The cascade in muonic deuterium atoms has been investigated experimentally, employing deeply depleted charge-coupled devices as x-ray detectors. The relative x-ray yields for the muonic deuterium transitions $K\alpha ,$ $K\beta$, and $K\gamma$ and the $K\alpha /K\beta$ ratios have been measured at densities between 0.0107 and 1.145 of liquid- hydrogen density. The results are compared with our measurements of the muonic x rays in hydrogen and in liquid-hydrogen deuterium mixtures in search for an isotopic effect. A comparison of our results with recent calculations is given.

Positron binding to anions is investigated within the work formalism proposed by Harbola and Sahni for the halide anions and the systems ${\mathrm{Li}}^{-}$ through ${\mathrm{O}}^{-}$ excluding ${\mathrm{Be}}^{-}$ and ${\mathrm{N}}^{-}$. The total ground-state energies of the anion-positron bound systems are empirically found to be an upper bound to the Hartree-Fock energies. The computed expectation values as well as positron and positronium affinities are in good agreement with their restricted Hartree-Fock counterparts. Binding of a positron to neutral atomic species is also investigated using an iterative method.

Some properties of the eigenfunction perturbation series $\Psi (\lambda ,x)={\sum }_{m=0\mathrm{}}^{\infty }{\psi }_m\mathrm{}\left(x\right)\mathrm{}{\lambda }^m$ for the self-adjoint eigenproblem $H\Psi =E\Psi$ with ${H=H}_0+\lambda V$ are studied. It is shown that both regular and singular perturbations V of the unperturbed Hamiltonian $H_0$ can generate partial-sum sequences $\{{\Psi }_n={\sum }_{m=0\mathrm{}}^n{\psi }_m{\lambda }^m{\}}_{n=0\mathrm{}}^{\infty }$ that converge in the norm of the Hilbert space in question and are nonuniformly bounded. This latter property is, for a given value of λ, characterized by an increasing separation between the tail of ${\Psi }_n$ on the large $|x|$ region and that of $\Psi$ as $\overrightarrow{n}\infty ,$ and causes the divergence of expectation value sequences $\{〈{\Psi }_n,S{\Psi }_n〉{\}}_{n=0\mathrm{}}^{\infty }$ with some symmetric operators S. As model examples we consider one-dimensional operators $H_0$ for which the perturbation V can be regular or singular and the eigenfunction series are obtained from the standard perturbation theory. The use of summability methods to get approximating sequences of wave functions with a correct convergence is explored. The results show that, independently of the regular or singular nature of V, a summability method (such as the Padé one) can yield approximations $R_n$ from the ${\Psi }_n$’s that are $L_2$ convergent and uniformly bounded, and hence correct physical quantities can be obtained from such $R_n$’s.

Considering the asymmetry of experimental profiles due to unresolved rotational bands, we have analyzed experimental photoabsorption spectra of molecular hydrogen based on quantum-defect theory. The vibrationally resolved optical oscillator strengths for all $\mathrm{np}\sigma {}^1{\Sigma }_u$ and $\mathrm{np}\pi {}^1{\Pi }_u$ Rydberg states are determined. We have also calculated the photoabsorption spectra of molecular hydrogen in the excited energy region of 11.0–19.0 eV based on the multiscattering self-consistent-field method. The theoretical calculations are in fair agreement with the experimental results.

We have developed and applied the relativistic coupled-cluster-based linear response theory (RCCLRT) for computing the principal as well as the shake-up ionization potentials (IP’s) of Li, Be, Na, and Mg where the single-particle orbitals are generated by solving the relativistic Hartree-Fock-Roothaan equations using the Gaussian basis functions on a grid. The computed principal and shake-up ionization energies by the RCCLRT approach are in favorable agreement with the experimental results. Since for the (one-valence) IP problem, there is a formal equivalence between the principal IP values as obtained from the CCLRT and those obtained as eigenvalues of the multireference coupled-cluster theory, the computed quantities are fully size extensive. The approach via the RCCLRT has the additional advantage of providing the shake-up IP’s as well. These are, however, not fully size extensive, but the error scales as the number of valence excitations $\mathrm{}(2h-1p)\mathrm{}$, so the inextensivity error is rather small.

It is shown that the recently observed $\Delta I=2\mathrm{}$ staggering seen in superdeformed nuclear bands is also occurring in certain electronically excited rotational bands of diatomic molecules. In the case of diatomic molecules the effect is attributed to interband interactions (bandcrossings).

The Thomas-Reiche-Kuhn and the Bethe sum rules are generalized to more general operators. The obtained sum rules can be readily applied to actual systems.

