We have calculated variational wave functions for the excited states of the tdμ molecule using a Coulombic Hamiltonian. These functions were used to find the probability, known as the sticking fraction, that after fusion the muon would remain bound to the alpha particle. The sticking fractions were found to be (0.888±0.002)×${10}^{\mathrm{-}2}$ for the J=0, ν=1 state and (0.29±0.01)×${10}^{\mathrm{-}2}$ for the J=1, ν=0 state. The sticking fraction of the highest bound state of tdμ, J=1, ν=1, did not converge. In addition, we have found the expectation values of the distances between particles for the lower (00), (01), and (10) states.

A purely algebraic approach to Green’s functions is presented. The new formulation allows the determination of a closed-form equation for Green’s functions which depends only on the ground state of the system. By a straightforward perturbation expansion of this state an interesting approximation scheme is obtained which is nonperturbative in the final states (e.g., excited or ionic states). This method, which can be used for various propagators, is explicitly applied to the particle-particle propagator carrying out the scheme up to third order. The approach is discussed in detail and briefly compared with the well-established algebraic diagrammatic construction approximation scheme.

The algebraic diagrammatic construction scheme at nth order includes all Feynman diagrams up to nth order and a partial summation of diagrams arising from the latter to infinite order. In the present work this scheme is carried out for the first time at third order for the particle-particle propagator. Because of the many diagrams involved in third order the approach requires a very careful analysis of terms which describe the corresponding perturbation expansion of the propagator. The relevant technical details of the analysis are presented.

The usual mathematical model of the single-mode electromagnetic field is the harmonic oscillator with an infinite-dimensional state space, which unfortunately cannot accommodate the existence of a Hermitian phase operator. Recently we indicated that this difficulty may be circumvented by using an alternative, and physically indistinguishable, mathematical model of the single-mode field involving a finite but arbitrarily large state space, the dimension of which is allowed to tend to infinity after physically measurable results, such as expectation values, are calculated. In this paper we investigate the properties of a Hermitian phase operator which follows directly and uniquely from the form of the phase states in this space and find them to be well behaved. The phase-number commutator is not subject to the difficulties inherent in Dirac’s original commutator, but still preserves the commutator–Poisson-bracket correspondence for physical field states. In the quantum regime of small field strengths, the phase operator predicts phase properties substantially different from those obtained using the conventional Susskind-Glogower operators. In particular, our results are consistent with the vacuum being a state of random phase and the phases of two vacuum fields being uncorrelated. For higher-intensity fields, the quantum phase properties agree with those previously obtained by phenomenological and semiclassical approaches, where such approximations are valid. We illustrate the properties of the phase with a discussion of partial phase states. The Hermitian phase operator also allows us to construct a unitary number-shift operator and phase-moment generating functions. We conclude that the alternative mathematical description of the single-mode field presented here provides a valid, and potentially useful, quantum-mechanical approach for calculating the phase properties of the electromagnetic field.

In a previous paper the analytically reduced form was found for the general class of integrals containing multicenter products of 1s hydrogenic orbitals, Coulomb or Yukawa potentials, and plane waves. The method consisted of combining all angular dependence within a single quadratic form by means of a three-dimensional Fourier transform and a one-dimensional Feynman transform for each term in the product and an additional integral transformation to move the resulting denominator into an exponential to be summed with the vector products in the plane waves. This quadratic form was then diagonalized with respect to the (introduced) momentum integrals and diagonalized again with respect to the (original) spatial integrals. In the present paper the four-dimensional Fourier-Feynman transformations are replaced by the one-dimensional Gaussian transformation so that only one diagonalization is required, yielding a simpler reduced form for the integral. The present work also extends the result to include all s states and pairs of states with l≠0 summed over the m quantum number.

We have calculated Δn=0 dielectronic recombination cross sections and rate coefficients for the B-like ions ${\mathrm{C}}^{+}$, ${\mathrm{N}}^{2+}$, ${\mathrm{O}}^{3+}$, and ${\mathrm{F}}^{4+}$ in the LS-coupling and intermediate-coupling approximations, using the program autostructure, as well as in a partitioned configuration-average approximation (PCA). There is broad agreement between the zero-field PCA results and the LS-coupling and intermediate-coupling results, which differ by no more than 10%. The experimental cross sections obtained by Dittner et al. lie between the zero-field and the maximum-field-enhanced PCA results, the enhancement being a factor of 3. In the case of the rate coefficients the general formula of Burgess was found to overestimate the zero-field results by a factor of between 1.3 and 1.8, mainly due to the neglect of autoionization into excited states.

