Using the polar-coordinate method of Peak and Inomata [J. Math. Phys. 10, 1422 (1969)], we obtain first the exact propagator of a charged particle in a constant magnetic field and also with the vector potential of a solenoid of zero size. We then derive the eigenvalues and eigenfunctions by expanding the propagator obtained. Finally, we evaluate the propagator beyond and at caustics by including the Morse index.

The energy and relative intensities of L-MM Auger lines show that for low-MeV ${\mathrm{Kr}}^{+}$-Kr collisions most of the ionization takes place during the collision, due to the prompt emission of as many as 12 electrons per atom. The later decay of L-shell vacancies contributes in only a minor way to the final ionization state. These results provide insights into a variety of collision phenomena, including shifts in Auger and x-ray energies, fluorescence yields, and equilibrium charge distributions in high-Z foils.

Two-electron one-photon x-ray transition energies are calculated, using the Slater transition-state concept within the approximate local density-functional theory given by the Xα model, for the krypton atom and isoelectronic Rb, Yt, and Zr, respectively. The new theoretical results suggest that the transition energy is a linear function of the atomic number within the isoelectronic series.

Applying the perturbative method, it is shown that the Cauchy-Schwarz inequality is violated in the process of second-harmonic generation. Moreover, anticorrelation between the fundamental and harmonic modes takes place.

Nonstationary stimulated Brillouin backscattering of a laser pump wave, exhibiting nonlinear pump depletion when propagating in a long material medium (optical or plasma fiber), generates strong acoustic field modulation combined with amplification and compression of the backscattered wave. The complete evolution equation for the sound wave (without the envelope approximation) is needed for describing the inertial response of the material. The strong sound pressure produced may explain the observed damage and even the mechanical fracture of an optical fiber supporting high laser flux intensities. This effect can be important too in laser electron accelerators using plasma fibers, and in laser-plasma interaction experiments on inertial fusion devices, where a long-scale-length plasma surrounds the target.

The distance dependence along the radial direction of the radiation emitted by a monoenergetic electron in a circular orbit is analyzed. It turns out that the angular spread of the radiation decreases with distance as we approach the orbit, while the radiation intensity increases. Near the orbit, this focusing effect of the radiation in the orbit plane is strongly dependent on distance, so it might be useful for studying the electron-beam structure in high-energy accelerators.

A novel method for the reconstruction of the electron momentum density (EMD) from directional Compton-profile data, based on the use of the radon transform, is presented. It supersedes all the previously suggested reconstruction techniques in simplicity and practicability. As an illustration, we reconstruct the EMD of vanadium, which is one of the most widely studied transition metals.

The creation of a bend periodic distortion by the action of magnetic fields (H) in a nematic lyotropic liquid crystal is discussed. The wavelength of this distortion ($P$), in the limit of small deformations, allows the measurement of $\frac{K_3}{{\chi }_a}$, where $K_3$ is the bend elastic constant and ${\chi }_a$ the anisotropy of magnetic susceptibility. In this limit, the dependence of $P^{-2\mathrm{}}$ with $H^2$ presents a linear behavior, predicted by the continuum elastic theory. The relation between $P$ and $H$ also allows us to determine an "effective field" in nematic samples doped with ferrofluid.

Small-angle neutron scattering experiments investigating the structure of porous Vycor glass are reported. The long-wave-length behavior ($0.004{\AA }^{-1\mathrm{}}\le q\le 0.025{\AA }^{-1\mathrm{}}$) of the measured structure factor $S\left(q\right)\mathrm{}$ is in good agreement with Cahn's prediction for spinodal decomposition. The high-$q$ data do not conclusively establish whether the internal surfaces are fractally rough over the length scales probed. Experiments on Vycor contrasted with protonated and deuterated cyclohexane reveal local composition gradients within the glass.

The large principal-quantum-number limit is investigated. Several concrete examples are worked out and the correspondence principle is reexamined under the light shed by these calculations. In particular, it is shown that a simple linear combination of three one-dimensional harmonic-oscillator eigenstates leads to results at variance with classical physics, in the high quantum-number limit. The possibility of actually observing these phenomena is also briefly discussed.

