Diverse semianalytical constructions of wave functions, approximate or exact, are combined through the introduction of novel concepts. These include representing wave functions by a mosaic of analytic functions of a phase variable φ, each of them adapted to the problem’s features over a restricted range of a coordinate x, and focusing the numerical effort on the metric relation between φ and x. This shift of attention from the wave function proper to metric relations is viewed as the essence of the Milne approach and of its WKB approximation. Illustrative examples are worked out and discussed.

Euclidean quantum mechanics is not limited to an analytical continuation in time from the Schrödinger equation to the heat equation. It is a new classical statistical theory founded on a new probabilistic interpretation of the heat equation and constitutes the closest classical analogy of quantum mechanics.

A new experimental test of H. A. Lorentz’s $[—Theory of Electrons (Columbia University Press, New York, 1909)] theory of relativity exploits a neglected concept of Lorentz, that the physical contraction of macroscopic matter moving with a velocity v, with respect to a postulated preferred inertial frame S (the ether), is caused by the relativistic shortening of the equilibrium lengths of the low-mass electronic bonds in a direction parallel to v. Following a change in the orientation of the bond with respect to v, this contraction generates what we call a transient Lorentzian stress. In all prior experiments in which a macroscopic structure is rotated with respect to a hypothesized v, this stress is so rapidly relieved that the macroscopic length adiabatically follows the length demanded by the bonds and no experimental consequences are observable, even with v as great as ${10}^{\mathrm{-}3}$c. In the new experiment, a structure of length L is rotated at an angular frequency ${\omega }_R$ about one end in a horizontal plane containing the postulated velocity v. At low rotation rates, when 2${\omega }_R$ (the frequency of the transient Lorentzian stress) is small compared to ${\omega }_V$ (the radial resonant vibration frequency of the rotating structure) both Einstein and Lorentz predict that its outer end should enscribe an exact circle, but, when 2${\omega }_R$ approaches ${\omega }_V$ (a requirement which causes very large stretching of the structure over its normal length) the Lorentz theory uniquely predicts that the transient stress does not have time to be fully relieved, and the outer end should enscribe an elliptical path which deviates from an exact circle by an amount ∼${\mathrm{Lv}}^2$/$c^2$, since the length of each atomic bond parallel to v changes by the factor (1-$v^2$/$c^2$${)}^{1/2}$. A null result was observed for the case where the postulated velocity v is that of the frame in which the cosmic background radiation is isotropic.

Carbon K-shell x-ray and Auger-electron-production cross sections are reported for 0.6–2.0-MeV protons incident on ${\mathrm{CH}}_4$ (methane), ${\mathrm{C}}_2$${\mathrm{H}}_2$ (acetylene), n-${\mathrm{C}}_4$${\mathrm{H}}_{10}$ (normal butane), i-${\mathrm{C}}_4$${\mathrm{H}}_{10}$ (isobutane), ${\mathrm{C}}_6$${\mathrm{H}}_6$ (benzene), CO, and ${\mathrm{CO}}_2$. A variable-geometry end-window proportional counter with an alternate procedure for the determination of its transmission was used in collection of the x-ray data. A constant-energy-mode π/4 parallel-plate electrostatic analyzer served in the detection of Auger electrons. K-shell Auger-electron-production cross sections are compared with the predictions of the first Born theory and the perturbed-stationary-state theory which accounts for energy-loss, Coulomb deflection, and relativistic effects (ECPSSR). These data show fair agreement with the ECPSSR theory when the chemical shifts, of the carbon K-shell binding energy in molecules, are included in the calculations. This agreement is even better after effects of intramolecular scattering are considered. Validity of the geometrical model by Matthews and Hopkins [Phys. Rev. Lett. 40, 1326 (1978)] is established after a scrutiny of the inelastic cross sections for scattering of Auger-electrons within the molecule and their effective dislocation out of the detector’s window. The x-ray cross sections show particularly strong variations with the target molecular species because of additional changes due to modifications in the fluorescence yields for molecular carbon. The correlation of these changes with the molecular character of carbon and a scaling procedure for the fluorescence yields in molecules will be discussed elsewhere.

The first numerical tests, for a real system, of the quasiclassical description of redistribution of polarized radiation through atomic collisions are presented. Polarization results are reported for red-wing redistribution of Sr${(}^1$${\mathrm{S}}_0$→${\mathrm{}}^1$${\mathrm{P}}_1$) in the presence of Ar colliders. They compare favorably to recent quantal, nonadiabatic computations. It is shown that the effects of bent trajectories are important. Modified quasiclassical formulas to account for some of these are presented and tested. The results indicate that quasiclassical analysis can be used to probe the transformation from molecular to atomic states as atoms separate in a half-collision.

Dielectronic recombination rates via 2s-2p excitation have been measured for the Li-like ions ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, ${\mathrm{N}}^{4+}$, and ${\mathrm{O}}^{5+}$. We observe the amount of electron capture attending the passage of MeV/amu ion beams through a collinear, magnetically confined space-charge-limited electron beam as a function of relative energy. The measured rates show the predicted increase with Z but are higher than the rates calculated from the theoretically predicted cross sections. This is in contrast to the good agreement, between our measured rates and predictions from the same theory, found for Na-like ions.

