We present here the front form of electromagnetism with boundary data on the hyperplane z-ct=0. Two topics are discussed: a generalization of the splash-wave-mode solutions and the definition of the power-flow vector.

We present a simple theory for obtaining the semiclassical approximation for inelastic scattering. The theory gives explicit expressions for the expectation values of a wide class of quantum operators, generally valid up to O(ħ), which may be used to characterize the final distribution of a scattered particle. We illustrate the method with a one-dimensional model consisting of a particle scattering from a harmonic oscillator. In addition, we apply the theory to examine under what conditions the so-called trajectory approximation is and is not valid.

Quantum simulation of the electronic structure of atoms and molecules provides a rigorous upper bound to the true ground-state energy in these systems. Two approximations that are normally invoked, the short-time approximation for the Green’s function and the fixed-node approximation for the true ground-state wave function, are investigated. It is found that certain approximations to the short-time Green’s function introduce significant errors in the wave function near the nodes and Coulomb singularities. These errors can cause the rigorous upper bound to be violated. Introducing a multiple-time-step method we will show how this can be treated properly.

Two-body integrals involving orbital products containing one-particle spherical harmonics in the angular part and a potential f($r_{12}$) depending on the interparticle distance are reduced to an integration over three coordinates. Two alternative forms to evaluate atomic electron-repulsion integrals without using a series representation for f($r_{12}$) are derived. These equations allow handling of many types of correlation factors and also provide a new framework to carry out atomic-structure calculations.

We discuss the occurrence of orientation- or area-preserving diffeomorphism groups in quantum mechanics. We show that the generators of these groups are contained in the generators of the symmetry group of a central potential, as is demonstrated by the example of the Coulomb problem. Our approach is based on the recently introduced concept of a factor space of scattering states.

The continuous-variable representation of the dynamic group is discussed in general terms, based on the differential of the group manifold. The unified formalism of various continuous-variable representations of the dynamic group is presented, and the essential common features of different continuous-variable representation theories are exploited from the general mathematical-physical point of view. The right-hand isomorphic representation and the left-hand anti-isomorphic representation of the dynamic group, and their relationship and physical implication are discussed in detail. Specialization of the general formalism to the function spaces of the group, based on both the Hilbert space of quantum-mechanical states and the von Neumann space of the quantum-statistical states (density matrices), leads to the results of both the generator coordinate approach to the dynamic-group representation and the generalized quantum characteristic function method. Techniques for calculating the continuous-variable representation of the group algebra are proposed and illustrated with the Lipkin SU(2), the Elliott SU(3), and its extension Sp(6) symmetries as examples. The results obtained for these dynamic groups are instructive for both physicists and mathematicians.

A semiclassical formalism for the optical absorption in a coupled electron-ion system is developed. The formalism assumes (a) an initial periodic trajectory whose frequency is much lower than electronic energies, and (b) a short-memory condition, i.e., the excited-state trajectories diverge away from the initial one within one period. The result shows nonadiabatic features such as level broadening, sidebands, and tails in nonclassical regimes. The formalism is demonstrated on a model for polyacetylene and can account for unusual absorption data.

We present a theory appropriate for both the interaction-induced and the pressure-broadened rototranslational Raman spectra based on the binary-collision approximation. Assuming that the anisotropic part of the intermolecular interaction is a small perturbation, we compute the Raman spectrum of hydrogen in the wings of the rotational Raman lines and compare it with an experimental spectrum recently reported.

The time-dependent description of the dynamics of electron-molecule collision complexes is outlined within the framework of Feshbach’s projection-operator formalism. It is shown that the equation of motion for the quantum-mechanical wave packet representing the collision complex contains effective-potential terms which are nonlocal as well as non-Markovian, that is, the time development depends on the previous history of the system. The space-time integro-differential equation of motion is explicitly (numerically) solved for a class of simple models using expansions into complete sets of functions in both space and time. The exact wave-packet dynamics is compared with the results obtained in the local-complex-potential approximation, which corresponds to the Markovian approximation for the decay dynamics. The concepts and numerical methods are illustrated for a model of the well-known ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$ shape resonance in electron-${\mathrm{N}}_2$ scattering, where the boomerang effect is reproduced. For a model of a p-wave shape resonance near threshold, novel qualitative effects are revealed, namely, nonmonotonic electronic decay (recapture of electrons from the continuum) as well as strong frictional effects in the vibrational motion. The time-dependent description of virtual-state threshold effects in s-wave scattering is also briefly considered.

