We study a matrix formulation for the WKB quantization rule (mWKB) where the real momenta of the type p={2m[E-V(q)]${\mathit{\}}}^{1/2}$ are replaced by elements of Clifford algebras. The WKB and mWKB spectra for two kinds of potentials are compared and some mathematical, physical, and pedagogical issues concerning the mWKB approach are stressed.

Potential curves have been calculated for the ground electronic state of ${\mathrm{HD}}^{+}$ within the framework of an improved adiabatic approximation. Both the J=0 and J=1 rotational states have been examined in detail using the new approach. This formulation takes into account the symmetry-breaking effects due to the unequal masses of the two nuclei, in contrast to the standard adiabatic approximation. The technique is found to yield significant improvement over the standard adiabatic approach for the highly excited vibrational states of ${\mathrm{HD}}^{+}$.

The local-density approximation (LDA) of density-functional theory is applied to the computation of static hyperpolarizabilities of rare-gas atoms. It is found that simple LDA predicts cubic hyperpolarizabilities γ that are too large by approximately a factor of 2. It is argued that the excessive deformability of the electronic clouds in atoms predicted by LDA is an artifact of the way this approximation treats the tail of the electronic distribution. One of the causes for the poor performance of LDA in the tail region of an atom is ascribed to the presence in such a scheme of interactions of the electrons with themselves. Therefore, a modification of the LDA is considered in which self-interactions are subtracted. When applied to He, the method yields both linear and cubic dipole polarizabilities in reasonable agreement with experiments. The modified scheme is also applied to heavier rare gases and to some negative ions (${\mathrm{H}}^{\mathrm{-}}$, ${\mathrm{F}}^{\mathrm{-}}$, ${\mathrm{Cl}}^{\mathrm{-}}$). Difficulties that are encountered in dealing with atoms (ions) with more than two electrons are overcome by limiting the self-interaction corrections to the unperturbed atom problem. A systematic reduction of the discrepancies between the calculated static hyperpolarizabilities and those inferred from recent finite frequency measurements is found.

An explicit relation between the density matrix and its s-state part is derived for electron closed shells moving in a bare Coulomb potential, thus extending previous work of one of us [N. H. March, Phys. Rev. A 33, 88 (1986)] to off-diagonal elements of the density matrix. Further polynomial models are considered and generalization of previously known relations is sought. For one-dimensional polynomial approximations it is shown that the wave function assumes a definite form irrespective of the weight function so that there is no need for the calculation of the coefficients of the orthogonal polynomials for determining the density matrix. The use of the established relations in functional theories is also discussed.

A canonical description of a harmonic oscillator with energy dissipation is sought which combines the advantages of the Kanai-Caldirola Hamiltonian and a simple model of strangulation previously considered by the authors. The treatment is in the Heisenberg picture of quantum mechanics or alternatively in classical mechanics. A strangulation β is superimposed on the damping (or growth) γ, represented by an oscillator mass m(t)=$m_0$exp(2γt). In general, the expected dissipation of energy occurs only if β>‖γ‖. If β<‖γ‖ the attempted strangulation induces a long-term growth in energy unless a special initial motion is chosen. A slight deviation from this initial motion results in a temporary decay in energy followed by growth. β<0 always induces a growth in energy.

The nuclear fusion reaction in the (dtμ${)}^{+}$ molecule is affected by the presence of the muon in the relatively loosely bound mesomolecular orbit. Due to the sharing of the available energy between the muon and the nuclei in the final state, a muon attached to the recoiling α particle reduces the energy available to the nuclear fusion reaction by about 90±50 keV and thus detunes the resonant d-t reaction amplitude by an important factor.

The analytic expressions of the second-order eikonal exchange amplitudes are derived for electron-hydrogen scattering in both post and prior forms. In the case of the Glauber exchange amplitude, these expressions are shown to be reducible to closed forms. The results are applied to the calculation of elastic e-H(1s) scattering. Useful conclusions are drawn.

Absolute cross sections have been measured for electron-impact ionization of Fe ions of initial charges 5+, 6+, and 9+ from below threshold to 1500-eV collision energies. Distorted-wave calculations including only direct ionization from ground-state ions underestimate the measured peak cross sections by 60–70?due to the effects of metastable states and contributions of excitation autoionization to the total cross sections. Ionization rate coefficients and fitting parameters are presented for this data and for ${\mathrm{Fe}}^{+}$ and ${\mathrm{Fe}}^{2+}$.

