Antisymmetric, radially correlated and LS-coupled hyperspherical channel functions are constructed for an analysis of the dynamics of atomic electrons at high density. A fractional parentage expansion, utilizing analytic transformations between alternative couplings of radial motions, is developed and applied. A program for the construction of states for an arbitrary number of electrons has been developed, and sample results are reported for as many as six electrons with equal orbital quantum numbers, l.

We develop approximate WKB-like solutions to the radial Schrödinger equation for problems with an angular momentum barrier using Riccati-Bessel, Coulomb, and harmonic-oscillator functions as basis functions. The solutions treat the angular momentum singularity near the origin more accurately in leading approximation than the standard WKB solutions based on sine waves. The solutions based on Riccati-Bessel and free Coulomb wave functions continue smoothly through the inner turning point and are appropriate for scattering problems. The solutions based on oscillator and bound Coulomb wave functions incorporate both turning points smoothly and are particularly appropriate for bound-state problems; no matching of piecewise solutions using Airy functions is necessary.

The Fermi-Segrè formula, which relates the value of a normalized S-state radial wave function at the origin to the derivative ${\mathrm{dE}}_n$/dn of the bound-state spectrum in a Schrödinger problem, has been used extensively in problems in atomic and quarkonium physics. The extensions which have been proposed for angular momenta l>0 are quite inaccurate for large l for the confining potentials typical of the quarkonium system. We derive modified formulas for arbitrary l which remove this difficulty.

Ground-state dissociation energies $D_e$ and equilibrium distances $R_e$ for the series of homonuclear alkali-metal diatomic molecules ${\mathrm{Li}}_2$,${\mathrm{Na}}_2$,..., as well as those for six heteronuclear alkali-metal diatomic compounds, are evaluated on the basis of a simple valence-bond model. Each alkali-metal atom in a diatomic molecule is characterized by two quantities: a Gaussian parameter ${\beta }_e$ of the valence-electron function and a valence-to-core ‘‘relative-size’’ parameter γ≡(${\beta }_c$/${\beta }_e$${)}^2$, with ${\beta }_c$ the Gaussian parameter for the core-electron charge distribution. For the homonuclear diatomic molecules, accurate results are obtained with a 2s Gaussian valence function ($r^2$-$a^2$)G orthogonalized to the core. For each homonuclear diatomic molecule there exists an optimal (${\beta }_e$,γ) set yielding values of $D_e$ and $R_e$ in practically quantitative agreement with experiment. The quantities ${\beta }_e$ and γ exhibit the expected physical behavior over the series in that ${\beta }_e$ decreases from ${\mathrm{Li}}_2$ to ${\mathrm{Cs}}_2$, and γ is highest for the lightest diatomic molecule ${\mathrm{Li}}_2$. The compounds ${\mathrm{K}}_2$, ${\mathrm{Rb}}_2$, and ${\mathrm{Cs}}_2$ are found to be ‘‘Heitler-London’’ molecules to within 5% of their binding energies. An approximate, similar, analysis of six heteronuclear diatomic compounds yields close agreement with experiment for LiNa and RbCs, whereas with the other four compounds (LiK, NaK, NaRb, and NaCs) the agreement with experimental $D_e$ and $R_e$ is to within at most 5%. Also RbCs is a ‘‘Heitler-London’’ molecule to a very good approximation.

We introduce a gauge-invariant Wigner operator (GIWO) and a gauge-independent Wigner function (GIWF) that allow for both quantized and classical electromagnetic fields. If only classical fields are present, a Weyl transform analogous to the one associated with ordinary Wigner functions can be defined for any operator; in the case of quantized fields this is at least possible for Weyl-ordered functions of the position and kinetic momentum operators. We show how the evolution of the operators having a Weyl transform can be followed with the aid of the GIWF defined as the Heisenberg-picture expectation value of the GIWO, and derive for the GIWO the Heisenberg equation of motion which only involves the physical electric and magnetic fields. Some aspects of the case of entirely classical fields are discussed in more detail. (i) The GIWF in conjunction with the postulate that physical observables can be measured without referring to the gauge permits a quantum-mechanical treatment of a full experimental run without the problem of relating the measured values to the gauge-dependent density operator. (ii) A closed equation of motion for the GIWF is obtained. (iii) In the dipole approximation quantum features of the dynamics are lost. (iv) Quantum corrections to dynamics are associated with recoil effects.

