The entropy maximization and the divergence minimization, two related optimization techniques coming from standard statistical mechanics and often applied nowadays to probabilistic modeling, are used here together in order to organize the space of wave functions as a probability space when the only available information on the quantum system at the initial moment is the density matrix, which describes the mean behavior of a quantum ensemble. The Schroumldinger equation determines a nonconservative flow in this probability space transforming the independent Gaussian product measure, at the initial moment, into a dependent Gaussian product measure at an ulterior moment. Such a transformation can be viewed as a generalization of the Liouville theorem from classical statistical mechanics.

We present an approximate method for obtaining spin-orbit coupling constants of 3d atoms and ions from an effective one-body Hamiltonian. The method, suggested by numerical results of the analytical theory of Blume and Watson [Proc. R. Soc. London, Sect. A 270, 127 (1962); 271, 565 (1963)], incorporates the model potential approach of Bonifacic and Huzinaga [J. Chem. Phys. 60, 167 (1974)] for representing the core-valence interactions. In combination with reduced valence basis set, the new procedure gives accurate spin-orbit constants for the 3d atoms, and slightly less accurate values for di- and tripositive 3d ions. These results suggest that this method can be an accurate economic route to crystal calculations of the spin-orbit constants within any cluster-model approach involving the Hamiltonian of Misetich and Buch [J. Chem. Phys. 41, 2524 (1964)].

The laser-rf double-resonance technique has been used to make high-precision measurements of the hyperfine structure of the 4$f^7$${(\mathrm{}}^8$$S^0$)5d ${\mathrm{}}^9$$D_2$,3,4,$5^0$ metastable levels in ${}_{}{}^{151}{}_{}{}^{}$,153${\mathrm{Eu}}^{+}$. A new apparatus which uses a collinear laser and a slow ion beam (∼1.35 keV) enables us to achieve a long transit time in the rf region. Consequently, narrow linewidths of ∼60 kHz have been observed for the first time in such systems. The magnetic dipole and electric quadrupole hyperfine constants (A and B, respectively) of these metastable levels have been determined with a higher precision (2–3 orders of magnitude) than before. A J-dependent magnetic hyperfine anomaly has been observed in the ${}_{}{}^9{}_{}{}^{}\mathrm{D}_{\mathrm{J}}^0{}_{}{}^{}$ states. In addition, more accurate values of nuclear quadrupole moments of the two isotopes ${}_{}{}^{151}{}_{}{}^{}$,153${\mathrm{Eu}}^{+}$ have been determined.

Potential-energy curves of six ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$, two ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$, and one ${}_{}{}^1{}_{}{}^{}\mathrm{\Delta }$ states have been determined for the ${\mathrm{N}}^{5+}$+He→${\mathrm{N}}^{4+}$+${\mathrm{He}}^{+}$ process by means of ab initio calculations with configuration interaction. The matrix elements of the operator d/dR between the four ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ states and the two ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$ states involved in the collisional process have been calculated by the rigorous finite-difference technique. A very peaked radial coupling matrix element is observed at 8.30 a.u. corresponding to an avoided crossing between the entry channel and the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ state dissociating to {${\mathrm{N}}^{4+}$(3d)+${\mathrm{He}}^{+}$}. Two other avoided crossings between ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ states are observable at 7.50 and 6.35 a.u. Rotational and radial couplings involving ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$ states have also been determined.

A pseudopotential approach is used to calculate phase shifts, differential, total, and momentum-transfer cross sections for the elastic scattering of electrons by argon atoms in the low-energy region 0–3 eV. The results are found to be in satisfactory agreement with the existing experimental and theoretical data.

The effects of angular scattering on the production of ${\mathrm{D}}^{\mathrm{-}}$ beams by two-step electron capture of ${\mathrm{D}}^{+}$ in Cs are investigated both theoretically and experimentally. A model is developed that describes the evolution of all three charge states in the system as a function of the target thickness using only thin-target, single-collision cross sections. Many of the nine absolute differential cross sections required as input for the model are measured at energies between 250 eV and 2 keV. Additional cross sections are estimated using scaling laws. The model yields a beam-quality parameter: the current density of negative ions whose scattering angles lie within cones containing an arbitrary fraction of the total yield. For cone angles containing 50% and 90% of the negative ions, the maximum density occurs at about 2.0 and 1.7 keV, and at target thicknesses near 4.5×${10}^{14}$ and 3.5×${10}^{14}$ ${\mathrm{cm}}^{\mathrm{-}2}$, respectively. These values differ substantially from the conditions that produce the maximum total negative-ion yield.

