The time evolution of a quantum single-quartic anharmonic oscillator is considered. The study is carried on in operational form by use of the raising and lowering operators of the oscillator. The equation of motion is solved by application of a new integration method based on iteration techniques, and the rigorous solutions that describe the time development of the displacement and momentum operators of the oscillator are obtained. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals. Finally, the results are employed to describe the time evolution of a quasiclassical anharmonic oscillator.

We show that the set of Wigner functions associated with the excited states of the harmonic oscillator constitutes a complete set of functions over the phase space. An arbitrary probability distribution can be expanded in terms of these Wigner functions. By studying the time evolution, according to stochastic electrodynamics, of the expansion coefficients, we are able to separate explicitly the contributions of the radiative reaction and the vacuum field to the Einstein A coefficients for this system. We also supply a simple semiclassical explanation of the Weisskopf-Heitler phenomenon in resonance fluorescence.

The $Z^{\mathrm{-}1}$ perturbation expansion is used to derive an expression for the atomic binding energy E in terms of the nuclear charge Z and the number of electrons N of the form E(Z,N) =${\mathcal{J}}_{\mathit{n}}$ ${\mathcal{J}}_{\mathit{j}}$b ${}_{\mathit{jn}}{}^{}{}_{}{}^{}$${\mathit{Z}}^{2\mathrm{-}\mathit{j}}$${\mathit{N}}^{\mathit{j}+\left(1\mathrm{}\mathrm{-}\mathit{n}\right)/3\mathrm{}}$. Analytical expressions for $b_{\mathrm{jn}}$ with 0≤n≤4 and 0≤j≤2 are obtained from the neutral-atom binding energy, the asymptotic expansion of the zeroth-order perturbation coefficient, and the relation (∂E/∂Z${)}_{\mathit{N}=\mathit{Z}}$=(∂E/∂Z${)}_{\mathit{N}}$+O(${\mathit{Z}}^{\mathrm{-}1/3}$), which results from the fact that the leading term in the chemical potential of neutral atoms is of the order of $Z^{\mathrm{-}1/3}$. It is found that the nuclear-electron attraction energy of neutral atoms shows oscillations periodic in $Z^{1/3}$ with an amplitude proportional to $Z^{5/3}$, in contrast with the $Z^{4/3}$ amplitude of the oscillations in the atomic binding energy. The estimates of E(Z,N) from the approximate analytical expressions of $b_{\mathrm{jn}}$ are in excellent agreement with the corresponding Hartree-Fock values.

With the use of two-step laser excitation, it is shown that the state distributions of highly excited barium atoms are substantially altered by inelastic collisions with barium atoms. For ‘‘pure’’ Rydberg states the initially produced ns or nd eigenstates are rapidly mixed with nearly degenerate n’l’ states. For initially produced states that may be viewed as admixtures of Rydberg and doubly excited independent-electron eigenstates, collisions convert the distribution to one with nearly pure, albeit state-mixed, Rydberg character. Broadening of the absorption profiles of the highly excited states is also observed. This effect results from quasistatic interaction between two highly excited atoms during the excitation. Beyond a critical excited-atom density, avalanche effects lead to an apparent narrowing of these profiles which subsequently broaden at still higher atom density.

Effects of configuration interaction and relativity on the dielectronic satellite spectra and total dielectronic rate coefficients for the hydrogenlike ions were investigated. The calculations were carried out for the intermediate autoionizing states of the 2l2l’ and 2l3l’ configurations by using relativistic and nonrelativistic Hartree-Fock models. The effect of relativity has been found to change the Auger rates by as much as a factor of 18 at Z=54. The inclusion of the Breit interaction in calculations of the Auger matrix elements could change the Auger rates by as much as a factor of 4 for the ${\mathrm{Xe}}^{52+}$ ion. The effect of configuration interaction has been found to alter some of the transition rates by a factor of 2. The dielectronic satellite spectra become much more complex due to the inclusion of configuration interaction and intermediate coupling. The effects of relativity and configuration interaction, however, have been found to change the total dielectronic recombination coefficients by amounts less than 20% and a few percent, respectively, for the ${\mathrm{Cr}}^{23+}$ and ${\mathrm{Xe}}^{53+}$ ions.