We have studied the critical properties of an irreversible cellular automaton using numerical renormalization-group and finite-size scaling methods. We have determined the values of the correlation-length exponent $\nu$ and an appropriately defined dynamic scaling exponent $z$. Our values are consistent with those of the kinetic Ising model. This provides numerical support for the result that continuous ferromagnetic transitions in irreversible systems belong in the same universality class as that of the Ising model.

We consider a model in one space dimension which simulates the helium atom, and show that the relativistic Hartree-Fock (HF) equation for the model can be solved analytically. When the HF solution is used as a variational wave function by varying some of the parameters in it, the expectation value of the Hamiltonian exhibits saddle-point behavior around the HF values of the parameters.

An analytic formula for the three-electron generating integral I(${\mathrm{\alpha }}_1$,${\mathrm{\alpha }}_2$,${\mathrm{\alpha }}_3$,${\mathrm{\alpha }}_{12}$,${\mathrm{\alpha }}_{23}$,${\mathrm{\alpha }}_{31}$) :=F${(}_{123122331}$${)}^{\mathrm{-}1}$ exp(-${\mathrm{\alpha }}_1$${\mathrm{r}}_1$-${\mathrm{\alpha }}_2$${\mathrm{r}}_2$-${\mathrm{\alpha }}_{33}$-${\mathrm{\alpha }}_{12}$${\mathrm{r}}_{12}$-${\mathrm{\alpha }}_{23}$${\mathrm{r}}_{23}$ -${\mathrm{\alpha }}_{31\mathrm{r}31}$)${\mathrm{d}}^3$${\mathrm{r}}_1$${\mathrm{d}}^3$${\mathrm{r}}_{23}^3$ is given which is valid for all values of ${\mathrm{\alpha }}_1$,${\mathrm{\alpha }}_2$,${\mathrm{\alpha }}_3$,${\mathrm{\alpha }}_{12}$${\mathrm{\alpha }}_{23}$,${\mathrm{\alpha }}_{31}$ for which this integral converges. A large class of integrals can be evaluated analytically by taking derivatives of I with respect to the α’s. More general integrals whose integrands contain products of spherical harmonics can also be evaluated analytically. In particular, all of the matrix element integrals which arise in a variational calculation on the lithium atom with Hylleraas-type basis functions can be evaluated in closed form. Certain difficult two-electron integrals can be obtained as a limiting case. Two-center two-electron molecular integrals can be obtained via an inverse Laplace transform; this observation is used to discuss the computation and convergence of series expansions for these molecular integrals.

By applying the large-N expansion to the more general case of a screened Coulomb potential, V(r)=-(a/r)[1+(1+br)$e^{\mathrm{-}2\mathrm{br}}$], the energy eigenvalues of the ground state and the first excited state and the corresponding wave functions are obtained analytically up to 14 terms.

We present formulas for reduced Wigner phase-space functions for atoms, with an emphasis on the first-order spinless Wigner function. This function can be written as the sum of separate contributions from single orbitals (the natural orbitals). This allows a detailed study of the function. Here we display and analyze the function for the closed-shell atoms helium, beryllium, neon, argon, and zinc in the Hartree-Fock approximation. The quantum-mechanical exact results are compared with those obtained with the approximate Thomas-Fermi description of electron densities in phase space.

Elastic and charge-transfer scattering of protons by Kr and Xe targets has been investigated in a crossed-beam experiment at collision energies $E_{\mathrm{c}.\mathrm{m}.\mathrm{}=30.6\mathrm{}}$ and 51.7 eV. The charge-transfer collisions led to the formation of ${\mathrm{Kr}}^{+}$(${\mathrm{}}^2$${\mathrm{P}}_{3/2}$,${\mathrm{}}^2$${\mathrm{P}}_{1/2}$)+H(n=1) and ${\mathrm{Xe}}^{+}$(${\mathrm{}}^2$${\mathrm{P}}_{3/2}$,${\mathrm{}}^2$${\mathrm{P}}_{1/2}$)+H(n=1,n=2) products respectively. Interference patterns in the state-selected relative differential cross sections were clearly resolved and have been ascribed to primary and secondary rainbows and/or Stueckelberg-type oscillations. The ${\mathrm{H}}^{+}$+Xe collisions have also been investigated theoretically by the exact close-coupling method. A good agreement between theory and experiment has been found. A novel method for determining the absolute H-atom detection efficiency is suggested.

