The convergence of the Magnus expansion in the Schrödinger representation is investigated with the aid of two exactly solvable models. A baffling observation regarding the dynamics of a spin-(1/2 system driven by a superposition of a constant and a rotating magnetic field is elucidated. Perturbation theory is applied to the exponential solution to the Schrödinger equation for a time-dependent harmonic oscillator. The first terms of the perturbation expansion for the singularity of the exponent are exactly calculated. The scope and limitations of perturbation theory in obtaining the range of validity of the Magnus expansion are discussed.

The energies of systems composed of a point negative charge (e.g., antiproton, p¯, or negative muon, ${\mu }^{\mathrm{-}}$) and an atom or small molecule (He,Ne,Ar,${\mathrm{C}}_6$${\mathrm{H}}_6$) have been calculated using large-basis-set, correlated ab initio electronic-structure methods. By invoking the Born-Oppenheimer approximation, these energies are used to generate potential surfaces for the interaction of a negative particle with an atom or small molecule. The results indicate that the particle-induced polarizations are significant even at 10-bohr separations in neon. Unusual behavior of the dipole moments of both argon and neon was calculated to occur as a function of separation. The molecular-orbital approach used here may also be useful in analyzing recent ionization behavior in low-energy p¯–inert-gas scattering experiments. Furthermore, the calculated large degree of polarization further constrains the design of materials for long-term normal matter storage of antiprotons for advanced energy sources.

It is shown that for highly excited atomic states, quantum-mechanical operators involving position and momentum can be approximated by O(4,2) generators. The resulting Schrödinger equation is solved exactly in the case of hydrogenlike systems, for both eigenvalues and eigenvectors. The precision of the approximations involved in these replacements can thus be tested. It is verified that the new solutions converge to the hydrogenlike solutions as n/Z goes to infinity. n is the principal quantum number and Z the charge of the nucleus in atomic units. The O(4) dynamics symmetry of the hydrogenlike atoms is preserved and the new constant of the motion identified. The resulting Schrödinger equation for two electron atoms is then presented and formulated in terms of scaled doubly excited states basis vectors previously introduced with the o(4) algebra. This equation is equivalent to a sparse infinite system of linear equations whose nonzero coefficients have very simple analytical expressions.

We discuss the Legendre conjugate of the Hohenberg-Kohn energy-density functional, i.e., the total energy of an inhomogeneous many-electron system, considered as a functional of the external Coulomb potential (the nuclear Coulomb skeleton of a molecule, for instance) as the starting point of an alternative formulation of a theory of electronic correlations. We then relate this functional to the nonrelativistic or relativistic microscopic many-body theory. The essential bridge between the two theories is many-body perturbation theory perturbing around a mean field. We then point out that a particular choice for the latter, the g-Hartree mean field, leads to a transparent physical picture: The relevant functional of the external field, $g_0$-1, representing electronic correlations, is interpreted as a polarization charge density induced by the latter. This picture, in turn, leads to a Clausius-Mosotti type of equation for this correlation functional. Applications to atomic- and molecular-structure calculations are discussed.

The direct solution of the Schrödinger equation for the ground state of the ppμ, ddμ, and ttμ molecular ions is obtained with the help of the correlation-function hyperspherical harmonic method. Given the proper correlation function, chosen from physical considerations, the method generates wave functions, accurate in the whole range of interparticle distances, which leads in turn to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. Our results are compared with those obtained in other precision calculations.

A density-functional model of atoms in strong magnetic fields is proposed along lines parallel to Hohenberg-Kohn-Sham density-functional theory. We derive a Thomas-Fermi-Weizäcker-like (TFW) functional by using the classical-path approximation to the relevant one-particle Green’s function. We also address the correlation effect between the effective potential and the magnetic field. The TFW-like model provides a simple way of calculating ground-state energies and charge densities of atoms in magnetic fields, and can be systematically improved.

