We report measurements of the ${\mathrm{MgH}}_2$(3s ${}_{}{}^1{}_{}{}^{}4s$ ${}_{}{}^1{}_{}{}^{}\Sigma$) collision-induced dipole-absorption profiles. Two distinct exit channels are possible: the nonreactive excitation of ${\mathrm{Mg}}^{\mathrm{*}}$(4s ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$) and the reactive formation of MgH. We have obtained evidence for the direct reactive formation of MgH as the laser is tuned into the blue wing of the collision-induced molecular-absorption band. We interpret these observations in terms of a weak barrier to reaction in the excited ${\mathrm{MgH}}_2$(4s ${}_{}{}^1{}_{}{}^{}\Sigma$) state, with the laser supplying the energy necessary to surmount this barrier.

Calculations of the exchange asymmetry in elastic scattering of electrons by sodium atoms are reported at incident electron energies of 10 and 54.4 eV. The close-coupling calculations are performed with the four lowest target states of the sodium atom. At 10 eV, the present calculations predict nearly pure singlet-state scattering and nearly pure triplet-state scattering at certain angles. At 54.4 eV, the theoretical results are compared with recent measurements. Qualitative agreement is obtained, although some discrepancy remains.

Zocchi, Shaw, Libchaber, and Kadanoff recently discovered that when two wires are symmetrically placed along the center of a Hele-Shaw cell, symmetric but narrow fingers of dimensionless width λ<(1/2 develop. λ decreases as the pushing velocity increases, but at a certain critical finger width the finger suddenly undergoes a transition to the asymmetrical state. We present a simple theory to predict this critical finger width as a function of D, the dimensionless distance between two wires, by assuming that the finger opens up a negative angle at the contact point.

The nonlinear scalar field equation governing the propagation of an unsteadily convected interface is used to derive a convenient expression for the average volume flux through such an interface in a homogeneous flow field. For a particular choice of the initial scalar field, the average volume flux through any such interface is expressed as a volume-averaged functional of the evolving scalar field, facilitating analysis based on renormalized perturbation theory and numerical simulation. It is noted that this process belongs to a different universality class from the propagation model of M. Kardar, G. Parisi, and Y.-C. Zhang [Phys. Rev. Lett. 56, 889 (1986)].

The structure of a monolayer of pentadecanoic acid at a water-air interface has been studied through its gas, liquid, and condensed phases by use of a very sensitive ellipsometry technique. The results clearly show the presence of two coexistence regions on the isotherm and a nonuniform film at full coverage.

We point out for the first time that the classical Lehmann effect, which arises when a temperature gradient is applied parallel to the helical axis of a cholesteric droplet, is not only due to a dynamic cross-coupling between director orientation and temperature, but has also a static contribution. In addition it is demonstrated that the analogous effect in an external homogeneous electric field is purely dynamic, in an external concentration gradient it is a mixture of a static and a dynamic contribution, whereas in a density gradient there are only static cross-couplings involved. The latter possibility has apparently never been discussed before.

The theory of neural networks is extended to include discrete neurons with more than two discrete states. The dynamics of such systems are studied. The maximum number of storage patterns is found to be proportional to Nq(q-1), where q is the number of Potts states and N is the size of the network. The properties of the Potts neural network are compared with the Ising case, and the similarity between the Potts neural network and a diluted multineuron interacting Hopfield model is discussed.

A method for solving three-body problems in mass-weighted hyperspherical coordinates in the adiabatic approximation is presented. The adiabatic channel function is expanded in terms of analytical functions expressed in different sets of Jacobi coordinates to describe each dissociation limit naturally. Evaluation of matrix elements between functions in different Jacobi coordinates is achieved through the known transformation properties of hyperspherical harmonics in these coordinates. The method is applied to study the lowest channels for various Coulombic three-body systems such as ${\mathrm{H}}^{\mathrm{-}}$, $e^{\mathrm{-}}$$e^{\mathrm{-}}$$e^{+}$, $p^{+}$$p^{+}$${\mu }^{\mathrm{-}}$, $d^{+}$$d^{+}$${\mu }^{\mathrm{-}}$, $e^{+}$$p^{+}$$e^{\mathrm{-}}$, $p^{+}$$d^{+}$${\mu }^{\mathrm{-}}$, and $d^{+}$$t^{+}$${\mu }^{\mathrm{-}}$ using only one or two analytical basis functions, and the results are compared with some known calculations. The behavior of the potential curves with respect to the variation of the masses of the three-body system is also examined.