An electron-optical double-resonance excitation scheme in a molecular beam has been used to observe the $c_4^{\mathcal{’}}$(3p) ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$(v=3) Rydberg level of ${\mathrm{N}}_2$ at a sub-Doppler limited resolution of about 90 MHz. The widths of rotational transitions in the $c_4^{\mathcal{’}}$ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$←a’’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$(3,0) band were measured to obtain the lifetime of the $c_4^{\mathcal{’}}$(3) level as a function of J. The average lifetime is 0.19 ns, which suggests that this level decays partially through predissociation. The J dependence of this lifetime reflects the configuration mixing between the $c_4^{\mathcal{’}}$ ${\Sigma }_u^{+}$(v=3) and b’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$(v=10) levels.

A distorted-wave Born approximation method has been used to calculate the differential cross sections and angular-correlation parameters for individual 1s→3l (l=0,1,2) transitions in hydrogen by electrons and positrons. The distortion in both the initial and final channels is incorporated due to static, polarization, and exchange effects. Calculated results are compared with the available other theoretical results.

It is demonstrated, in calculations on one- and two-electron systems, that K-matrix (real-valued) boundary conditions in the trial wave function in the minimum-variance method can give anomalies at certain energies, while T-matrix (complex) boundary conditions do not. A Monte Carlo procedure is proposed for computing scattering amplitudes in a many-electron system that uses the minimum-variance approach to treat incident and target electrons on the same footing. Successful exploratory calculations on $e^{\mathrm{-}}$-H scattering in the radial limit suggest that this approach may provide a path to direct Monte Carlo scattering calculations on many-fermion systems.

Single-electron-capture cross sections in collisions of protons and α particles with ground-state ${\mathrm{H}}_2$ molecules have been studied for projectile energies in the range of 1–500 keV/amu. By treating the ground-state ${\mathrm{H}}_2$ wave function as a linear combination of atomic orbitals from the two atoms, the electron-capture amplitude in ion-molecule collisions is expressed as the coherent superposition of two single-electron-capture amplitudes in ion-atom collisions with the relative phase between the two amplitudes dependent on the collision velocity and the orientation of the molecule. The dependence of the capture cross sections with respect to the molecular orientation was examined. Total electron-capture cross sections averaged over the molecular orientations were obtained and found to be in good agreement with experiments.

A relativistic version of electron-scattering close-coupling theory (in the static approximation) is developed for the 1$s_{1/2}$, 2$s_{1/2}$, 2$p_{1/2}$, and 2$p_{3/2}$ states of hydrogenlike (or frozen-core, alkali-metal-like) target ions. Comparisons are made among close-coupling, distorted-wave, and semiclassical distorted-wave results as a function of scattering-electron energy and the charge of the target.

Absolute elastic differential cross sections of atomic hydrogen have been measured by a modulated crossed-beam method. The energy and angular range covered were from 5 to 30 eV and from 12° to 156°, respectively. The present results agree with the previous measurements within the experimental uncertainty below 15 eV, but it is found that the present results show stronger backward scattering (>120°) than the previous measurement and theoretical results by more than a factor of 2 above 20 eV.

We study laser excitation of a hydrogen atom in the presence of a static electric field in the energy region slightly above the zero-field photoionization threshold. With the help of a multiple-scattering expansion, we derive an analytic expression for the time evolution of the initial-state probability, which is nonperturbative with respect to the laser field and which is asymptotically valid in the limit of small electric fields. This allows us to study how the characteristics of the classical periodic orbit, which qualitatively has been associated with the Stark-induced resonances above the zero-field photoionization threshold, manifest themselves in the dynamics of the laser-excitation process.

Simple analytic formulas are presented for the photodetachment cross section of ${\mathrm{H}}^{\mathrm{-}}$ in the presence of parallel electric and magnetic fields. A rich array of photodetachment spectra are displayed that illustrate the strong dependence of the cross section on the polarization of the photons and on the electric and magnetic fields.

Some of the unsolved problems concerning the form factors of hydrogenic atoms for discrete-discrete, discrete-continuum, and continuum-continuum transitions are solved by a new group-theoretical method. We give exact analytic formulas for these form factors and their summation over angular momenta and indicate analytic continuation procedures among the three cases.

Second-order and fourth-order intensity-dependent corrections to the energy levels of the hydrogen atom are calculated. By comparing the results obtained for these two orders and for various values of the principal quantum number, it is seen that, at a given intensity, the second-order correction becomes more and more questionable as one approaches the ionization limit. It is shown how the divergences, which appear in calculating the matrix elements of the shift operator in a discrete basis of continuum functions, can be avoided by performing the computation in the velocity gauge. The relevant second-order numerical results indicate serious modifications of the continuum spectrum. Intrinsic limitations of the second-order calculations are discussed.

Photon-counting experiments have been conducted to test the conjecture that at sufficiently high laser irradiance, atomic inner-shell excitations can be induced by laser-driven outer-shell oscillations. Using KrF light at an irradiance ≊3×${10}^{17}$ W/${\mathrm{cm}}^2$ on low-density noble-gas targets, we detect no prompt photons which are characteristic of inner-shell processes.