Excitation-autoionization contributions to the electron-impact ionization of ${\mathrm{Fe}}^{5+}$, ${\mathrm{Fe}}^{6+}$, ${\mathrm{Fe}}^{9+}$, ${\mathrm{Fe}}^{11+}$, and ${\mathrm{Fe}}^{13+}$ are calculated in the distorted-wave approximation. Calculations for ${\mathrm{Fe}}^{5+}$ which include only excitations from the 3$p^6$3$d^3$ ground configuration agree well with the experimental crossed beams measurements of Gregory et al. [preceding paper, Phys. Rev. A 34, 3657 (1986)]. For ${\mathrm{Fe}}^{6+}$ the agreement between theory and experiment is also good. Calculations for ${\mathrm{Fe}}^{9+}$ are in reasonable agreement with experiment when only excitations from extremely metastable states of the 3$p^4$3d excited configuration are included. Theoretical predictions for ${\mathrm{Fe}}^{11+}$ and ${\mathrm{Fe}}^{13+}$ are based on ground-configuration excitations and detailed branching-ratio calculations. Excitation-auto- ionization contributions in ${\mathrm{Fe}}^{13+}$ are found to enhance the total ionization cross section by a factor of 2 near threshold.

A multistate two-center atomic-orbital-expansion method is applied to study the subshell capture cross sections from helium atoms in collisions with bare ${\mathrm{C}}^{6+}$ and ${\mathrm{O}}^{8+}$ ions. The energy dependence of subshell capture cross sections, i.e., the n, nl, and nlm distribution, is examined. In view of the lack of detailed subshell cross section measurements, we compare our calculations with experimental total capture cross sections and with polarization fraction for the 2p-1s transition in ${\mathrm{O}}^{8+}$-He collisions. For the latter process, the cascade effect must be included in the theoretical analysis. We show that our results are in good agreement with existing experimental data.

The 3s-3p excitation of spin-polarized Na atoms by ${\mathrm{Ne}}^{+}$ ions has been studied for impact energies $E_{\mathrm{lab}=200\mathrm{}}$ eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the ‖$m_l$‖=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled ${\mathrm{Ne}}^{+}$ 2$p^5$ core in the quasimolecule formed during the collision.

In this paper the variational method is applied to the Dirac equation for heliumlike atoms. We use screened hydrogenic wave functions and find accurate energy values, corresponding to saddle points in parameter space. The energies and one-photon radiative transition rates for the 1$s^2$, 1s2s, and 1s2p states are calculated with little numerical effort.

The residual ranges of (900±3)-MeV/amu gold nuclei accelerated at the Lawrence Berkeley Laboratory Bevalac have been measured in several different media. The energy of the beam of nuclei was measured directly using a new time-of-flight system. The ranges were measured by absorption in linear wedges of polyethylene, carbon, aluminum, copper, tin, and lead and in circular wedges of polystyrene, aluminum, and gold, and by total absorption in nuclear emulsion. The measured ranges were significantly different from those calculated from the best available theoretical estimates of the energy loss of highly charged nuclei. It is concluded that at present energy losses and residual ranges of relativistic heavy ions in an arbitrary medium cannot be predicted with better than an approximately 2% accuracy.

Electron-${\mathrm{CH}}_4$ scattering is investigated in a wide energy range (0.1–500 eV) by using a previously proposed spherical model [A. Jain, J. Chem. Phys. 81, 724 (1984)]. The study is divided into three energy regions: the 0.1–1.0-eV region, where a well-known minimum occurs in the total cross section [Ramsauer-Townsend (RT) effect], between 2 and 20 eV, with a d-wave broad structure around 7–8 eV, and from 20 to 500 eV, where inelastic channels (mainly ionization and dissociation) dominate over the elastic process. It is shown that a simple model, in which the total optical complex potential is spherical, is capable of reproducing qualitative features in the total, differential, and momentum-transfer cross sections in the present energy region.

