A missing paragraph from the original work [A. Redondo, Phys. Rev. A 39, 4366 (1989] that is being commented upon [preceding paper, Cioslowski and Levy, Phys. Rev. A 40, 6727 (1989)] is included. The relationship between this work and a theorem by Lieb [E. Lieb, Phys. Rev. Lett. 46, 457 (1981); 47, 69 (1981)] is also noted.

We have investigated the polarization effects in very-low-energy (below 1 eV) electron- ${\mathrm{CH}}_4$ collisions in an exact-exchange treatment. The two models of the parameter-free polarization potential are employed; one, the $V_{\mathrm{pol}{}^{\mathrm{JT}}}$ potential, introduced by Jain and Thompson [J. Phys. B 15, L631 (1982)], is based on an approximate polarized-orbital method, and two, the correlation-polarization potential $V_{\mathrm{pol}{}^{\mathrm{CP}}}$, first proposed by O’Connel and Lane [Phys. Rev. A 27, 1893 (1983)], is given as a simple analytic form in terms of the charge density of the target. In this rather very low-energy region, the polarization effects play a decisive role, particularly in creating structure in the differential cross section (DCS) and producing the Ramsauer-Townsend minimum in the total cross section. Our DCS at 0.2, 0.4, and 0.6 eV are compared with recent measurements. We found that a local parameter-free approximation for the polarization potential is quite successful if it is determined under the polarized-orbital-type technique rather than based on the correlation-polarization approach.

The singlet (${\sigma }_s$) and triplet (${\sigma }_t$) parts of the total ionization cross section were determined in the energy range from threshold to five times the threshold value with a crossed beam arrangement of polarized electrons and spin-polarized He($2^3$S) atoms. The measured spin asymmetry, $A_I$=(${\sigma }_s$-${\sigma }_t$)/(${\sigma }_s$+3${\sigma }_t$), is compared with results for the lithium atom. Both asymmetries are quite similar. Comparison with a distorted-wave Born approximation shows strong disagreement in the vicinity of the threshold.

The K-shell photoabsorption spectrum of the ${\mathrm{N}}_2$ molecule, recorded with unprecedented energy resolution and statistical accuracy, reveals several new Rydberg transitions and double-excitation states. The nearly identical term values, vibrational frequencies and internuclear separations of the 1s-excited states of ${\mathrm{N}}_2$ and of the 2π-excited states of NO, allow for a complete peak assignment for the ${\mathrm{N}}_2$ Rydberg series and strongly support both the core-hole localization picture and equivalent-core model. Subtle differences are related to the final-state charge distribution in the vicinity of the nuclei and to the bonding character of the valence orbitals.

We give a simple analytic solution that describes a novel method for population transfer in a three-level system driven by delayed pulses and which accounts for recent experimental results. This solution describes a procedure that is counterintuitive, and yet it is shown to be, in fact, one of the simplest solutions for multilevel systems arising from the adiabatic theorem. Its possible application to many-level systems is suggested.

It has been predicted that quantum fluctuations will lead to the formation of spontaneous solitons in stimulated Raman scattering. We present experimental data in support of this prediction. From an ensemble of 1000 shots we found solitonlike pulses in 101 shots. We have measured the distribution of soliton heights and delay times.

We numerically study the effect of a stabilizing quintic term and a destabilizing cubic term in the coupled Ginzburg-Landau equations that describe the onset of traveling-wave convection in binary fluid mixtures. We present bifurcation diagrams which show that for large enough group velocity and coupling between the counter-propagating traveling waves, the expected hysteresis at onset is not present. We also show how a measure of the convected heat transport and its period vary with scaled Rayleigh number. While this model can explain certain features of recent experiments, a number of difficult issues remain.

A short pulse of intense electromagnetic radiation may excite large-amplitude wake fields (E>1 GeV/m) in a magnetized electron-positron plasma and, consequently, electron or positron bunches may be accelerated to high energies. Such a mechanism exists in the pulsar magnetosphere, and its realization in the laboratory may accomplish the promising method for the generation of high-energy accelerators.

We report a theoretical and numerical study of diffusion in two dimensions in the presence of quenched random bias fields. The local bias field is taken to be the gradient of a random scalar potential V(i,j). We consider the special case V(i,j)=$V_1$(i)+$V_2$(j), where the gradients of $V_1$ and $V_2$ are chosen to be randomly ±${\epsilon }_0$ with 0<${\epsilon }_0$≤1. We find that asymptotically (t→∞) the mean square displacement grows with the time t as (lnt${)}^4$, just as in the one-dimensional Sinai model.

Calorimetric investigations have been carried out on five different liquid-crystal compounds near their smectic-A(Sm-A)–smectic-C (Sm-C) [or–smectic-$C^{\mathrm{*}}$ (Sm-$C^{\mathrm{*}}$)] transitions. Contrary to the previous observation, our experimental results demonstrate that the Sm-A–Sm-C (or–Sm-$C^{\mathrm{*}}$) transition may not become first order with reducing the Sm-A phase temperature range alone. We have also found that the magnitude of the transverse dipole moment of the constituent molecules, but not the bulk polarization only, has a strong effect on the nature of these phase transitions.