Ions stored in a radio-frequency quadrupole trap were subjected to pulses of a small oscillating potential. The frequency of oscillation within each pulse (dipolar or quadrupolar) was variable up to one-half of the rf drive frequency. Ions that were ejected axially from the trap were detected with an electron multiplier. Ion signal intensity was observed as a function of the small oscillating potential frequency for pulsed excitation in each of two time domains in the duty cycle. Thus it was possible to see either the ejection in the z direction, or the ejection in the x or y direction and the z direction. According to the nature of the ejection pulse, the signal shows lines at secular frequencies, at doubled secular frequencies, and other lines that can be sharp and numerous. The influence of space charge is clearly shown. The observed couplings are discussed by taking into account anharmonicity and relaxation mechanisms.

By considering the formation of excited muonic molecular ions [(${\mu }^{\mathrm{-}}$He${)}_{2\mathrm{S}}^{+}$ He${]}^{\mathrm{*}+}$ in the triplet state a ${}_{}{}^3{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$, it is possible to explain the presence of metastable muonic helium levels at late times, observed when negative muons are stopped in a high-pressure (p≥6 atm) helium-gas target at room temperature. A comparison of the different experimental results with the present idea is reported, and measurements to obtain independent checks of this scheme are proposed.

The condition that the Thomas-Fermi solution produces a minimum in the energy requires that the eigenvalues of a stability matrix are all positive. The eigenfunctions and eigenvalues of this matrix are studied for various cases: the atomic nucleus, the atom in two dimensions where analytic solutions are possible, and the atom in three dimensions.

With multistep laser excitation via 4sn’s Rydberg states, doubly excited msns ${}_{}{}^1{}_{}{}^{}S_{}^e{}_{}{}^{}$ states (m=6, 9≤n≤20; m=7, 9≤n≤20; m=10, 10≤n≤20 except n=11) of Ca atoms have been observed, and their energy levels have been obtained. The large-scale configuration-interaction calculation for Ca atoms has also been executed using a discrete two-electron basis set, in which a frozen ${\mathrm{Ca}}^{2+}$ core is assumed and the total number of the bases is 1714. The calculated energy levels are in good agreement with the observed ones, including those of the 8sns and 9sns states observed in our previous studies [Phys. Rev. A 38, 551 (1988); J. Phys. B 21, L439 (1988)]. Based on the good agreement, charge-density plots have been drawn for the nsns states (4≤n≤10), using the calculated eigenvectors. In all the nsns states investigated, a reasonably large part of the charge density has been seen to be localized on the Wannier’s potential ridge and to show a fairly strong angular correlation. In lower nsns states, the angular-correlation pattern has been found to support the moleculelike picture, although an unusual pattern has been seen in a smaller radial region. In higher states, two types of unusual angular correlation have been seen. In particular, one of them is suggestive of a bent structure of the charge-density distribution, in spite of the zero-angular-momentum states. The cause of this correlation has been discussed from a viewpoint of configuration mixing, although its physical meaning is still unknown.

The Feshbach-type idempotent-projection procedure, developed recently by the author, is applied to closed-channel resonances of ${\mathrm{He}}^{\mathrm{-}}$. The energies of the well-known two ${}_{}{}^2{}_{}{}^{}\mathrm{S}$, two ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$, and one ${}_{}{}^2{}_{}{}^{}\mathrm{D}$ resonances lying below the 3 ${}_{}{}^3{}_{}{}^{}S$ threshold are obtained. Quartet QHQ spectra of the same symmetries are investigated, and one ${}_{}{}^4{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$ autoionizing resonance below the 3 ${}_{}{}^3{}_{}{}^{}S$ threshold is found.

In this work we give the values of traces of p-order reduced-density operators. These traces are obtained by application of the spin functions and of the symmetric-group properties. The relations obtained here will allow an easy and fast evaluation of the high-order spin-adapted reduced Hamiltonian matrix elements and high-order Hamiltonian moments.