Secondary electron production as a consequence of inner-shell vacancy decay for the Kr-Kr system has been studied. Electron-energy spectra differential in impact parameter have been obtained by detecting electrons in coincidence with projectile ions scattered through a known angle. The spectra exhibit structure attributable to Auger decay of L-shell vacancies. The collision-energy dependence of the L Auger yields is consistent with the L-shell excitation being due to rotational coupling of the 4fσ, 4fπ, 4fδ, and 4fcphi orbitals of the Kr-Kr quasimolecule, as originally proposed by Shanker and co-workers. The L Auger electron energies and relative transition-group intensities suggest that L-shell vacancy decay occurs in Kr ions with initial charge states greater than +10, indicating that a surprisingly large number of electrons are emitted prior to the decay of the L-shell vacancy. These prior ionizations, most of which occur during the collision, are the source of the 100–800-eV continuum electrons that dominate the low-energy region of the electron spectrum.

The wake potential of a fast charged particle is derived for an atomic system using first-order quantum-mechanical perturbation theory. The Coulomb excitation cross sections of the target atoms by this wake potential are then derived and found to be considerable. Numerical results on a model system of condensed atomic hydrogen show that the wake potential is very important and must be included in calculating the integrated Coulomb excitation cross sections in condensed matter.

Discrepancies between previous experimental values of differential cross sections for electron-impact ionization of water vapor and recent model calculations have been largely resolved. A new measurement with improved suppression of spurious electrons has removed most of the discrepancy in the midrange of detected electron energies. A second discrepancy at secondary energies just below the primary energy has been explained by a more accurate accounting for electrons scattered at angles between zero and the minimum angle of the experimental apparatus. The improved data show more clearly the oxygen K-shell edge in the spectra at small angles and the Bethe ridge at angles up to 90°. The forward peak seen in the earlier data is no longer present.

We report differential, integral, and momentum-transfer cross sections for the elastic scattering of electrons by ${\mathrm{CF}}_4$ from 5 to 35 eV. The calculations were carried out at the fixed-nuclei, static-exchange level using the Schwinger variational principle. Analyses of the partial channel amplitudes show four broad shape resonances; two in $T_2$, one in $A_1$, and one in E symmetries. The positions of these resonances agree with experimental data from total-cross-section measurements, dissociative attachment studies, and low-energy electron excitation spectra, the only exception being the 8.9-eV structure in the total-cross-section data. No experimental measurements on differential cross sections are available, but comparing with the corresponding static-exchange calculations for the e-${\mathrm{CH}}_4$ system, the e-${\mathrm{CF}}_4$ cross sections generally are less backward peaked.

In processes in which one electron is transferred from a target to a projectile and the other electron is ionized, called transfer ionization, two second-order terms arise in the transition amplitude at high collision velocities. There is a kinematic singularity and a weaker Thomas singularity. These second-order singular terms are formulated to first order in the projectile electron and first order in the electron-electron interactions. Using standard peaking approximations, the T matrix is reduced to an approximate closed-form expression. Our expression is qualitatively similar to the expression found earlier by J. S. Briggs and K. Taulbjerg [J. Phys. B 12, 2565 (1979)], who used a different formulation and evaluation and omitted an exchange contribution which we include. In this paper we evaluate cross sections for both the Thomas peak in the angle of scattering of the projectile and a kinematic ridge in the momentum distributions, ${\mathrm{k}}_2$, of the ejected electron, both of which in principle could be observed experimentally. The ridge in transfer ionization has not been previously discussed in the literature, nor has it been observed experimentally.

We have investigated the contributions of doubly excited, autoionizing resonances to the rate coefficients for electron-impact excitation of the n=2 to n=2 transitions in oxygenlike selenium. The cross sections for direct excitation were calculated using a relativistic distorted-wave approximation. The detailed Auger and radiative rates required for evaluating the resonance contributions were calculated using a multiconfigurational Dirac-Fock model. The largest effect is on the electric-dipole-forbidden transitions. For some J=0 to J=0 transitions involving two-electron excitations, the resonances enhance the collisional excitation rates by factors up to ${10}^4$ at electron temperatures relevant for laboratory plasmas.

Closed-form expressions for 1s-1s electron-capture amplitudes for ${\mathrm{H}}^{+}$+H collisions in three different approximations are compared. We find that all three approximations agree well in the region of the Thomas peak, but significant differences are noted at the minimum in the angular distributions of scattered neutral hydrogen atoms.

The simple shake probability for electron capture is formulated and evaluated for 1s-1s electron capture at high collision velocity v for projectiles and targets of charge $Z_P$ and $Z_T$, respectively. By introducing orthogonalized wave functions, corresponding to asymptotically correct first Born calculations, a shake probability is obtained that goes to zero when the electron screening s remains unchanged during the collision. When $Z_T$≠$Z_P$, our shake probability varies as ${\mathit{Z}}_{<}$${\mathit{Z}}_{\mathrm{\gtrsim }}^5$${\mathit{s}}^2$/${\mathit{v}}^8$, where ${\mathit{Z}}_{<}$ (≳) is the smaller (larger) of ${\mathit{Z}}_{\mathit{P}}$ and ${\mathit{Z}}_{\mathit{T}}$. First Born probabilities vary as $Z_P^5$$Z_T^5$/$v^{12}$. A minimum in the shake probability is predicted for charge-symmetric systems.

