefactor valid also for low-lying states. This result coincides with that of instanton calculations in the limit of ħ→0.

We report a series of calculations of error bounds to the Hartree-Fock approximation for the 2s-2p and 3s-3p transitions in lithium and sodium, and the singly ionized ions ${\mathrm{Be}}^{+}$ and ${\mathrm{Mg}}^{+}$. Our purpose is to test the efficacy of various modifications of Weinhold’s effective-bounds formula for several simple but realistic examples of multielectron systems. We therefore assume the overlap error ε to be known, adopting overlap values from extensive variational calculations. We find angular momentum projection of the transition operator to be effective in tightening the bounds, while the variational optimization of a mixture of length and velocity operators is not. We also found a wave-function projection based on Brillouin’s theorem to be especially effective. When used in conjunction with angular momentum projection, this last procedure has yielded bounds for lithium very close to the known Hartree-Fock error.

A new experiment has been performed as a step toward settling an unresolved issue in the testing of the special theory of relativity. The experiment is a test for velocity or direction-dependent variation of the one-way speed of light due to particular motion of a light source and an observer. The apparatus consists of a novel type of radio-frequency bridge, in the configuration of a Mach-Zender interferometer, one arm of which is a waveguide operated near its lowest cutoff frequency (at 40 GHz) to give a very large phase velocity. Clock-transport effects have been avoided by employing only one clock that effectively remains at rest in the laboratory. Our results have not yielded a measurable direction-dependent variation of the one-way speed of light. A clear null result is obtained for a hypothesis in which anisotropy of the cosmic background radiation is used to define a preferred reference frame.

A theory for calculating a many-transition spectrum of electron-ion collisional excitations in the distorted-wave approximation (DWA) is presented. First, it is shown that the collision strength including exchange can be factorized into (i) a radial part, involving one-electron wave functions only, and the summation over partial waves of the continuum electron; and (ii) an angular part, involving the coupling between bound electrons in the target states only, specific to each transition. Factorized representations of the collision strengths are derived in various coupling schemes. Second, the computationally involved radial part is shown to be a smooth function of transition energies over a very wide range, allowing easy interpolation. These two results enable one to obtain a complete collisional-excitation array with a drastic reduction of the number of time-consuming radial calculations compared with standard methods. This allows the solution of problems which were heretofore considered impractical. As an illustration, the whole array of excitation rate coefficients for Ni-like Gd xxxvii including the lowest 107 levels (5671 transitions) was calculated in the DWA, and used in a steady-state collisional-radiative model. Resulting population inversions are presented versus plasma density.

We study the inelastic scattering, accompanied by the transfer of L photons, of fast electrons by hydrogen and helium atoms in the presence of a laser field. A detailed analysis is made of the excitation of the n=2 and n=3 states of atomic hydrogen, and of the 1 ${}_{}{}^1{}_{}{}^{}$S–$2^1$S and 1 ${}_{}{}^1{}_{}{}^{}$S–2 ${}_{}{}^1{}_{}{}^{}$P transitions in helium. It is shown that the ‘‘dressing’’ effect due to the dipole distortion of the target by the laser field produces important modifications of the cross sections at small momentum transfers for S-S and S-D transitions. However, this dressing effect is reduced in the case of S-P transitions. Our results exhibit qualitative differences from the case of laser-assisted elastic collisions; this is mainly due to the possibility of intermediate resonances in the laser-atom interaction during the collision event.

We present small-signal gain coefficients for soft x-ray transitions in nickel-like gadolinium. The gains are predicted by a steady-state collisional-radiative model containing 181 detailed levels, including n=5 states. All possible electron collisional transitions among these levels are calculated in the distorted-wave approximation. Our calculations display features that may help to explain discrepancies between design predictions and the gains recently observed in a europium plasma. Also, we identify for the first time n=3 to n=3 inversions in the nickel-like ion that suggest that the ‘‘water window’’ at 43.7 Å might be reached using such relatively low-Z elements as gadolinium.

It is shown that the dependence of electron-impact cross sections σ for the excitation of ions on the incident energy T can be represented by compact expressions for a wide range of T from thresholds to 10 keV. These expressions are σT=A lnT+B+C/T+D lnT/T for dipole- and spin-allowed transitions, σT=A+B/T+C/$T^2$+D/$T^3$ for dipole-forbidden but spin-allowed transitions, and σT=(A+BT)/(1+CT+${\mathrm{DT}}^2$) for spin-forbidden transitions, where A, B, C, and D are constants that depend on target properties but not on T. These formulas should provide accurate cross sections in applications where many atomic cross sections are needed. Examples are presented for the excitations of Be-like ${\mathrm{Fe}}^{+22\mathrm{}}$ ion by electron impact.

Charge transfer reactions involving collisions of ${\mathrm{N}}^{+}$ and $N_2^{+}$ ions and Hg$X_2$ (X=Cl, Br, and I) molecules have been studied in the kinetic energy range of 1–1000 eV (laboratory frame). Emission spectra from the (B-X) transition of HgX radicals as well as mercury atomic lines from various highly excited energy levels have been observed and analyzed. By using the integrated intensity of the most intense bands of HgX (X=Br or I) radicals and strong mercury atomic lines, emission cross sections have been measured at various laboratory kinetic energies of the projectile ions.

The Feshbach formalism is employed in a study of the effects of interference between direct radiative recombination and dielectronic recombination. A general result is obtained, valid for an arbitrary number of interacting resonances and an arbitrary number of coupled continua. The results of explicit model calculations, based on the pole approximation, are described, and comparison is made with earlier, related work.