Energies of n=2 states for ions of the lithium isoelectronic sequence are calculated from Z=3–92, starting from a Hartree-Fock potential and including second- and third-order correlation corrections, the lowest-order Breit interaction with retardation treated exactly, the second-order correlation corrections to the Breit interaction, and corrections for reduced mass and mass polarization. The resulting differences between theory and experiment for the 2p fine structure and the 2s-2p splittings are found to be in rough agreement with the one-electron Lamb shift, but clear deviations can be seen. A discussion is given of the calculations required to evaluate these deviations within the framework of quantum electrodynamics.

The energy spectrum from the spin-forbidden electronic autodetachment from the metastable ${\mathrm{He}}_2^{\mathrm{-}}$${[}^4$${\mathrm{\Pi }}_{\mathrm{g}}$] ion has been measured. The single-peaked continuum, resulting from a vertical transition to the repulsive wall of the ${\mathrm{He}}_2$[${\mathrm{X}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$] ground state, has a maximum at 15.70±0.15 eV. For a rotationally cool beam, the spectrum is inconsistent with the existing potentials of ${\mathrm{He}}_2^{\mathrm{-}}$ and ${\mathrm{He}}_2$[${\mathrm{X}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$]. A suitable fit, neglecting rotational effects, would require an increase of 0.06 Å in the calculated $R_e$ of ${\mathrm{He}}_2^{\mathrm{-}}$. However, a very good fit can also be obtained from the existing potentials by assuming a rotationally hot (15 000 K) distribution. Surprisingly, both fits require contributions from levels v>0, which are known to undergo vibrational autodetachment to ${\mathrm{He}}_2$[${\mathrm{a}}^3$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$]. For such contributions, the latter process must be exceptionally slow (${<10\mathrm{}}^6$/s).

Changes in the frequency of the 2$S_{1/2}$→2$P_{1/2}$ transition in hydrogen when the atom is placed between two parallel, perfectly conducting plates are investigated. It is shown that the transition frequency depends on the distance between the plates and that a change in the frequency of Δν=-0.894 MHz results for plates separated by 1 μm. This is sufficiently large to be measurable.

Recently, A. Comtet, A. D. Bandrauk, and D. K. Campbell [Phys. Lett. 150, 159 (1985)] introduced a modified semiclassical quantization rule motivated by the structure of supersymmetric quantum mechanics. In this paper, following their modified semiclassical framework, we provide a method to obtain wave functions in a uniform approximation. We demonstrate our method by constructing wave functions for the Morse, Rosen-Morse, and anharmonic oscillator potentials. Accurate fits to the wave functions are found for all three potentials.

The Rayleigh-Ritz minimization principle is generalized to ensembles of unequally weighted states. Given the M lowest eigenvalues $E_1$≤$E_2$≤...≤$E_M$ of a Hamiltonian H, and given M real numbers $w_1$≥$w_2$≥...≥$w_M$>0, an upper bound for the weighted sum $w_1$$E_1$ +$w_2$$E_2$+...+$w_M$$E_M$ is established. Particular cases are the ground-state Rayleigh-Ritz principle (M=1) and the variational principle for equiensembles ($w_1$=$w_2$=...=$w_M$). Applications of the generalized principle are discussed.

