The soluble model of an oscillator coupled to a scalar field is used as an example of irreversible behavior. By studying the reduced density operator for the oscillator, a generalized Fokker-Planck-Kramers-Chandrasekhar equation for the Wigner distribution function is derived. The diagonal matrix elements of the reduced density operator satisfy a generalized non-Markovian master equation. By application of a time-averaged method, the ordinary Pauli master equation is derived. The time evolution of the occupation probabilities of the oscillator levels has been numerically computed, and compared with the solutions of the Pauli equation.

A recently developed method to study ion-motion effects on plasma line broadening in the dipole approximation is extended to the general interaction. Coupling-constant and binary-collision expansions are obtained for the "width and shift" operator. This operator is investigated for a model system to show the limits of the static-ion approximation.

It is pointed out that the inhomogeneity correction term to the Gaspar-Kohn-Sham exchange potential proposed recently by Herman, Van Dyke, and Ortenburger follows, to within a numerical factor, from a similar correction to the statistical energy derived previously by Hohenberg and Kohn. The numerical coefficient in the latter case, obtained from Hubbard's work on electronic polarizabilities, is about four times larger than the average variational value of Herman, Van Dyke, and Ortenburger.

Measure theory shows that irreversible thermodynamics is applicable only to experimental situations which can be adequately characterized by a finite number of parameters known to finite-figure accuracy. It is suggested that irreversible thermodynamics cannot be used near critical points or in turbulent media because this fundamental constraint is not satisfied.

The optical-scale time-averaged motion of an electron in an intense laser beam is governed by the intensity gradient of the light beam. This motion is solved for an electron traversing a focused laser beam under the assumption of a triangular beam profile. The associated bremsstrahlung spectrum is calculated and estimated to be experimentally observable.

The theory presented earlier demonstrates in a very simple fashion that regardless of the degree of saturation, the degree of degeneracy, or the displacement from line center, two circularly polarized pulses of opposite polarization will not produce a photon echo; and circular and linear polarization form very special canonical states of polarization.

The general Hellmann-Feynman theorem (derivative of energy with respect to a parameter = expectation value of derivative of Hamiltonian) is proved for theories in which the electron density is determined by making the energy functional stationary. Some simple applications are given.

The spontaneous decay of an atom located between two parallel plane mirrors of reflectivity $R$ is calculated using the Weisskopf-Wigner method, both when the two mirrors are very large and when they are small. When the mirrors are large and of high reflectivity, the atom radiates more rapidly than in free space and into the Fabry-Perot modes of the mirror system. When the mirrors are small, their effect on the total radiation rate is small, but radiation into the few modes defined is enhanced if the reflectivity is high. It is concluded that the effect of the presence of a laser etalon is insufficient to justify omitting the coupling of the atom to non-Fabry-Perot modes from the Hamiltonian of an atomic system in a laser etalon.

An independent-particle potential-scattering model is proposed for electron scattering by atoms, which is similar in approach to the recent study by Green et al. for bound states of atoms. The general model is discussed, including specific scattering considerations, and specialized to the case of helium. Results of calculations for $e-\mathrm{H}\mathrm{e}$ elastic scattering are given and compared with experimental results and with the calculations by LaBahn and Callaway. By allowing the polarization part of the potential to be slowly energy dependent, the agreement becomes quite satisfactory. The relevance of this study to future efforts to develop an optical model for elastic electron scattering by atoms and molecules is discussed.

We discuss the elastic scattering of electrons from helium atoms in terms of an energy-dependent central-potential model having the form $V\left(r\right)=2Zlimit\; of\left(\frac{-{\Lambda }^2}{{\Lambda }^2-{\mu }^2}\frac{e^{-\mu r}}{r}+\frac{{\mu }^2}{{\Lambda }^2-{\mu }^2}\frac{e^{-\Lambda r}}{r}\right)-\frac{\alpha }{{(r^2+d^2)}^2}\text{as}\Lambda \to \mu ,$ where $\mu ,\alpha$ are fixed constants (for He, $\mu =3.375\mathrm{}$ and $\alpha =1.39\mathrm{}$), and $d$ is an energy-dependent phenomenological parameter. The method of partial waves is adapted for a generalized Yukawa potential and a polarization potential. Phase shifts and scattering cross sections are calculated from our potential model using the first Born approximation and a modified form of it. We develop an effective-range theory for a generalized Yukawa and a polarization potential, and apply it to generate a set of energy-dependent electron-helium phase shifts in the region 0-500 eV. Recent experimental angular distribution data in the region 100-500 eV are rather satisfactorily accounted for by our potential model. Our results compare favorably with those of LaBahn and Callaway.

Effects of final-state correlation on the photoionization cross sections for the $3p$ shell in argon and the $4d$ shell in xenon are calculated by the reaction-matrix method, starting from the Herman-Skillman model Hamiltonian, for photoelectron energies $0<~\epsilon <~1.2$ a.u. and $0<~\epsilon <~2.52$ a.u., respectively. The results for argon complement Hartree-Fock and other final-state correlation calculations; the results for xenon are the first ab initio calculations of this kind. Although length and velocity forms of the transition matrix element agree in the initial local-field approximation, they are shown to diverge necessarily when only the final state is improved.

The two-state Stueckelberg-Landau-Zener theory of curve crossings can be utilized to explain qualitatively many of the observed asymmetric-inelastic total cross sections. It predicts not only a broad maximum in the inelastic total cross sections as a function of velocity, but also a rapid rise to this maximum followed by a slow decline past the maximum. If the difference in the potentials between the two states possesses an extremum, oscillations superimposed upon the general velocity dependence of the inelastic total cross sections may also be expected because of the existence of a stationary phase. At high velocities, the spacing of these oscillations will be proportional to $v^{-1\mathrm{}}$.

A modified Ramsauer technique has been used to measure the total low-energy scattering cross sections of electrons in ${\mathrm{O}}_2$ over an energy range from 2.35 to 21 eV, and in Ne over a range from 0.37 to 20 eV. A broad clearly defined "bump" is observed in the $e-{\mathrm{O}}_2$ cross section with the maximum occurring between 11 and 12 eV. Both the ${\mathrm{O}}_2$ and Ne cross-section data are in good agreement with Brüche's measurements at energies above 2 eV. Extrapolation of the low-energy Ne data to zero energy, using modified effective-range theory, yields a zero-energy scattering length of $(0.\mathrm{}30\pm 0.03)a_0$, where $a_0$ is the Bohr radius.