We have calculated Δn=0 dielectronic recombination (DR) cross sections and rate coefficients for ${\mathrm{O}}^{\mathrm{q}+}$, q=1–5, in configuration-mixing LS-coupling and intermediate-coupling approximations, using the program autostructure, as well as in a partitioned configuration-average (PCA) approximation. The intermediate-coupling cross sections (rate coefficients) are about 45% (25%) greater than the LS-coupling results in the case of ${\mathrm{O}}^{+}$ and ${\mathrm{O}}^{5+}$, due to the effect of core fine-structure interactions, while the increase is no more than 10% (5%) for ${\mathrm{O}}^{2+}$, ${\mathrm{O}}^{3+}$, and ${\mathrm{O}}^{4+}$. There is good agreement between the zero-field PCA results and the intermediate-coupling results when DR takes place through a single core term, as in ${\mathrm{O}}^{+}$, ${\mathrm{O}}^{4+}$, and ${\mathrm{O}}^{5+}$, but the PCA approximation gives poorer results when DR proceeds through more than one core term, as in ${\mathrm{O}}^{2+}$ and ${\mathrm{O}}^{3+}$. The maximum-field-enhanced PCA results are about a factor of 3 greater than the zero-field results. In the case of the rate coefficients the general formula of Burgess was found to overestimate the zero-field results by a factor of between 1.3 and 1.8 due to the neglect of autoionization into excited states or the averaging over incident angular momentum.

This paper proposes a quantum-fluid density-functional theory (an interlinking of quantum-fluid dynamics and density-functional theory) for dealing with molecular collisions, in order to incorporate both time dependence and excited states. Using a new kinetic energy density functional for ion-atom collisions, we have derived a single-particle time-dependent single density equation for many-electron systems. The equation is a new generalized nonlinear Schrödinger equation whose solution directly yields the time-dependent charge density, current density, and a pulsating effective potential surface on which the process occurs. The new equation is also derived through Nelson’s stochastic interpretation of the single-particle Schrödinger equation. A ‘‘thermodynamics’’ of the entire time-evolving system is suggested in terms of space- and time-dependent quantities. New algorithms have been devised for solving the above equation in one and two spatial dimensions, in a succession of time steps. Results have been obtained and analyzed in the approach regime for proton-neon high-energy (25-keV) collisions, which permit excitation but not ionization. These results show distinct nonlinear features.

The Kα hypersatellite spectra of oxygen, obtained by bombardment of various solid oxides with 2-MeV/amu beams of C and Ar ions, were measured using a curved-crystal spectrometer. In the spectra for the compounds CaO, SrO, ${\mathrm{CeO}}_2$, and three of the oxides of Ti, some of the hypersatellite peaks appeared to be enhanced while others were suppressed. These features are indicative of resonant electron transfer processes caused by the energy matching of valence levels in the multiply ionized oxygen ion with those of its neighboring metal ions. In all cases except CaO, the spectra suggest that correlated multielectron transfer is involved, in which as many as four electrons are exchanged between the two ions. A method developed previously for estimating the energy change associated with the electron exchange was generalized to cover multielectron transfer, and corrections for extra-atomic relaxation were included. Calculations employing this method strongly support the resonant multielectron transfer hypothesis.

Absolute total cross-section measurements are presented for electron capture in ${\mathrm{O}}^{5+}$+H(D) collisions over the energy range 0.9–800 eV/amu. These are the first experimental data to be reported using a new multicharged-ion–atom merged-beams apparatus developed at Oak Ridge National Laboratory. The experimental method and the cross-section measurements are described in detail. At energies below 2 eV/amu, the data show a cross-section enhancement which may be attributed to the ion-induced dipole attraction between the reactants. Agreement with recent unpublished quantum-mechanical calculations ranges from fair at the lower energies to excellent at the higher energies.

We report calculations of cross sections for electron capture to individual doubly excited states for 150–500-keV ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions colliding with helium atoms. By adopting an independent-electron approximation, the capture probability to each doubly excited state is calculated in terms of single-capture amplitudes to each substate which are properly weighted with configuration-interaction coefficients. The validity of such an approximation is checked by comparing the results with calculations in which the electron correlation was considered explicitly. The calculated final results for double capture to the (2$s^2$) ${}_{}{}^1{}_{}{}^{}S$, (2s2p${)}^1$P, and (2$p^2$${)}^1$D states are in fair agreement with the recent experiment of Zouros et al. [Phys. Rev. A 35, 1963 (1987)].