A density-functional theory for ensembles of unequally weighted states is formulated on the basis of the generalized Rayleigh-Ritz principle of the preceding paper. From this formalism, two alternative approaches to the computation of excitation energies are derived, one equivalent to the equiensemble method proposed by Theophilou [J. Phys. C 12, 5419 (1979)], the other grounded on an expression relating the excitation energies to the Kohn-Sham single-particle eigenvalues.

The two density-functional methods of calculating excitation energies proposed in the preceding paper, combined with the recently formulated quasi-local-density approximation for the equiensemble exchange-correlation energy functional [W. Kohn, Phys. Rev. A 34, 737 (1986)], are applied to the He atom. Although the splittings between nearly degenerate levels with different angular momenta are badly overestimated, in both approaches the averages over angular momentum and spin of the experimental excitation energies measured from the ionization threshold are reproduced within a few percent. The computed self-consistent ensemble-averaged densities and the Kohn-Sham potentials associated with them are discussed.

Analytic expressions are derived for the multicenter (one-particle) integrals over &‖r${\mathrm{\Vert }}^{\mathrm{-}\mathrm{k}}$-type operators ($m_i$,k∈${\mathrm{openN}}_0$, k>2) employing Cartesian Gaussian basis sets of any angular momentum number. A Laplace transform of $r^{\mathrm{-}k}$ is used for solving the different kinds of integrals. In order to remove the pole at the origin and ensure the existence of the integrals a Gaussian cutoff function of the form [1-exp (-α${\mathrm{r}}^2$${\left)\right]}^{\mathrm{q}}$ [q∈openN, q≥κ(k)-${\mathcal{J}}_{i=1\mathrm{}}^3$κ($m_i$)-1], κ(n)=n/2 if n is even and κ(n)=(n+1)/2 if n is odd, is used. The integral has applications in atomic, molecular, and nuclear structure or scattering calculations.

The problem of time delay in one-dimensional quantum-mechanical scattering by a potential barrier is studied in the framework of time-dependent scattering theory. It is shown how the concept of sojourn time can be used to define three separate time delays: the time delay for transmission through the barrier, the time delay for reflection, and the total time delay (i.e., averaged over transmission and reflection). In addition to the anticipated dependence on the S matrix and its energy derivative, the time delays depend on certain parameters which can be interpreted as describing positions of detectors in a gedanken-experiment measurement. The problem of defining separate time delays for transmission and reflection appears to be rooted in the foundations of quantum theory and its interpretation.

Ortho-positronium (o-Ps) annihilation rates have been measured in ${\mathrm{N}}_2$ at temperatures in the range 100–170 K. Deviations from the annihilation rates expected for free o-Ps are observed, and are analyzed by current models where applicable. A density-functional calculation using an optical potential indicates that the large deviations at higher densities are attributable to the formation of o-Ps–induced bubbles, and the o-Ps–${\mathrm{N}}_2$ scattering length is about 0.8 Å. Analysis by the density-fluctuation model suggests, on the other hand, that the relatively small deviations observed at lower densities are due to the existing density fluctuations. A semiclassical approach is also attempted to apply to problems of the density of states and the annihilation rates of ortho-positronium in gases.

It is proposed that by evaluating pth-order spin-adapted reduced Hamiltonians and applying a model of independent groups of p electrons we can approximate the pth-order reduced density matrix (p-RDM). Subsequently this pth-order matrix is contracted to the corresponding 2-RDM. As a test example we calculate the total energy of the beryllium-atom isoelectronic sequence using an independent-trio model. The results, as expected, have a higher accuracy than those obtained with the independent-pair model.

An algorithm for the calculation of the spin-adapted reduced-Hamiltonian (SRH) matrix in a geminal basis has been recently reported. In this way a general reformulation of the SRH theory was given. Here we present the corresponding reformulation in this space basis for the direct approximation of the first- and second-order reduced density matrices (1- and 2-RDM), within the independent-pair model. The equation satisfied by a 2-RDM obeying the hypervirial theorem is also reformulated in this representation. These theoretical developments are tested in the calculation of the carbon-atom lower states. The influence of the basis set is also studied.