Cross sections for formation of protonium (pp¯) in low-energy collisions of antiprotons with hydrogen atoms (H) and negative hydrogen ions (${\mathrm{H}}^{\mathrm{-}}$) are calculated using the classical-trajectory Monte Carlo (CTMC) method. Full four-body dynamics is performed for p¯+${\mathrm{H}}^{\mathrm{-}}$. Previously unpredicted differences between p¯+H and p¯+${\mathrm{H}}^{\mathrm{-}}$ collisions, stemming from the dynamics of the weakly bound electron in ${\mathrm{H}}^{\mathrm{-}}$, are exhibited. A maximum protonium formation cross section of nearly 2 A${̊}^2$ for p¯+${\mathrm{H}}^{\mathrm{-}}$ is found, smaller than previous theoretical estimates, but the reaction window is found to extend to higher energies. The electron stripping cross section for p¯+${\mathrm{H}}^{\mathrm{-}}$ collisions is also calculated and yields results in agreement with our previous three-body CTMC calculation and with a very recent experimental determination. The implications of these results for experiments with corotating beams of p¯ and ${\mathrm{H}}^{\mathrm{-}}$ are discussed.

Electron-impact ionization rate coefficients in nitrogen at values of E/N, the ratio of the electric field to the neutral density, up to 12 000 Td (1 Td${=10\mathrm{}}^{\mathrm{-}17}$ V ${\mathrm{cm}}^2$), are reported. In addition, we report experimental measurements of the ionization induction time, the time during the early portion of an applied electric field when the electron energy distribution function is transient and the plasma is characterized by nonexponential growth of the electron density. For nitrogen, we show that the induction period is approximately equal to the inverse of the ionization frequency for a large E/N range. Time-dependent Boltzmann calculations of the electron energy distribution function yield instantaneous ionization rates that are in good agreement with both the measured ionization rates and the induction period. The measurements were made in an electrodeless cell contained in an S-band waveguide immersed in a dc magnetic field and subjected to a pulsed rf electric field at cyclotron resonance. We show that our measurements are equivalent to experiments in dc electric fields; the equivalent dc electric field strength being uniquely related to the rf electric field strength. The use of an rf field for these high-E/N measurements circumvents complications that would be introduced by electrode effects. This is the first direct measurement of ionization rates at these extreme values of E/N.

We present ab initio calculations for the differential and integrated (over impact parameters) density matrices of the excited hydrogen atoms (n=2 and 3 manifolds) formed in 25–100-keV proton-helium charge-transfer collisions. The transition amplitudes for excited states are determined in a modified two-center atomic-orbital-expansion approach within the close-coupling treatment. The target helium atom is described in a one-electron picture. The calculated partial (nlm) and total charge-transfer cross sections are in good agreement with earlier theoretical and experimental data in this energy range. From the scattering amplitudes, the integrated density matrix and its various first-order moments for the n=3 manifold are compared with recent measurements. From the three-dimensional charge-density plots, it is illustrated that the captured electron lags behind the projectile in the present energy range. From the impact-parameter-dependent density-matrix analysis, an approximate ‘‘classical’’ picture of the captured electron is presented.

Measurements of charge exchange between ${\mathrm{N}}^{+}$ and ${\mathrm{N}}_2$ are reported for low product-ion energies and nearly zero center-of-mass scattering angles. The principal scattering is attributed to ${\mathrm{N}}^{+}$${(\mathrm{}}^1$S) with major contributions from the ${}_{}{}^5{}_{}{}^{}\mathrm{S}$ state. Fine structure corresponding to the transfer of excitation energy between the incident ion and the vibrational states of the target species has been measured. The results are interpreted in terms of a model involving the compensation of deflections produced by attractive and repulsive potentials at distances larger than the potential minimum of the ${\mathrm{N}}^{+}$-${\mathrm{N}}_2$ system. No ‘‘selection rule’’ for vibrational energy transfer such as has been observed for ${\mathrm{N}}_2$${\mathrm{}}^{+}$ on ${\mathrm{N}}_2$ is found.

We establish a connection between the Kohn variational principle, with (complex) outgoing-wave boundary conditions, and the Kapur-Peierls form of the R-matrix theory. We show that the complex Kohn method, unlike the usual Kohn method, does not suffer from the problem of spurious singularities. We also discuss a generalization that allows the calculation of scattering cross sections over a continuous range of energies from a single diagonalization of the Hamiltonian. Several numerical examples are presented.

The cross section for excitation of Na atoms from the 3s ground level to the 3p level by incident protons of energies 0.5–1000 keV, as well as by ${\mathrm{H}}_2$${\mathrm{}}^{+}$, ${\mathrm{H}}_3$${\mathrm{}}^{+}$, ${\mathrm{H}}^{\mathrm{-}}$, and ${\mathrm{H}}^0$ of equal impact velocity have been calculated. The alignment of the 3p level and the linear polarization of the light subsequently emitted were also determined. In addition, the proton-impact excitation cross sections for the 15 lowest excited levels were calculated and the obtained data were utilized to determine the cascade contributions to the population of the 3p level. The results of the calculations, carried out in the first Born and Vainshtein-Presnyakov-Sobel’man approximations, are compared with other theoretical calculations using atomic and molecular state approaches, as well as with experimental results, and good agreement is found for charged projectile impact.