Cross sections for electron-impact ionization of neonlike selenium have been calculated using close-coupling wave functions. We report cross sections for ionization of the 2$s^2$2$p^6$ ${}_{}{}^1{}_{}{}^{}S$ ground state and the 2$s^2$2$p^5$3s ${}_{}{}^3{}_{}{}^{}P$ excited state of the ion. We found numerous resonances in the ejected electron channels due to excitation of 2$s^2$2$p^4$3snl autoionizing states. The resonances are very narrow, but some have peaks that are several orders of magnitude above the nonresonant background cross section. Even with radiative decay taken into account, the resonances enhance the total integrated cross section by nearly a factor of 4.

The total cross sections for positron-impact ionization of helium are evaluated by using the distorted-wave polarized-orbital method taking into account the effects of screening and final-channel distortion. The present results are in fair agreement with other elaborate theoretical calculations and experimental results.

Measurements of elastic angular differential cross sections have been carried out for four quasi-one-electron collision systems at intermediate energies. Data are presented for ${\mathrm{Na}}^{+}$+H collisions at laboratory energies of 35.94, 51.75, 63.89, and 143.75 keV, for ${\mathrm{Li}}^{+}$+H collisions at energies of 19.44 and 43.75 keV, for ${\mathrm{Mg}}^{+}$+He collisions at energies of 30, 66.7, and 150 keV, and for ${\mathrm{Be}}^{+}$+He collisions at an energy of 56.25 keV. The highest energy in each case corresponds to a projectile velocity of (1/2 a.u. Born and Eikonal calculations, in which we model the projectile ion as a heavy structureless ion of charge +1e, are also presented. Our model calculations are in fair agreement with the experimental data over the range of measured scattering angles.

We have measured the laboratory energy distribution of ${\mathrm{H}}^{\mathrm{-}}$ produced by the collision-induced dissociation of ${\mathrm{H}}_3^{+}$ from He targets for incoming beam energies ranging from 2.417 to 7.0 keV. An approximate projectile frame energy distribution of ${\mathrm{H}}^{\mathrm{-}}$ is also obtained. The most probable ${\mathrm{H}}^{\mathrm{-}}$ projectile frame energy is estimated to be approximately 0.75 eV. We have also determined, from the shift in the position of the ${\mathrm{H}}^{\mathrm{-}}$ laboratory peaks, an inelastic energy loss of 60±12 eV for the excited ${\mathrm{H}}_3^{+}$ ions producing near zero kinetic energies of ${\mathrm{H}}^{\mathrm{-}}$ in the projectile frame. Our results suggest that ${\mathrm{H}}^{\mathrm{-}}$ is produced by the electronic excitation of ${\mathrm{H}}_3^{+}$ with subsequent dissociation into ${\mathrm{H}}^{+}$+${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{-}}$. In this case the motion of the two ${\mathrm{H}}^{+}$ ions is highly correlated. For the most probable c.m. energy of ${\mathrm{H}}^{\mathrm{-}}$, we put a lower limit of 163° on the correlation angle between the protons in the c.m. of dissociating ${\mathrm{H}}_3^{+}$.

We perform a nonrelativistic calculation of the first retardation and multipole corrections to the dipole angular distribution of 1s photoelectrons from light elements. A simple formula for this correction is obtained which compares well with the results of exact relativistic numerical calculations, for Z≲40 and final electron energies between 1 eV and 2 keV. These effects are small for the lightest Z, but their magnitude in general increases with increasing Z, reaching as much as 0.2–0.3 for Z=20–30. The correction can change signs one or more times. The relatively large values of the first retardation-multipole correction to the ${\sin }^2$θ dipole angular distribution results in some tendency towards forward or backward peaking of the final electron angular distribution with respect to the direction of the incident photon.

Using synchrotron radiation, an atomic beam technique, and a time-of-flight spectrometer the photoion yield spectra of the singly and doubly charged lanthanides La, Ce, Pr, Nd, Sm, and Eu in the region of the 5p excitation between 20 and 40 eV were measured. The experimental results are discussed within the concept of autoionizing atomic states and the production of doubly charged photoions by stepwise processes. For Pr, as an example, the partial cross sections of the subshells 6$s_{1/2}$, 4$f_{5/2}$, 5$p_{3/2}$, and 5$p_{1/2}$ were calculated with the method of the time-dependent local-density approximation, and the results are compared with the ${\mathrm{Pr}}^{+}$ and ${\mathrm{Pr}}^{2+}$ signals.