Detailed calculations of the electron-impact excitation of ${\mathrm{Ca}}^{+}$ are performed using both perturbation theory and the close-coupling approach. Particular attention is focused on the resonance (4s-4p) excitation since experimental emission-cross-section data are available for this transition. The results of the most sophisticated model, a six-state (4s, 3d, 4p, 5s, 4d, 5p) close-coupling calculation with semiempirical Hartree-Fock target wave functions and including one- and two-body core-polarization potentials are in better agreement with the experimental cross section and resonance-fluorescence polarization data than any other calculation. At incident electron energies below the 5s, 4d, and 5p thresholds, the six-state calculations are essentially in agreement with the experimental data, although rich resonance structures predicted by theory are not seen experimentally due to the finite energy resolution. At energies above the 5s, 4d, and 5p thresholds the six-state emission cross sections exceed the experimental cross sections by about 20%, once allowance is made for cascades from the 5s, 4d, and 5p levels.

Photon emission from collisions of 100–350-keV ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{He}}^{+}$ with ${\mathrm{CO}}_2$ were studied. All emissions were found to originate from the ${\mathrm{CO}}_2^{+}$ molecular ion. Emission cross sections were measured for the two major transitions found. The data indicate that a form of the Bethe-Born theory could possibly give an adequate description of the cross-section data. Comparison is made to other work with ions at lower bombarding energies, with total ionization cross sections using positive ions, and with electron-impact data.

Ar K x rays produced by 22- and 42-MeV ${\mathrm{C}}^{5+}$ and ${\mathrm{C}}^{6+}$ ions were measured in coincidence with the various emergent charge states resulting from the collision process. Single-electron K-shell capture and ionization cross sections are obtained through an analysis based on the independent-particle model (IPM). The comparison among various theoretical models and the present experiment shows that the present theoretical description of the electron capture is more precarious than that of ionization in the intermediate-velocity regime studied. The IPM analysis also allows one to obtain estimates of the probability of ${\mathrm{C}}^{5+}$ electron loss for small-impact-parameter collisions.

A wide variety of finite-basis-set expansion methods is applied to electron–hydrogen-atom scattering in the static-exchange approximation. All these methods are based on the Lippmann-Schwinger formalism. A careful analysis of the numerical results is presented with the aim of selecting efficient approaches to the solution of realistic electron-atom (and electron-molecule) scattering problems. The results show that the efficiency of the expansion methods may depend sensitively on the characteristics of the interaction terms. Some difficulties of the simple method of moments are pointed out. A particular least-squares method is proposed to avoid the spurious singularities encountered in applications of the Schwinger variational method to singlet scattering processes.

We discuss the interactions and energy dissipation of subexcitation electrons in homogeneous and isotropic condensed materials in the framework of a perturbative, generalized polaron theory. The polaron structure includes only Fourier components of the Coulomb interaction with momentum transfers ħq less than the polaron momentum p, thus limiting the treatment to long-range coupling. The coupling between the electron and rovibrational modes of the material is represented by off-diagonal form factors. The energy contributed to the polaron by virtual excitations is represented by the real part of a perturbation term, whose imaginary part represents energy dissipated (irreversibly) into other excitations. Quantitative knowledge of the relevant parameters remains undeveloped.

The transitions between the 2S and 2P states of a hydrogen atom in collisions with a proton are examined. Inclusion of electron spin, neglected in previous treatments, is shown to be crucial for the rigorous formulation of the problem. In a basis of the eight n=2 eigenfunctions, a first-order system of coupled differential equations is obtained by assuming classical straight-line trajectories. The solution of these equations yields the cross sections as functions of velocity. The cross sections are used to compute the transition rates in a plasma over a wide range of temperatures.

A rigorous derivation of the T matrix is presented to study the effects of direct and indirect reactive scattering processes of e+AB→A+$B^{\mathrm{-}}$, involving electron(e)–molecule(AB) systems. Analysis of dissociative attachment processes e+${\mathrm{H}}_2$→H+${\mathrm{H}}^{\mathrm{-}}$ and e+HCl→H+${\mathrm{Cl}}^{\mathrm{-}}$ is presented, with emphasis on the individual role of the direct and indirect processes in affecting the total cross sections. Marked differences among different electron-molecule collision systems are found from this analysis, and the cause of such differences is explained.