A careful numerical solution of the equations of the two-state theory of resonant collisions is presented. The particular process investigated is that of collisions of two sodium atoms in Rydberg states in the presence of a weak static electric field for which measurements have been carried out recently. Dipole-dipole interaction between the atoms is assumed as the interaction responsible for the transition. Comparison between calculations and experiments yields only moderately good agreement, this being ascribed mainly to simplifications adopted within the theoretical model.

The anisotropy of the interaction potential of the ${\mathrm{H}}_2$-He collisional complex is treated as a small perturbation in a computation of the zeroth and first spectral moment of the collision-induced rototranslational spectra in the far-infrared region. The moments of the rototranslational spectra are separated into sums of moments of rotational lines, characterized by rotational transitions j→j’ with j≠j’, and translational components (j=j’, for j=0,1,. . .). The quantum expressions thus obtained consist of a leading term computable from the isotropic component of the interaction potential and dipole operator, plus an anisotropic ‘‘correction term’’ accounting for the lowest-order ($P_2$) anisotropy. These are evaluated for temperatures between 77 and 195 K. The results provide a much needed basis for assessing the validity of line-shape computations based on the isotropic potential, distorted-wave, or infinite-order sudden approximations often employed to avoid the enormous cost and complexity of close-coupling computations. The spectroscopic effects of the anisotropy of the ${\mathrm{H}}_2$-He system are briefly discussed.

We consider collisions between (quasi-) one- or two-electron atoms, each of which has been prepared in a fixed distribution of hyperfine magnetic substates. The resulting ‘‘polarization-dependent’’ reaction rates are functions of (1) the (experimentally adjustable) orientation of the quantization axis associated with the hyperfine substates, (2) the hyperfine terms of the colliding atoms, and (3) the detailed reaction dynamics as characterized by preparation- and fine-structure-independent cross sections. These effects are deconvoluted and analyzed, and their use in elucidating reaction mechanisms is discussed. Particular emphasis is placed on the associative ionization of two Na(3p) atoms, each prepared by adsorption of resonant laser photons. The quasimolecular states of Na...Na that might react in this case are limited by selection rules. More information on the reaction mechanism is then obtained by using experimental data, in combination with the formal analysis, to draw further conclusions about the active quasimolecular states.

We have observed and measured the calcium–rare-gas (4s ${}^1$${\Sigma }^{+}$–5s ${\mathrm{}}^1$${\Sigma }^{+}$) molecular-band profiles. These collision-induced dipole absorption bands peak very near the resonance position of the strictly forbidden calcium 4$s^2$ ${}^1$$S_0$–4s5s ${}^1$$S_0$ transition. The band profiles for CaAr, CaKr, and CaXe show evidence of steplike or oscillatory structure which is not easily explained. These observations are contrasted with other studies of collision-induced absorption in alkali– and alkaline-earth–rare-gas molecular systems.

The derivative of the quantity S(k), where S(k) is the sum of dipole oscillator strengths weighted by the kth power of the excitation energy, provides a convenient technique for calculating stopping and straggling mean excitation energies. This implies knowledge of the S(k) for all k within a certain range that is usually obtained by interpolating the S(k) values available for integer k. A method that relates the components of S(k) for equivalent electrons of a target atom, $S_j$(k), to that of a hydrogenic ion with nuclear charge number $Z_j$(k) is constructed. This approach requires certain matrix elements and expectation values involving all occupied target orbitals plus any unoccupied target orbitals that have the same principal quantum number as an occupied orbital and a nonzero dipole matrix element with this occupied orbital. It is shown here that the resulting curve of $Z_j$(k) versus k can be interpolated with greater accuracy than can S(k) or $S_j$(k). The relationship between $S_j$(k) and $Z_j$(k) constructed here implies an S(k) curve for all k and, consequently, the stopping and straggling mean excitation energies. The average errors for interpolating $Z_j$(k) as compared to $S_j$(k) are improved by factors of 2–4 for a large range of targets. However, there are individual targets for which this error trend is reversed.

The Fock-Tani transformation in the Jacobi three→two-body reduced-mass system is carried out and the first-order T matrix is found to be identical to that for the full three-body transformation. The Fock-Tani transformation in the reduced-mass system in which particle b is fixed at the origin is found to give a first-order T matrix with an error of $m_c$/$m_b$ in the initial momentum wave function. First-order differential and total cross sections are calculated for ${\mathit{a}}^{+}$+(${\mathrm{b}}^{+}$${\mathrm{c}}^{\mathrm{-}}$)→(${\mathrm{a}}^{+}$${\mathrm{c}}^{\mathrm{-}}$)+${\mathrm{b}}^{+}$ where {abc}={ppe, epe, μpμ, μdμ, and μtμ}. .AE

Absolute cross sections for the emission of Lyman-α radiation have been measured for low-energy H impact on rare-gas-atom targets. Data were obtained for H energies from 2.5 keV down to about 0.05 keV, and include measurements of the Lyman-α polarization. Using previously measured cross sections for Balmer-α and Balmer-β emission for the same collisions, it was possible to approximately evaluate the cascade contributions to the measured Lyman-α signals, and to extract the cross sections for direct 2p-state excitation during the collisions. The results are compared with the work of other investigators where possible.

