A hybrid numerical scheme is applied to solve the Landau equation for the electron distribution function over all velocity space. At low velocities the distribution is approximated by using the Spitzer-Härm method [Phys. Rev. 89, 977 (1953)], while at high velocities it is described by the high-velocity form of the Landau equation. The two parts of the distribution function are then matched at a suitably chosen value of electron speed. The distribution function is determined for a thermal structure typical of an active region of the solar atmosphere or flaring solar coronal loop. The heat flux is then calculated from the distribution function and is compared with the classical Fourier law of Spitzer and Härm and with the models of Campbell [Phys. Rev. A 30, 365 (1984)] and Luciani et al. [Phys. Fluids 28, 835 (1985); Phys. Rev. Lett. 51, 1664 (1983)].

Theoretical calculations of the basic quantities that characterize the stopping of an interacting electron gas for slow ions are presented. An appropriate low-frequency expansion for the imaginary part of the density response function has been used to modify well-known results for the noninteracting electron gas. The inner dissipative nature of the elementary electron-hole excitation is characterized by a complex local-field correction function. The basic quantities are expressed in terms of the phase shifts determined from a nonlinear density-functional formalism.

The autocorrelation function, C(t)=〈$S_i$(0)$S_i$(t)〉-〈$S_i^2$ (0)〉, of Ising spins in an ordered phase (T<$T_c$) is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation for droplet fluctuations is studied in detail. The relaxation-rate spectra for the corresponding Fokker-Planck equation are found to be (1) continuous from zero for dimension d=2, (2) continuous with a finite gap for d=3, and (3) discrete for d≥4. These spectra are different from the gapless form assumed by Takano, Nakanishi, and Miyashita for the kinetic Ising model. The asymptotic form of C(t) is found to be exponential for d≥3 and stretched exponential with the exponent β=1/2 for d=2. Our results for C(t) are consistent with the scaling argument of Huse and Fisher, but not with Ogielski’s Monte Carlo simulations.

For high-spin multiplicity systems, inner-shell vacancies are usually implicitly present in the wave function. In the case of a resonance, ignoring the existence of this vacancy may lead to a breakdown in a variational or saddle-point calculation. In this work, model computations are carried out to search for a method to deal with vacancies in a resonance situation. A step-by-step procedure is suggested to control these vacancies in actual calculations.

We study the statistical properties of the spin S and magnetic dipole μ of a particle with two constituents bounded by a harmonic force. We find the relation between μ and S and also conclude that 〈${\mathrm{S}}^2$〉∼${ħ}^2$. The gyromagnetic factor can assume any value depending on the charges and masses of the constituents. In another example, we consider the case of a permanent magnetic dipole moving in an external magnetic field, under the influence of the fluctuations associated with the zero-point and thermal radiations characteristic of stochastic electrodynamics (SED). We conclude that the system contains paramagnetic features, and comparison with the experimental data shows excellent agreement with SED.

It is supposed that a single particle moves in ${\mathrm{openR}}^3$ in an attractive central power-law potential $V^{\left(q\right)}$(r)=sgn(q)$r^q$, q>-2, and obeys nonrelativistic quantum mechanics. This paper is concerned with the question: How do the discrete eigenvalues $E_{\mathrm{nl}}$(q) of the Hamiltonian H=-Δ+$V^{\left(q\right)}$ depend on the power parameter q? Pure power-law potentials have the elementary property that, for p<q, $V^{\left(q\right)}$(r) is a convex transformation of $V^{\left(p\right)}$(r). This simple fact makes it possible to use ‘‘kinetic potentials’’ to construct a global geometrical theory for the spectrum of H and also for more general operators of the form H’=-Δ+, $A^{\left(q\right)}$∈openR. This geometrical approach greatly simplifies the description of the spectra and also facilitates the construction of some general eigenvalue bounds and approximation formulas.

We present a new method for constructing explicit finite-difference schemes for solving equations of Schrödinger type. The procedure gives a forward Euler scheme that is conditionally stable.

From the work of Slater, which was formally completed by Kohn and Sham, a one-body potential V(r) can be constructed which will generate the ground-state density n(r) of a spherically symmetrical atomic charge cloud. For the case of the Be atom, the 1s and 2s wave functions are written in terms of the density amplitude [n(r${\left)\right]}^{1/2}$ and a common phase angle θ. It is then shown that V(r) can be characterized solely by this phase angle, and this motivates the setting up of a variational principle only in terms of the phase θ. As an illustration of the method, the Hartree-Fock ground-state density ${\rho }_{\mathrm{HF}(\mathrm{r}}$) is employed to numerically calculate ${\theta }_{\mathrm{HF}(\mathrm{r}}$), which is then used to calculate $V_{\mathrm{HF}(\mathrm{r}}$). This provides the practical completion of Slater’s proposal for treating exchange for Be. The effect of electron correlation on V(r) is finally estimated using a correlated wave function for Be due to Bunge.

For a damped harmonic oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) path integral, (ii) second quantization, and (iii) dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, overcomplete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator.

A relativistic 1/N expansion method has been developed for the Dirac equation. This formalism is applied to the screened Coulomb potential proposed by Mehta and Patil [Phys. Rev. A 17, 34 (1978)]. The 1/N expansion result is compared with numerical results and the envelope-method approximation.