A diagrammatic analysis is presented of the electronic correlation in second-order time-dependent molecular properties. It is shown that the solution of the first-order time-dependent perturbation equation in a configuration-interaction (CI) basis will give considerable errors, when the basis is truncated at the singly and doubly excited-state CI level and unperturbed orbitals are used. This is due to the occurrence of unlinked clusters for which correction formulas are derived in the present paper. The theory is illustrated by calculations on the Ne atom and the ${\mathrm{Ne}}_2$ dimer. Cluster-corrected polarizabilities and dispersion coefficients are compared with values obtained in large CI bases containing triply excited states.

Extensive variational calculations on the ${}_{}{}^2{}_{}{}^{}\mathrm{S}$ ground state of the lithium atom are reported. With use of a 352-term Hylleraas-type expansion, the nonrelativistic ground-state energy of ${}_{}{}^2{}_{}{}^{}\mathrm{S}$ Li i is determined to be -7.478 058 a.u., which lies approximately 3 ${\mathrm{cm}}^{\mathrm{-}1}$ above empirical estimates of the nonrelativistic ground-state energy. This variational upper bound to the ground-state energy is the lowest to our knowledge reported to date in the literature. A number of expectation values, including the individual energy terms, the Fermi-contact interaction, the electron density at the nucleus, and the moments 〈$r_i^n$〉, n=1–3, and 〈$r_{\mathrm{ij}}^n$〉, n=1,2, are also evaluated. The general rates of convergence of the calculation are discussed. The role played by the two doublet spin eigenfunctions is examined, and the importance of including both of these functions for the accurate calculation of the Fermi-contact interaction is discussed.

We analyze the sensitivity of parity experiments in singly ionized helium to the weak neutral-current interaction between electrons and nucleons. Such experiments could eventually provide measurements of the radiative corrections to the weak neutral-current coupling constants and precision measurements of the Weinberg angle. Some new ‘‘quasioptical’’ techniques for measuring parity nonconservation are discussed, and these appear to be particularly suitable for parity experiments in ${\mathrm{He}}^{+}$. The problem of systematic effects caused by unwanted electric fields is considered, and the effect of electric fields arising from motion of ${\mathrm{He}}^{+}$ ions transverse to a magnetic field is analyzed in detail.

Distorted-wave methods for electron capture are discussed with emphasis on the surface term in the T matrix and on the properties of the associated integral equations. The surface term is generally nonvanishing if the distorted waves are sufficiently accurate to include parts of the considered physical process. Two examples are considered in detail. If distorted waves of the strong-potential Born-approximation (SPB) type are employed the surface term supplies the first-Born-approximation part of the T matrix. The surface term is shown to vanish in the continuum-distorted-wave (CDW) method. The integral kernel is in either case free of the dangerous disconnected terms discussed by Greider and Dodd but the CDW theory is peculiar in the sense that its first-order approximation (CDW1) excludes a specific on-shell portion of the double-scattering term that is closely connected with the classical Thomas process. The latter is described by the second-order term in the CDW series. The distorted-wave Born approximation with SPB waves is shown to be free of divergences. In the limit of asymmetric collisions the DWB suggests a modification of the SPB approximation to avoid the divergence problem recently identified by Dewangan and Eichler.

We propose a direct iterative-variational scheme to solve the large sets of coupled integro-differential equations that arise in a variety of atomic and molecular scattering problems. The method, which is similar to direct configuration-interaction schemes of quantum chemistry, is applied within the linear algebraic (LA) prescription and involves the construction of an orthonormal basis from successive applications of the general LA matrix, labeled by channels and mesh points, to an initial guess for the solution vector. The solution vector is expanded in this basis, and the linear coefficients determined by a variational scheme. Since the basis is orthonormal, the procedure is guaranteed to converge within n iterations, where n is the order of the matrix. For all cases treated, the convergence is much more rapid. In addition, since a direct method is employed, only the potential, Green’s function, and solution vector need be stored. This formulation drastically reduces the central storage requirements of the LA method as well as improves the solution times since the integrals involved can be constructed from recursion relations. We apply the method to elastic scattering of electrons by ${\mathrm{N}}_2$ and LiH as well as inelastic collisions from ${\mathrm{H}}_2$${\mathrm{}}^{+}$.