Recent experiments have shown that optical pumping can produce line shapes with subnatural structure, and that this structure could prove to be useful for extracting oscillator strengths. A key question, however, regarding the optical-pumping technique’s potential usefulness is how well it allows the determination of resonance line center. In the present paper we address this question theoretically by considering laser optical pumping and probing of an atomic beam. From the analysis (i) we find that depending on laser polarization the optical-pumping subnatural feature is either a dip or a signal enhancement, (ii) we derive the rigorously correct formula relating the dip width to the transition oscillator strength for an alkali-like atom exhibiting a homogeneous line shape, and (iii) we show that, compared to shot-noise-limited laser-induced fluorescence, the optical-pumping technique of signal enhancement is capable of a 15% improvement in the ability to find resonance line center.

Based on the unified theory of random medium and random boundaries introduced in a previous paper [Furutsu, J. Opt. Soc. Am. A2, 913 (1985)], an exact version of the (normal) mode theory of both the coherent wave and the mutual coherence function is given without assuming a particular model. A mode equation for the second-order Green function is obtained from the governing (Bethe-Salpeter) equation based on a Maclaurin expansion at the set of poles of the first-order (renormalized) Green function, and is eventually given in the form of an equation of radiative transfer. The expansion would not be possible with the ‘‘bare’’ Green function. The overall unitarity of the Bethe-Salpeter equation is investigated in particular detail, and the involved optical relations are shown, not only of the entire system but also of the medium and each of the boundaries (of intrinsically dispersive property) separately. An exact theory of a fixed scatterer embedded in the waveguide is given with several expressions of the solution, including that with the conventional form in scattering theory of a coherent wave, in terms of an effective cross section having negative values in the shadow direction and its neighborhood. A detailed structure of the power equations, constructed by both coherent and incoherent waves in a complex way, is shown in terms of two optical relations for the scatterer’s two basic quantities that change the original Bethe-Salpeter equation. Whenever possible, the equations are so written in a general form that they hold true for a wide class of random systems with a fixed scatterer. Specific examples are given.

Hartree-Fock-Slater calculations of the photoionization cross section of the 6 ${\mathrm{}}^2$$D_{3/2}$ excited state of cesium predicted a sharp minimum near threshold. The properties of such an unusually narrow and deep minimum are examined. The narrowness arises from the large spatial extension of the bound excited-state function and the strong threshold region energy dependence of the inner lobes of a high-angular-momentum continuum state. The depth is caused by the near coincidence in position of the zeros of the two dominant dipole matrix elements. This coincidence can be fine tuned as a function of atomic number. Consequences of changes in the atomic model or the atomic number for the properties of the minimum are also examined.

The total absorption cross section of He and the ${\mathrm{He}}^{+}$(1s) partial cross section have been measured using photoelectron spectroscopy and synchrotron radiation in the photon-energy region of the 1$s^2$→3s3p resonance. The effects of autoionization are relatively small, causing deviations of 5–10 % from the nonresonant cross sections. These new measurements, along with a previous study of the 3s3p resonance behavior of the ${\mathrm{He}}^{+}$(n=2) satellite cross section, branching ratio, and angular-distribution parameter, allow the complete determination of all the parameters governing the 1$s^2$→3s3p resonance. From these experimentally determined parameters we have derived all of the relevant oscillator strengths and individual dipole and Coulomb matrix elements which describe He photoionization in the vicinity of the 3s3p doubly excited state.

The Kα x-ray spectra of molybdenum bombarded with 6.7-MeV/u ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and 5.5-MeV/u ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions were recorded with an on-line curved-crystal spectrometer in the DuMond geometry. The instrumental resolution was approximately 10.5 eV. K${\alpha }_1$$L^{n=0\mathrm{}}$,1,2,3 and K${\alpha }_2$$L^{n=0\mathrm{}}$,1 principal and satellite lines were observed and resolved for the first time for an atom in the mid-Z region. The relative yields, energies, and linewidths were determined. The yields in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{induced}$ spectrum deviate significantly from the binomial distribution. The width and energy shifts indicate additional multiple M-shell ionization.

An optogalvanic signal due to the photodetachment of ${\mathrm{O}}^{\mathrm{-}}$ has been successfully observed using an rf discharge. This signal is shown to be proportional to the photodetachment cross section. The transition strengths determined for various fine-structure levels agree well with the predictions by Rau and Fano [Phys. Rev. A 4, 1751 (1971)]. An optogalvanic signal due to the photodetachment of ${\mathrm{O}}_2$${\mathrm{}}^{\mathrm{-}}$ has also been observed.

Broadening and shift rates for Rb ${}_{}{}^2{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{D}$ Rydberg states with principal quantum number n∼10–50 have been measured for Ne, Kr, and ${\mathrm{H}}_2$ perturbers, using the technique of Doppler-free two-photon spectroscopy. From the shift rates at high n, we derived electron scattering lengths of (0.24±0.01)$a_0$ for Ne, (-4.0±0.3)$a_0$ for Kr, and (1.64±0.07)$a_0$ for ${\mathrm{H}}_2$. For Ne and Kr, these are in good agreement with other experimental values. Also, the n dependence of broadening and shift rates follows theoretical predictions for Ne and Kr, but not for ${\mathrm{H}}_2$.

Calculations are presented on the effect of radiation trapping on the electron-spin polarization that can be produced by optical pumping of an alkali-metal vapor in a weak magnetic field. Radiation trapping severely limits the polarization that can be obtained in a weak magnetic field.