The dynamics of a growing interface with conservation of total volume under the interface is investigated using both dynamic renormalization-group and computer simulation. The conservation law leads to a new universality class from that discussed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889 (1986)]. The growth exponents are calculated and compared with those from the simulation of a conserved restricted solid-on-solid model. Excellent agreement between theory and simulation is found.

Shortest-path aggregation is an irreversible process in which particles are attached to the cluster on the closer perimeter sites to the release site. Randomness is introduced via the choice of sites from which the particles are sequentially released. This model generates random fractals which have dendritic structures. Simulations on a two-dimensional square lattice with line seed and particle seed have been studied. We find $D_2$=1.21±0.01 for the fractal dimension of the clusters. A naive Flory-type argument based on a branched-polymer topology is presented for fractal dimension $D_d$.

The perennial aspect of the Newtonian foundation of mathematical physics is that the concept of ‘‘motion,’’ that is, ‘‘kinematics,’’ is to serve as the interface between mathematics and physics. Kinematics subdivides into the theory of orbital translation and that of undulation and spinning. Newtonian mechanics is based on giving to translational kinematics a priority over the other modes, since planetary revolution can be represented as translation modified by gravitation. The so-called breakdown of classical physics stems from giving the translational priority a canonical status and extending it to the constituents of matter. We claim that in this case the priority is to be reversed. The main content of this paper is to establish the algebraic model for an indivisible, undulating entity that we call a ‘‘wave simplex.’’ It is used as the point of departure for a non-Newtonian quantum dynamics in which physical and algebraic concepts are in close correspondence. The postulates of the classical phenomenological theories and those of the canonical theories based on translational priority are established as theorems under the proper limiting conditions, and forces are constructed rather than postulated. While the formal structure of two-level quantum mechanics is established as well, exception is taken to treating spin as a property of a point particle. It is considered self-evident that a spinning object is orientable, a property accounted for in terms of a unitary triplet. This is the point of departure for an intrinsic particle dynamics. A main result is the integration of classical and quantum physics, thus closing the gap created by the heuristic method of canonical quantization.

Maxwell’s equations associated with (2+1)-dimensional electrodynamics plus a Chern-Simons term are solved for the electromagnetic potentials $A^{\mu }$(r) using matrix methods originally proposed by Moses [Phys. Rev. 113, 1670 (1959)] for 3+1 dimensions. Static as well as time-dependent solutions in the presence of sources are obtained. Additionally, for the former, closed-form expressions, which agree with the asymptotic (r→∞) limit for $A^{\mu }$(r) in the literature, are worked out easily. Using these results for static potentials, a qualitative discussion of the relativistic hydrogen atom in 2+1 dimensions is presented. It is shown that the Klein paradox, which preempts the possibility of bound-state solutions with the usual logarithmically increasing Coulomb potential in 2+1 dimensions, is easily evaded with the presence of the Chern-Simons term. Attempts to formulate a quantitative approach to the problem are briefly discussed.

We analyze the semiclassical limit of the stationary Schrödinger equation in the coherent-state representation simultaneously for the groups $W_1$, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.

We demonstrate that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. While the WKB expansion formulas are basically the usual ones, in this representation they describe approximations that are uniform and nonsingular in the classically allowed region of phase space because no turning points appear there. The quantization of energy levels relies on a complex contour integral that tests the eigenfunction for analyticity. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions. All in all, the Bargmann representation appears to combine the advantages of a linear description and of a phase-space representation of the quantum state vectors.

We calculate the unpolarized triply differential cross section of bremsstrahlung from atoms with atomic number Z=13 and 79 for incident electrons of kinetic energy $T_1$=50 and 140 keV. It is an exact numerical nonrelativistic calculation in a partial-wave formulation. Our results show that the screening effect is important in the high-Z cases, as the behavior of angular distributions of recoiled electrons. When the Coulomb parameter is large, the nonrelativistic Born approximation is not good, as expected. Comparisons of our partial-wave results with experimental results of Faulk and Quarles [Phys. Rev. A 9, 732 (1974)] show large discrepancies.

The screened Coulomb potential problem is studied in the momentum representation. The eigenvalue equation for the spherical ground state is given. Using the solution of the H-atom problem as a basis, a functional form for the ground state of the screened Coulomb potential problem is proposed. In coordinate space it is shown that this form gives the wave function as a modified Bessel function multiplied by a power of radial distance. An integral involving the product of two modified Bessel functions and an exponential function is given in terms of hypergeometric functions.

A parameter-free local-density method called the Ξ method was developed earlier for atoms [N. Vaidehi and M. S. Gopinathan, Phys. Rev. A 29, 1679 (1984)]. This method, which considered only the Fermi correlation in the potential, was shown to be close to Hartree-Fock accuracy. Its relativistic extension [V. Selvaraj and M. S. Gopinathan, Phys. Rev. A 29, 3007 (1984)] was also shown to give results that were close to Dirac-Hartree-Fock accuracy. In the present article, the relativistic Ξ method is modified by incorporating the spin-orbit interaction term in the Hamiltonian and the Coulomb correlation between the electrons of opposite spin. Using this fully correlated relativistic method, total energy, expectation values of $r^n$ (n=-1,1,2), and spin-orbit parameters for various atoms are calculated. Correlation energies for all the atoms in the Periodic Table are reported. Ionization energy and electron affinity of atoms are also discussed.