Absolute cross sections for single ionization of ${\mathrm{Al}}^{+}$, ${\mathrm{Cd}}^{+}$, and ${\mathrm{Hg}}^{+}$ by electron impact have been measured for electron energies from threshold to 2 keV using the crossed-beams technique. The ${\mathrm{Al}}^{+}$ cross section shows a peak value of (74±6)×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ at about 46 eV. In addition, for ${\mathrm{Al}}^{+}$ there is significant structure around 80 eV, an energy corresponding to the 2$p^5$3$s^2$nl autoionizing states of ${\mathrm{Al}}^{+}$. The ${\mathrm{Cd}}^{+}$ and ${\mathrm{Hg}}^{+}$ cross sections show no major structures and have peak values of (147±6)×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ and (169±5)×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$, respectively, both at an electron energy of roughly 100 eV. Comparisons are made to semiempirical and theoretical predictions and to other existing experimental data.

Positronium formation from He, Be, C, O, and Ne by energetic positrons has been studied using an approximation which is complete through all second-order terms in collisional potentials. We have calculated differential and total positronium-formation cross sections for a wide range of energies. We obtain clear evidence of residual structure near the Thomas angle in the keV range of energies due to the destructive interference of second-order amplitudes. At a fixed energy this structure gradually disappears as the target charge increases and for a fixed target this structure becomes more prominent with the increase of energy. The total cross section for capture by positrons (${\sigma }_{\mathrm{Ps}}$) in the present method differs from the corresponding cross sections for capture by protons (${\sigma }_{\mathrm{H}}$) at least by an order of magnitude at the same velocity. Our cross sections are qualitatively different from the first-order Brinkman-Kramer results. For example, the ratio ${\sigma }_{\mathrm{Ps}/{\sigma }_{\mathrm{H}}}$ decreases with the increase of energy in the present method whereas in the Brinkman-Kramer approximation this ratio increases slightly. A number of possible experimental tests are discussed.

Cross sections are calculated for the electron-impact excitation of 1$s^2$2s-1s2s2l in Li-like ions (${\mathrm{C}}^{3+}$ and ${\mathrm{O}}^{5+}$). The results obtained by the distorted-wave method of Itikawa and Sakimoto [Phys. Rev. A 31, 1319 (1985)] are compared with those of a six-state close-coupling calculation for the electron energies E/ΔE=1–5 (ΔE being the energy of the respective threshold). When the same target wave functions are used, the distorted-wave method gives cross sections very close to those obtained by the close-coupling calculation.

Although dielectronic and radiative recombination are usually treated as distinct noninterfering processes, Alber, Cooper, and Rau [Phys. Rev. A 30, 2845 (1984)] have recently presented a scattering- or S-matrix analysis which provides a unified description of these processes. This description employs a diagonalization of the atom plus radiation field Hamiltonian using a limited basis set consisting of one discrete autoionizing state, a single-electron continuum, and a single-photon continuum. In the present work we extend Mo?ller scattering operator and resolvent operator techniques, which have previously been used to discuss the decay of prepared systems, in order to provide an S-matrix analysis of the electron-ion photorecombination process near an isolated autoionizing resonance. We explicitly allow for degenerate magnetic sublevels of the atomic system and for multiple angular momentum contributions in the partial-wave expansion of the electron-continuum eigenstate. After the introduction of the pole approximation, in which only the δ-function term is retained in the evaluation of the various self-energies that occur in the diagonalization of the Hamiltonian for the combined many-electron radiation-field system, we obtain the total electron-ion photorecombination cross section as the sum of the radiative and dielectronic recombination contributions together with the conventionally ignored interference term.

The radiative and dielectronic recombination cross sections reduce to the familiar forms when the continuum-continuum coupling effects are neglected. Alternatively, the combined cross section for the entire electron-ion photorecombination process may be represented by a modified Fano line profile, which is shifted and broadened as a result of the coupling between the autoionization and radiation continua. Recombination processes that involve more than a single state of the initial ion, of the autoionizing resonance, or of the final system can be treated by appropriately augmenting the unperturbed basis set. It is anticipated that the effects of the interference between radiative and dielectronic recombination and of the continuum-continuum coupling will be most important for individual transitions involving low-lying autoionizing levels and will probably be negligible for the total dielectronic recombination rates due to the highly excited levels.