The linear-algebraic method for electron-molecule scattering is generalized to treat inelastic collisions involving a set of primary coupled channels. The coupling between these channels is expanded in separable form using a set of Cartesian Gaussian functions. As a consequence of the separable expansion, we need only to solve a set of uncoupled, homogeneous and inhomogeneous equations in each channel to obtain the basis in which the final solution is expanded. The separable form of the coupling allows the physical solution to be obtained with use of the matrix elements of the interaction and the overlap integrals between the solutions and the basis used for the separable expansion. The method is applied to inelastic scattering from H, He, ${\mathrm{H}}_2$${\mathrm{}}^{+}$, and ${\mathrm{H}}_2$. Comparison with exact solutions of the close-coupling equations indicates that the method is quite accurate, provided that the basis set used in the separable expansion is flexible enough to span the interaction region.

It is demonstrated with the example of an atomic-physical model potential that the performance of the approximation method for determining resonances, based on a separable expansion of the potential (PSE method), is comparable with that of the Siegert method and of the complex rotation technique. In fact, it is shown that when converged, the PSE method with a real harmonic-oscillator wave-function basis is equivalent to the complex variational method with a trial function set containing a Siegert function; if the potential is dilation analytic the PSE method with a complex oscillator wave-function basis amounts to solving the complex rotated Schrödinger equation with the real PSE method and rotating back the obtained wave function. The results are tested against those yielded by direct numerical integration and against the complex virial theorem.

The differential cross section of the 3 ${\mathrm{}}^1$P ($m_l$=0) state in helium is investigated for scattering angles up to 50° for electrons with an incident energy of 70 eV. This is done by detecting the inelastically scattered electrons in coincidence with the 501.6-nm photons that are emitted when this state decays to the 2 ${\mathrm{}}^1$S state. The photon detector has a nonpolarizing filter and is located in the scattering plane at right angles to the incident beam. For this geometry, the data will yield a relative differential cross section for the 3 ${\mathrm{}}^1$P ($m_l$=0) state. The results are compared with several theories. It is found that the present results agree best with the excited-state model of a distorted-wave Born approximation by Madison.

We have calculated the total energy loss of an incident electron or positron due to the bremsstrahlung radiation from various atoms during a scattering. The kinetic energies considered for the incident electrons and positrons were 10, 50, and 500 keV. The calculations were performed with our relativistic partial-wave multipole-expansion numerical code [H. K. Tseng and R. H. Pratt, Phys. Rev. A 3, 100 (1971)]. The differences between the radiative energy loss of positrons and electrons are considerable and cannot be disregarded. We observe that the ratio of the radiative energy loss for positrons to that for electrons obeys a simple scaling law, being expressible fairly accurately as a function only of the quantity $T_1$/$Z^2$, where $T_1$ is the incident-particle kinetic energy and Z is the atomic number of the scatterer. This scaling law makes it possible to obtain the energy loss for positrons from existing electron bremsstrahlung data. The scaling is exact in the case of the point Coulomb potential, both in the classical bremsstrahlung formula and the nonrelativistic dipole Sommerfeld formula, not only for the ratio of total energy losses but also for the separate energy losses and even for the radiation energy spectrum. In the screened case scaling is significantly broken for the spectrum and for the total energy loss but remains fairly good for the ratio of the total energy losses. We will discuss scaling features of bremsstrahlung radiation energy loss and the behavior for both high and low energies.