In the system of coupled Schrödinger equations one can define a kinetic energy operator, corresponding to ‘‘interchannel wave propagation.’’ Exactly solvable models of motion along the axis of a discrete variable α, which numbers the channels (analogs of the rectangular well, Bargmann-type potentials, etc.), can be constructed. Thus the intuition developed in considering wave propagation in ordinary configuration space is easily transferred to the new dimension α. Particularly, there may exist resonances or bound states of a special nature corresponding to the α standing waves. The same idea of α motion allows one to consider the old problem of wave propagation in periodic potentials from a new viewpoint.

The Firsov model for calculating electronic stopping cross sections has been modified to take quasimolecule formation and charge polarization into account, since these effects are expected to become important at low collision energies. The cross sections predicted by the resulting molecular model ($S_{\mathrm{mol})}$ were compared to those obtained using spherically symmetric free-atom electronic distributions ($S_{\mathrm{free})}$. It is shown that $S_{\mathrm{mol}/S_{\mathrm{free}}}$ correlates with changes in electron density in the Firsov plane. Differences in the Firsov plane position and orbital contributions in the free-atom and molecular bases are also discussed.

A new phenomenon, light-induced viscous flow in a one-component gas, is observed in ${\mathrm{CH}}_3$F upon velocity-selective vibrational excitation. The effect originates from a state-dependent kinetic collision rate in combination with nonuniform illumination. The theory for this effect is derived using a Chapman-Enskog approach. Good agreement between theory and experiments in the near-hydrodynamic regime is found.

The electron-degradation spectrum is fundamental for describing a variety of quantities bearing on electron slowing-down processes in matter. We calculate the electron-degradation spectrum in Ar gas by solving the Spencer-Fano equation, using a realistic set of cross sections. The influence of Auger electrons on the degradation spectrum is studied in detail. As an application, we study the statistical fluctuations in the ionization yield, which are expressed in terms of the Fano factor F(T) for an electron incident at fixed energy T. The energy dependence of F(T) is greatly influenced by L-shell ionization. The Fano factor approaches an asymptotic value of 0.16 at T=2 keV. Our results are consistent with experimental results.

Configuration mixing of the rotational states of the [(dtμ)d2e${]}^{\mathrm{*}}$ complex formed in tμ+${\mathrm{D}}_2$ collisions arises because of the torque exerted on it by any neighboring molecule. The resulting three-body term in the resonant molecular formation rate is calculated in the quasistatic picture and turns out to be comparable to the two-body term. Numerical results are presented for several values of the (dtμ${)}_{11}$ binding energy. This effect may be large enough to explain the observed three-body effect in molecular formation without the collisional line-broadening contributions discussed previously.

The circular polarization of Lyman-α photons resulting from beam-tilted-foil excited H(2p) was measured at energies between 9 and 20 keV with foil tilt angles up to 60°. Various interaction models are used to fit the data, and their physical significance is discussed.

Using the polarization-propagator formalism, the dipole-oscillator-strength distribution for Be has been calculated. Comparison of correlated with Hartree-Fock results shows that inclusion of correlation is very important for calculation of properties of the dipole-oscillator-strength distribution. In particular, $I_0$ is calculated to be 43.6 eV, some 12% higher than previously reported.

The 1.4-MeV/u ${\mathrm{U}}^{32+}$+Ne collision system is studied in detail in order to elucidate the dynamics of multiple ionization in energetic, heavy-ion–atom collisions. Differential cross sections versus recoil-ion charge state, calculated by the n-body classical-trajectory Monte Carlo method, are presented for the θ and cphi angle dependences of the projectile, recoil ion, and ejected electrons. The calculations show a high degree of ejected-electron asymmetry towards the projectile side of the target nucleus which strongly effects the transverse-momentum balance between the heavy particles. Experimental and calculated cross sections differential in the recoil-ion charge state and transverse momentum are found to differ by orders of magnitude from those for the projectile, providing evidence for the importance of explicitly considering the ejected electrons’ momenta in the determination of the heavy-particle (both the projectile and the recoil-ion) angular differential cross sections. Polarization of the target electrons and screening of the recoil ion by the ejected electrons lead to ∼${10}^{\mathrm{-}6}$-rad negative-angle deflections of the projectile for recoil-ion charge states up to 4+. The angular scattering of the recoil ion departs significantly from that predicted for a two-body collision, and is found to be nearly isotropic for low recoil-ion charge states and peaked to angles θ>90° for high recoil-ion charge states. A stopping-power calculation for this system is in good agreement with the experimental value. Stopping powers differential in impact parameter and for energy deposition to δ electrons and multiple ionization are given to further describe the projectile energy loss.

Rate constants for electron exchange in collisions between thermal-energy, spin-polarized electrons and ${\mathrm{O}}_2$ and NO have been measured using a flowing-helium afterglow apparatus. The measured rate constants, ∼${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\sec }^{\mathrm{-}1}$, are substantially smaller than those for electron exchange in collisions with hydrogen or alkali-metal atoms.

Absolute electron-impact cross sections for single, double, and triple ionization of gallium and indium have been measured from 0 to 200 eV. Beams of Ga and In atoms are formed by charge-transfer neutralization of 3-keV-ion beams with triethylamine or xenon. The cross sections are considerably larger than previous measurements and are also larger than the predictions of various empirical formulas and classical and quantum-mechanical theories, due in part to significant contributions from autoionization. The double-ionization cross sections appear to be dominated by ionization of a d electron followed by autoionization, rather than by direct double ionization.