We have measured the ratio of the electric quadrupole $\mathrm{}\left(E2\mathrm{}\right)\mathrm{}$ to magnetic dipole $\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ transition amplitude within the ${6P}_{1/2}\to {6P}_{3/2}$ transition in atomic thallium. Defining $\chi$ to be this $E2\mathrm{}$ to $M1\mathrm{}$ amplitude ratio, we find that $\chi =0.2387\mathrm{}\left(10\right)\mathrm{}\left(38\right)\mathrm{}$, where the first error is statistical and the second represents a combined systematic error. In addition to providing a stringent test of theoretical wave-function calculations in thallium, accurate knowledge of this quantity is essential for existing and future measurements of parity nonconserving optical rotation on this same 1283-nm line in thallium.

The frequency shift of spectral lines is most often explained by the Doppler effect in terms of relative motion, whereas the Doppler broadening of a particular line mainly depends on the absolute temperature. The Wolf effect, on the other hand, deals with the correlation-induced spectral change and explains both the broadening and shift of the spectral lines. In this framework a relation between the width of the spectral line is related to the redshift z for the line and hence with the distance. For smaller values of z a relation similar to the Tully-Fisher relation can be obtained and for larger values of z a more general relation can be constructed. The derivation of this kind of relation based on dynamic multiple-scattering theory may play a significant role in explaining the overall spectra of quasistellar objects. We emphasize that this mechanism is not applicable for nearby galaxies, $z<~1$.

The Thomas-Fermi (TF) nonlinear differential equation for neutral atoms is reconsidered. A remarkably good representation for the TF exact solution was obtained by means of the Padé approximant procedure. The same approach allows us to make an accurate prediction for the TF initial slope, solving in this way the initial-value problem for the TF equation.

We have found closed-form solutions of the Schrödinger equation for a particle in a noncentral potential given by a two-body Coulomb potential plus a parabolic barrier. These kinds of potentials arise in the context of the three-body Coulomb continuum problem. Here we study the continuum and discrete spectrum eigenfunctions as well as their asymptotic behavior and the associated transition amplitudes.

Integral identities that hold between “desired” and “comparison” solutions of the radial Dirac equations for scattering processes are considered. Applications of these identities are discussed, particularly the determination of bounds to variational calculations of K-matrix elements.

The Z-matrix formulation of Brown and Light [J. Chem. Phys. 101, 3723 (1994)], based on a Kohn variational principle for a general class of finite-range scattering functionals, is applied to electron-molecule collisions employing a mixed basis of Gaussians and finite-element interpolation polynomials (times spherical harmonics). The local nature of the finite elements is particularly well suited for finite-range calculations, and all integrals involved are energy independent. The implementation of the method is designed to make use of sophisticated target functions. Numerical examples for both elastic collision of H and inelastic collision of ${\mathrm{H}}_2$ illustrate the applicability of this approach. The results are compared with data obtained using other theoretical methods as well as experimental data.

Measurements of the pressure dependence of the dissociative recombination (DR) reaction transition of ${\mathrm{Ar}}_2^{+}$ $\mathrm{}(v=0\mathrm{})\mathrm{}$ to the ${3d}^{\prime }\left[\frac{3}{2}\right]$ $J=1,$ the $4p\left[\frac{1}{2}\right]$ $J=1,$ and the ${4p}^{\prime }\left[\frac{1}{2}\right]$ $J=0\mathrm{}$ final product states of the argon atom have been done in an argon glow discharge using time-of-flight spectroscopy. The velocity of these final-product-state atoms is close to the most probable velocity (≈750 m/sec) of the argon atoms in the discharge, so that their distributions appear as spikes within the Boltzman distribution. The narrow velocity distributions of these DR product atoms suggests that the velocity of the ${\mathrm{Ar}}_2^{+}$ ion parents, which are created by associative ionization reactions, were very subthermal and nearly zero. One collision with an Ar atom would cause the ${\mathrm{Ar}}_2^{+}$ ion to gain, on the average, 47% of the velocity of that Ar atom, which would broaden the DR product distribution so that the peak would not be observable. However, if the ion parent dissociates before any collision, the DR distribution will be narrow and thus observable. Determining, experimentally, the pressure at which the narrow peaks broaden and by calculating the collision time corresponding to that pressure, the lifetimes of the DR transitions have been estimated.