Multiple-vacancy production in Ar atoms by 1.4-MeV/u highly stripped ion impact is studied. From a recoil-ion–projectile-ion coincidence experiment charge-state distributions of Ar ions were obtained distinguishing between pure ionization and capture of up to three electrons by ${\mathrm{N}}^{6+}$,7+, ${\mathrm{Fe}}^{12+}$,15+,20+,21+, ${\mathrm{Kr}}^{18+}$, ${\mathrm{Gd}}^{37+}$, and ${\mathrm{U}}^{30+}$,36+,41+,44+,4 ${}_{}{}^{8+}{}_{}{}^{}$ ions. With increasing projectile charge state the relative abundances of multiply charged recoil ions increase. However, for high-charge-state projectiles, the relative fractions of recoil ions for concomitant electron capture and ionization are found to be independent of projectile charge or species. To interpret the data, classical trajectory Monte Carlo calculations have been made assuming the applicability of the independent-electron model. The calculations indicate the dominant electron capture is from the L-shell of Ar while the ionization process includes both the L- and M-shell electrons. The use of a common ionization potential inherent in the application of the independent-electron model is not adequate for the high degrees of ionization obtained in the investigated collisions; the cross sections for the production of high recoil-ion charge states are overestimated. Nevertheless, the calculated total cross sections for ionization and electron capture are in reasonable agreement with the available experimental data.

X rays from an Al target bombarded with protons of 0.5, 0.75, and 1.0 MeV/amu and α particles of 0.5 MeV/amu were measured with a Si(Li) detector. Production cross sections and spectra of the continuum radiation were obtained in the x-ray energy region of 2–6 keV and were compared with theoretical predictions for atomic bremsstrahlung (AB), secondary-electron bremsstrahlung, radiative ionization, and nuclear bremsstrahlung. Good agreement between theory and experiment is obtained. It is shown that in the region of bombarding energy less than 1.0 MeV/amu, atomic bremsstrahlung is the most predominant process. The $Z_p^2$ dependence of the AB production cross section, $Z_p$ being the projectile charge, is experimentally confirmed, and the angular distribution of AB measured for 0.5-MeV/amu protons is found to be symmetric about 90° with respect to the incident beam, in agreement with the theoretical prediction.

We have used collinear fast-beam–laser fluorescence spectroscopy to obtain precise measurements of the fine structures and absolute wavelengths of the 1s2s ${\mathrm{}}^3$S–1s2p ${\mathrm{}}^3$P transitions in ${}_{}{}^7{}_{}{}^{}\mathrm{i}\mathrm{i}$. Our results are about 50 times more accurate than the best nonrelativistic calculations for these energy differences, and they have a precision equivalent to 150 ppm of the QED corrections for the 2s-2p transitions.

Isolated-multipole-moment photon-echo techniques for atomic collision studies are described and analyzed. The techniques employ three-pulse photon echoes observed in a polarization rotation configuration such that the echo intensity depends on the square of an isolated J=1 multipole moment for which the velocity-changing kernel is diagonal. This scheme is applied to resolve clearly classical and wave-mechanical features of ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ orientation kernels for ${}_{}{}^{174}{}_{}{}^{}\mathrm{gas}$ scattering. The diagonality (in the sense to be described) of the one-dimensional kernels chosen for study is discussed physically and derived in detail.

The partial cross sections for production of slow recoil ${\mathrm{Ar}}^{\mathrm{i}+}$ ions in 1.05-MeV/amu ${\mathrm{Ne}}^{\mathrm{q}+}$ (q=2,7–10) and ${\mathrm{Ar}}^{\mathrm{q}+}$ (q=4,6,10–14) -ion impact have been determined. It is confirmed that the partial cross sections are dependent upon the charge state q of ${\mathrm{Ne}}^{\mathrm{q}+}$ and ${\mathrm{Ar}}^{\mathrm{q}+}$ ions but not significantly on the projectiles themselves. The measured partial cross sections were compared with the independent-electron approximation for low-charge-state recoil ions which were produced in collision with large impact parameters and with the ‘‘compound atom’’ model for high-charge state of the recoil ions which were produced in relatively close collisions. Experimental data were appreciably well reproduced by the combination of the approximation and the model.

Potential scattering of electrons in a strong laser field is reconsidered. The laser beam is described by a quantized single-mode plane-wave field with a finite number of quanta in the mode. The scattering amplitude is expanded in powers of the potential, and the first two Born terms are considered. It is shown that in the limit of an infinite number of field quanta, the Kroll-Watson approximation is recovered. Additional insight is gained into the validity of this low-frequency theorem. The approach rests on the introduction of electron-dressed quantized-field states. Relations to earlier work are indicated.