The electronic energy-transfer process ${\mathrm{Na}}^{\mathrm{*}}$(3${\mathrm{P}}_{3/2}$)+M→${\mathrm{Na}}^{\mathrm{*}}$ (3$P_{1/2}$)+M, where M is an Na or K atom, has been measured differentially with respect to scattering angle. This has been done with crossed beams and by establishing the final (3$P_{1/2}$) state velocity distribution from the Doppler spectrum of 3$P_{1/2}$→4$D_{3/2}$ absorption. The differential cross section for Na perturbers is highly forward peaked (within a few degrees) with a small but extended high-angle tail. Forward angles are also dominant for K perturbers, but these cover a larger angular range with a very substantial large-angle contribution.

Density matrices describing H(n=3) atoms produced in collisions of 20- to 100-keV protons with He atoms have been determined experimentally. In the experiment the intensity and polarization of Balmer-α radiation emitted from a He gas cell are measured as a function of the strength of an externally applied electric field. Electric fields are applied in a direction either axial to or transverse to the proton beam. Density matrices are extracted by detailed analysis of the optical data. Data are obtained for each field direction and then analyzed, separately and in combination, to yield density matrices. Satisfactory agreement is found between density matrices determined from axial and transverse electric field data except at the lowest energies studied. Some nonzero density-matrix elements are determined more accurately using axial electric fields than with transverse fields, while other elements are more accurately determined using transverse electric fields. The combined analysis using data from both field directions gives a better determination of the density matrix than the separate data sets. Results for the H(n=3) electron-transfer cross sections (relative to 3s), the electric dipole moment of the charge distribution 〈d${〉}_z$, a first-order moment of the current distribution 〈L×A${〉}_z$,s, and the average coherence Tr(${\sigma }_3^2$) are obtained. The experimental results are compared to two recent calculations using the augmented atomic orbital (AO+) theory and the continuum distorted-wave approximation with post-collision interaction theory, and to one recent experimental measurement of the diagonal density-matrix elements. Both theories show qualitative agreement with the general trends in the data. The AO+ method gives better quantitative agreement. The experimental results are displayed in graphical form as distributions of the electronic charge D(r) and of the electronic current density j(r).

We have calculated dielectronic recombination (DR) cross sections from the ground state (1 ${}_{}{}^1{}_{}{}^{}S$) and excited states (2 ${}_{}{}^3{}_{}{}^{}S$, $2^1$S, and 2 ${}_{}{}^3{}_{}{}^{}P$) of the He-like ions ${\mathrm{C}}^{4+}$ and ${\mathrm{O}}^{6+}$ in the LS-coupling and intermediate-coupling approximations, using the program autostructure. We find the effects of configuration interaction, intermediate coupling, and external electric fields to be small. We compare our results with the recent high-resolution measurements of DR from the excited states of these ions by Andersen et al. [Phys. Rev. Lett. 62, 2656 (1989) and Phys. Rev. A 41, 1293 (1990)] by convoluting our cross sections with their electron velocity distribution. For the case of ${\mathrm{C}}^{4+}$, we obtain excellent agreement when we choose the 2 ${}_{}{}^3{}_{}{}^{}S$ to 2 ${}_{}{}^1{}_{}{}^{}S$ population ratio to be 18. For the case of ${\mathrm{O}}^{6+}$, we obtain good agreement with experiment with a 2 ${}_{}{}^3{}_{}{}^{}S$ to $2^1$S population ratio of 70, except in the 6- to 8-eV energy region, where a model calculation indicates that coupling between resonances via the continuum may be important. By comparing experiment with theory, we have also estimated the metastable fraction of the 2 ${}_{}{}^3{}_{}{}^{}S$ term to be 70% in ${\mathrm{C}}^{4+}$ and 20% in ${\mathrm{O}}^{6+}$. The reason for this large difference is not understood.