The impact-parameter Faddeev approach to atomic three-body collisions which has been developed for, and successfully applied to, ion-atom scattering processes, has now been developed further by including, instead of the Coulomb potentials, the full two-particle off-shell Coulomb T matrices in all “triangle” contributions to the effective potentials. Results of calculations of proton-hydrogen collisions with only the ground states of the hydrogen retained in both the direct and the rearrangement channels are presented. Total and differential electron transfer, as well as differential elastic scattering cross sections, are obtained simultaneously in very good agreement with experiment, over a wide range of (nonrelativistic) incident energies.

A computational scheme based on the infinite-order sudden approximation (IOS) is proposed for treating molecular and screening effects in muonic atoms scattering at low energies. With this scheme the differential cross sections $(d\sigma /d\Omega )(\varepsilon ,j\leftarrow 0|\theta )$ and the total cross sections ${\sigma }_{\mathrm{tot}}\left(\varepsilon \right)$ for the scattering of the muonic atoms on molecules of hydrogen isotopes are calculated at energies ${\varepsilon }_{\mathrm{rot}}=ħ{\omega }_I<~\varepsilon <~{\varepsilon }_{\mathrm{vib}}=ħ{\omega }_{\nu }.$ The IOS permits a quantitative analysis of the dependence of the differential cross sections on the scattering angle and on the rotational excitations, particularly of the rotational rainbow effects. An attractive feature of this approach is that the energy and angular dependencies are included in the “input” cross sections for the scattering of the muonic atom on the bare nuclei of the molecule.

The formalism applied to superelastic electron scattering from laser-excited atoms has to date assumed perfect polarization of the laser light. We consider the effects of imperfect polarization, deriving an expression for the superelastic scattering rate from target atoms optically pumped with elliptically polarized light, and show how imperfect polarization effects can be measured and minimized under experimental conditions. In particular, we find that in measuring the scattering for linearly polarized light with a small circular component, the errors are proportional to the undesired circular polarization component and to $P_3$, the scattering sensitivity to circular light. We also present in detail a polarizer design which generates both linear and circular polarizations, allowing measurement of all scattering polarization sensitivities without requiring interchange of optical elements.

An exact method for direct calculation of the Jost function and Jost solutions for a repulsive singular potential is presented. Within this method the Schrödinger equation is replaced by an equivalent system of linear first-order differential equations, which after complex rotation, can easily be solved numerically. The Jost function can be obtained to any desired accuracy for all complex momenta of physical interest, including the spectral points corresponding to bound and resonant states. The method can also be used in the complex angular-momentum plane to calculate the Regge trajectories. The effectiveness of the method is demonstrated using the Lennard-Jones (12,6) potential. The spectral properties of the realistic interatomic ${}^4\mathrm{He}{-}^4\mathrm{He}$ potentials HFDHE2 and HFD-B of Aziz et al. [Mol. Phys. 61, 1487 (1987)] are also investigated.

Charge-transfer processes in collisions of ${\mathrm{C}}^{+}$ ions with ${\mathrm{H}}_2,$ ${\mathrm{D}}_2,$ CO, and ${\mathrm{CO}}_2$ molecules have been studied based on joint experimental and theoretical approaches in the collision energy from 0.15 to 4.5 keV. In the present experiment, the ground-state ${\mathrm{C}}^{+}{(}^{2}P)$ ion projectiles have been produced by carefully energy-controlled electron impact to minimize the influence of the metastable-state ions. The observed cross sections are compared with the present theoretical prediction, and while the theoretical results are somewhat smaller than the measurements, they are found to be in reasonable agreement for ${\mathrm{H}}_2,$ ${\mathrm{D}}_2,$ and CO above around 1 keV. The present experimental cross sections for CO and ${\mathrm{CO}}_2$ are smaller by a factor of 2 to 3 than those of earlier measurements. We provide some remarks on the effect of the metastable-state ions.

Total cross sections for single-electron transfer from two selected heliumlike atomic systems by bare projectiles are computed by means of the four-body continuum distorted-wave approximation. The effect of dynamic electron correlations is explicitly taken into account through the complete perturbation potentials. Specifically, we consider the symmetric ${\mathrm{He}}^{2+}-\mathrm{H}\mathrm{e}$ and asymmetric ${\mathrm{H}}^{+}{-\mathrm{L}\mathrm{i}}^{+}$ collisions in a large energy range from 50 to 10 000 keV. With regard to a previous work of Belkić et al. [Phys. Rev. A 56, 3675 (1997)], where a major influence of electronic correlations on single-electron capture by fast protons in helium was found, the present paper expands the study to higher projectile $\left({\mathrm{He}}^{2+}\right)$ and target $\left({\mathrm{Li}}^{+}\right)$ nuclear charges, with the purpose of determining whether electronic correlations remain important. The prior and post total cross sections are found to be in satisfactory agreement with the available experimental data.