The T matrix is derived for the potential scattering of electrons in an elliptically polarized ultra- strong laser pulse. Special attention has been paid to the scattering of electrons that are initially nonrelativistic, but, due to the effects of the strong laser pulse, the full relativistic treatment has been applied. Possible energy ranges of the scattered electrons are discussed versus the laser field intensity. The detailed expressions in the first Born approximation are derived for linearly and circularly polarized laser fields. Numerical results for the angular distributions and energy spectra of the scattered electrons on the Yukawa-type potential in circularly polarized laser fields are presented.

The Si 1s, 2s, 2p, and Cl 1s, 2p photoabsorption spectra of ${\mathrm{SiCl}}_4$ have been assigned with the aid of multiple-scattering Xα calculations. The strongest pre-edge absorptions are assigned to transitions to Si-Cl antibonding orbitals. The weaker complex features observed near the ionization threshold can be ascribed to electronic excitations into Rydberg orbitals. The calculations also show that the weak structures beyond the Si absorption edge are mainly due to resonances in the $e^{\mathrm{*}}$ and $t_2^{\mathrm{*}}$ continuum channels. Eigenphase sums indicate that the high-energy (≥20 eV) above-edge resonances are due to photoelectron diffraction.

We present a detailed two-dimensional (2D) quantal study of the dynamical evolution of microwave-driven Rydberg H atoms. We examine the range of validity of the conventional one-dimensional (1D) models and explore the frequency- and intensity-dependent excitation and ionization mechanisms. The main findings of this paper can be summarized as follows: (i) The excitation spectra of Rydberg H atoms are strongly frequency dependent and can be roughly grouped into three characteristically different regions, each with a different excitation mechanism. In this paper, we emphasize the study of the two major excitation mechanisms: quantum diffusion and multiphoton resonant excitation. The region dominated by quantum diffusion lies in the frequency range ${\omega }_c$<${\omega }_0$<${\omega }_d$, where ${\omega }_0$ is the rescaled field frequency (${\omega }_0$=ω$n_0^3$; $n_0$ is the principal quantum number of the initial state); ${\omega }_c$, the classical chaotic threshold; and ${\omega }_d$, the quantum delocalization border.

In this region, quasienergy levels are strongly perturbed and mixed and excitation is efficient, leading to the so-called underthreshold photoelectric ionization phenomenon. On the other hand, we found a series of frequency regions (in ${\omega }_0$>${\omega }_d$) where the ionization is mainly due to multiphoton resonant excitation through the more isolated quasienergy avoided crossing points. (ii) The excitation pathways (1D versus 2D) are strongly intensity dependent. For microwave (rescaled) field strength ${\varepsilon }_0$ (≡ɛ$n_0^4$) in the range ${\varepsilon }_c$<${\varepsilon }_0$<${\varepsilon }_q$ (where ${\varepsilon }_c$ is the onset of classical chaos and ${\varepsilon }_q$ the quantum delocalization threshold), large discrepancies exist between 1D and 2D results. It is found that the 1D model seriously underestimates the ionization probabilities and, more importantly, the dominant channels for Rydberg atom excitation and ionization proceed through $n_2$>0 ladders rather than the $n_2$=0 ladder, as often assumed in the 1D model. As field strength increases above ${\varepsilon }_q$, however, the 1D model improves significantly. (iii) The quantum localization phenomenon is observed in the classically chaotic region (${\omega }_c$<${\omega }_0$<${\omega }_d$) when the field strength ${\varepsilon }_0$ is less than ${\varepsilon }_q$. However, quantum delocalization can appear when ${\varepsilon }_0$>${\varepsilon }_q$. (iv) The stability of quantum diffusive motion is analyzed in terms of the quantal phase-space diagram and the autocorrelation function. The results lend support to the view that quantum mechanics can impose limitations on classical chaotic motion. (v) The way of turning on the field (sinωt or cosωt) does not affect significantly the dynamical evolution of the system. (vi)

Finally, a computationally powerful new technique, invoking the use of artificial intelligence algorithms as well as the generalized Van Vleck perturbation theory for effectively reducing the dimensionality of the Floquet matrix, is introduced to facilitate the study of multiphoton resonant excitation of Rydberg atoms.