Absolute cross sections for the production of photons in the ${\mathrm{N}}_2^{+}$ first negative (0-0) and (0-1) bands by collisions of 1-MeV ${\mathrm{H}}^0$, ${\mathrm{H}}^{\mathrm{-}}$, and ${\mathrm{H}}^{+}$ on ${\mathrm{N}}_2$ have been measured. The (0-0) cross sections are, respectively, 0.091±0.03, 0.19±0.06, and 0.15±0.05 A${̊}^2$ per ${\mathrm{N}}_2$ molecule, for ${\mathrm{H}}^0$, ${\mathrm{H}}^{\mathrm{-}}$, and ${\mathrm{H}}^{+}$ projectiles. The (0-1) cross section is 0.060±0.02 A${̊}^2$ per ${\mathrm{N}}_2$ molecule for ${\mathrm{H}}^{\mathrm{-}}$ projectiles. Pressure dependences are observed in the apparent cross sections for ${\mathrm{H}}^0$+${\mathrm{N}}_2$→391 nm and ${\mathrm{H}}^{\mathrm{-}}$+${\mathrm{N}}_2$→391 nm, at nitrogen pressures below 3.5×${10}^{\mathrm{-}4}$ torr, and are ascribed to stripping of electrons from ${\mathrm{H}}^0$ and ${\mathrm{H}}^{\mathrm{-}}$. The cross section for ${\mathrm{H}}^{\mathrm{-}}$+${\mathrm{N}}_2$→${\mathrm{H}}^0$+... is measured to be 6.8(+2.3,-2.9) A${̊}^2$ per ${\mathrm{N}}_2$ molecule. Where data for comparison exist, our measured cross sections are a factor of 2 or more higher than previously reported values.

We report differential, integral, and momentum-transfer cross sections and the scattering length ($A_0$) for positron ($e^{+}$)-argon scattering at low energies below the positronium formation threshold. An optical-potential approach is employed in which the repulsive Coulombic interaction is calculated exactly at the Hartree-Fock level and the attractive polarization and correlation effects are included approximately via a parameter-free positron correlation polarization (PCP) potential recently proposed by us. The PCP model is based on the correlation energy ${\varepsilon }_{\mathrm{corr}}$ of one positron in a homogeneous electron gas; in the outside region, the ${\varepsilon }_{\mathrm{corr}}$ is joined smoothly with the correct asymptotic form of the polarization interaction (-${\alpha }_0$/2$r^4$, where ${\alpha }_0$ is the target polarizability) where they cross each other for the first time. The total optical potential of the $e^{+}$-argon system is treated exactly in a partial-wave analysis to extract the scattering parameters. It is found that the PCP potential gives much better qualitative results, particularly for the differential cross sections and the scattering length, than the corresponding results obtained from an electron polarization potential used as such for the positron case. We also discuss the ‘‘critical’’ points (representing the minima in the differential scattering) in the low-energy $e^{+}$-Ar scattering. The present results involve no fitting procedure.

Cross sections for the production of ${\mathrm{O}}^{\mathrm{-}}$ from ${\mathrm{N}}_2$O by the process of dissociative electron attachment have been measured for electron-impact energies ranging from 0 to 50 eV. Three new ${\mathrm{O}}^{\mathrm{-}}$ peaks are observed. The present data above 5-eV electron-impact energy differ considerably from the previous measurements.

Electron capture into the 3 ${}_{}{}^3{}_{}{}^{}D$ state of He was measured by the detection of 5876-Å photons from the $3^3$D–2 ${}_{}{}^3{}_{}{}^{}P$ transition following collisions of ${\mathrm{He}}^{+}$ with various polyatomic molecules. The photon-emission cross section for this transition was measured for each target over the helium-ion energy range of 100 to 300 keV. The targets used were ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, CO, ${\mathrm{CO}}_2$, ${\mathrm{N}}_2$O, ${\mathrm{CH}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_2$, ${\mathrm{C}}_2$${\mathrm{H}}_4$, and ${\mathrm{C}}_2$${\mathrm{H}}_6$. For all targets, the cross sections could be fitted very well with a 1/$v^2$ function, where v is the helium-ion velocity.

Two different types of counterpropagation neural networks are applied to the problem of classifying unknown Cm i energy levels. Four features—energy level, angular momentum, g factor, and isotope shift—are used to describe each level. One type of network is trained at the 100% level, while the other type is trained in excess of 96%. Performance on test sets is not as good, ranging from 81.2% to 93.7%. These results equal or surpass pattern recognition results obtained in an earlier study. Classifications for 12 odd-parity unknowns and 42 even-parity unknowns are also obtained and compared with the previous pattern recognition predictions.