The present results are almost equivalent to more rigorous close-coupling calculations at low energies (E<20 eV), where the rotationally elastic channel dominates. Below 20 eV, the total optical potential is real and consists of three spherical terms, namely, a static term calculated accurately from near-Hartree-Fock one-center methane wave functions, a parameter-free polarization potential of Jain and Thompson (however, below 1 eV we employ a cutoff-type phenomenological polarization potential), and a local-exchange interaction in the asymptotically adjusted version of the Hara free-electron-gas exchange (AAHFEGE) potential (however, below 1 eV, we consider just the HFEGE form). At and above 20 eV, we employ a complex optical potential with the same real part as in the 2–20-eV region, while the imaginary part is an energy-dependent absorption potential calculated from target electron density and short-range static-exchange potential in the quasifree model with Pauli blocking [Staszewska et al., J. Phys. B 16, L281 (1983)].

Two versions of this absorption potential are used; one with undistorted charge density and the other with a polarized density. The final complex total optical potential is treated exactly in a partial-wave analysis to yield various cross sections. The results are compared with the available experimental and other theoretical data. The absorption cross sections are not sensitive to various forms of real part of the optical potential, and in general, reduce the elastic cross sections significantly.

Using the $X^{n+}$(1$s^2$)+${\mathrm{He}}^{2+}$ colliding systems as specific examples, we study the origin dependence of results in the application of the two-state exponential model, and we show the relevance of polarization effects in that study. Our analysis shows that polarization effects of the ${\mathrm{He}}^{+}$(1s) orbital due to interaction with $X^{(n+1)+}$ ion in the exit channel yield a very small contribution to the energy difference and render the dynamical coupling so strongly origin dependent that it invalidates the basic premises of the model. Further study, incorporating translation factors in the formalism, is needed.

The atomic-eigenfunction-expansion method is used to investigate the influence of laser radiation on charge-transfer processes in proton–alkali-metal-atom collisions. The radiation is treated classically. The cross sections for charge transfer into the ground state of hydrogen in collisions between a proton and any of the atoms sodium, potassium, rubidium, and cesium in the presence of radiation of wavelengths varying between 3000 and 6000 Å are determined for incident-ion energy values of 1, 2, and 10 keV. Calculations are made for two different radiation intensities, 0.1 and 1 TW/${\mathrm{cm}}^2$. It is found that the effect of the radiation is to increase the charge-transfer cross section in some cases and decrease the cross section in others.

Electron-impact excitation cross sections have been calculated for transitions from the ground state 2$s^2$2$p^4$ ${}^3$P to the n=2 and n=3 excited states of oxygenlike krypton. Configuration-interaction-type wave functions were employed, and the cross sections were calculated in a close-coupling approximation for impact energies ranging from near threshold to 10 keV. Coupling between the n=2 and n=3 excitation levels was generally found to be weak, and a two-state close-coupling approximation should be adequate for calculating reliable cross sections for most transitions.

The distribution of excitation energy for the ${\mathrm{H}}_2$(v=0, j=0,1)→${\mathrm{H}}_2$${\mathrm{}}^{2+}$ process has been measured by the technique of double charge transfer, and is compared with the results of a Franck-Condon calculation. It is shown that this calculation accurately describes double ionization of ${\mathrm{H}}_2$ by charge transfer apart from a small scale shift.

Minima in the photoionization cross sections (Cooper minima) are known to occur for all types of transitions in atoms, even for dipole transitions from the ground state. These minima are caused by zeros in the transition matrix elements which are, in turn, the result of a zero value for the radial integral of a particular energy. For transitions involving the point Coulomb field there are no zeros in the dipole matrix elements, but there are zeros in higher multipole transitions. The zeros in the quadrupole matrix elements involve transitions between low-angular-momentum bound states and free states with two more units of angular momentum. Zeros in octupole matrix elements fall into two categories. The first involves transitions between low-angular-momentum bound states and free states with three more units of angular momentum and the second involves transitions between all s and p states. In this paper the position (energy) of the zeros in the multipole matrix elements of the point Coulomb field are examined. Why the dipole matrix elements of hydrogen have no zeros and what causes the zeros in the higher-multipole matrix elements are then discussed.

A complete theoretical survey of low-energy photoionization cross sections, angular asymmetry, and spin-polarization parameters for the ground states of the alkali-metal atoms Li, Na, K, Rb, and Cs, including virtual core excitations in a gauge-independent relativistic random-phase approximation (RRPA) is presented and compared with length- and velocity-form Dirac-Fock results and with available experimental data. The ab initio RRPA formulation substantially improves the agreement of cross sections with experiment at energies above the Cooper minimum.