The spin-exchange rates and spin-relaxation rates for thermal electrons colliding with noble-gas atoms are calculated using the orthogonalized-plane-wave approximation and via partial-wave analysis. The two techniques give similar results and are in order-of-magnitude agreement with the experimental rate in Ar.

It is shown that the conventional two-state theory of laser-induced collisional energy transfer (LICET) cannot be expected to provide an adequate description of the quasistatic wing behavior observed in a number of high-resolution LICET experiments. The theory breaks down whenever the detuning parameter Δ of the LICET reaction is comparable to some frequency mismatch δω between either the initial or final state and a (virtual) intermediate state in the reaction. A simple extension of the conventional two-state theory is presented which leads to good agreement with experiment. For a van der Waals collisional interaction, the quasistatic wing is shown to fall off as ‖Δ${\Vert }^{\mathrm{-}1/2}$(δω+‖Δ‖${)}^{\mathrm{-}3/2}$ instead of ‖Δ${\Vert }^{\mathrm{-}1/2}$ predicted by the two-state theory.

We describe further a method we recently introduced for calculating cross sections for multiphoton ionization of alkali-metal atoms in the regime where the laser field can be treated as a perturbation. We present numerical results, some of which we compare with experimental data.

The Dicke-narrowed line shape of an atom in a wall-coated, bufferless atomic storage cell is composed of two parts, a sharp central spike and a broad underlying pedestal. To understand the pedestal shape we find that it is necessary to account for various atom-surface scattering channels. Conversely, analysis of the pedestal shape yields information concerning these scattering channels. In particular, nearly-Doppler-broadened pedestals, observed for alkali-metal hyperfine transitions in cells with paraffin coatings, indicate that both a trapping-desorption channel and a direct inelastic or quasielastic channel are accessible in the atom-surface scattering process. Alternatively, the appearance of much narrower pedestals, observed in cells with dichlordimethysilane coatings, indicates that the trapping-desorption channel dominates the atom-surface scattering process.

The standard theory for laser- (or light-) induced collisional processes is applied to excitation transfer and charge transfer. Detailed calculations are carried out for specific processes which have been studied experimentally, with good understanding resulting for most of the observed features. We study the variation in cross-section magnitude and line shape with transfer laser intensity, and find characteristic differences between the excitation-transfer and charge-transfer processes.

The Rydberg-Klein-Rees potentials for the ground states of alkali-metal diatomic molecules, recently obtained on the basis of new measurements employing modern techniques, have been analyzed with the use of the reduced-potential curve (RPC) method. It is shown that the behavior of this group of chemically related molecules is fully in accord with the overall regularities observed for many other groups of diatomic molecules. The RPC scheme seems to lead to a picture that might be loosely called ‘‘a periodic system of diatomic molecules.’’ The method also permits a rather accurate estimation of dissociation energies and detection of errors in the analysis of the spectra or in the calculation of the potentials in general, which is applied to a critical evaluation of some papers on alkali-metal diatomic molecules.

The nonresonant, three-photon ionization spectrum of atomic Xe in the region between the ${\mathrm{Xe}}^{+}$ ${}_{}{}^2{}_{}{}^{}\mathrm{}_{3/2}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{}_{1/2}^{}{}_{}{}^{}$ fine-structure limits is reported. Using linearly polarized light, four autoionizing Rydberg series are observed converging to the ${\mathrm{Xe}}^{+}$ ${}_{}{}^2{}_{}{}^{}\mathrm{}_{1/2}^{}{}_{}{}^{}$ limit, corresponding to ${(}^2$P°${\mathrm{}}_{1/2}$)ns’[(1/2)]°${\mathrm{}}_1$, (2P°${\mathrm{}}_{1/2}$)nd’[(3/2)]°${\mathrm{}}_1$, ${(}^2$P°${\mathrm{}}_{1/2}$)nd’[(5/2)]°${\mathrm{}}_3$, and ${(}^2$P°${\mathrm{}}_{1/2}$)ng’[(7/2)]°${\mathrm{}}_3$; as expected, using circularly polarized light only the J=3 series are observed. These results are in contrast to earlier experimental work in which no resonant structure was observed. Photoelectron angular distributions are reported for the ${(}^2$P°${\mathrm{}}_{1/2}$)9s’[(1/2)]°${\mathrm{}}_1$ and the ${(}^2$P°${\mathrm{}}_{1/2}$)7d’[(3/2)]°${\mathrm{}}_3$ autoionizing resonances. The results are compared with the recent theoretical calculations by P. Gangopadhyay et al. [Phys. Rev. A 34, 2998 (1986)].