The molecular-state expansion method within the impact-parameter formalism is applied to the processes ${\mathrm{H}}^{+}$+He(1$s^2$) →H(nl)+${\mathrm{He}}^{+}$(1s) and ${\mathrm{H}}^{+}$+He(1$s^2$) →${\mathrm{H}}^{+}$+He(1s,2l). Electron translation factors are incorporated into the scattering wave function, so that the cross sections obtained are free from the origin dependency. It is shown that stepwise flux promotion is the primary mechanism for excitation and electron capture into excited states at lower energies, and hence it is necessary to include all these channels in the close-coupling method to achieve reliable results.

The infinite set of coupled equations in the adiabatic hyperspherical representation of two-electron correlated states is solved in the asymptotic region. The solution reveals that the longest-range couplings represent a partial transformation to independent-electron coordinates. Simple corrections to the phase shifts of ${\mathrm{H}}^{\mathrm{-}}$ are obtained. Adiabatic and corrected phase shifts in the monopole approximation are compared with the Hartree-Fock phase shifts. Good agreement is obtained. The correction is applied to previously reported adiabatic phase shifts.

New precise measurements for positron-helium absolute total cross sections have been performed over the energy range from 0.6 to 22 eV. A high-resolution time-of-flight spectrometer with a straight flight tube and weak axial magnetic field was designed to achieve effective reduction of forward-scattering errors. Observed results around the Ramsauer-Townsend minimum are close to the theoretical results by Campeanu and Humberston, and the remaining slight discrepancies are fully explained by taking account of incomplete discrimination against forward scattering. The results for the energy region excluding the vicinity of the minimum have been obtained with a few percent overall errors, and they are in excellent agreement with some theoretical results. The sources of systematic errors associated with the use of an axial magnetic field are clearly assessed.

A low-frequency approximation for the bremsstrahlung transition amplitude is derived for a relativistic electron scattered by a central potential which is Coulombic at great distances. The Coulomb tail is shown here to have the effect of introducing correction terms, not present in previous relativistic treatments, which depend logarithmically on the photon frequency. The approximation procedure, in the form presented here, is based on the fact that at low frequencies the dominant contribution to the matrix element comes from the domain where r, the electron distance from the scattering center, is large. An asymptotic representation of the Dirac wave function is derived which includes a correction term of relative order 1/r compared to the leading term. This enables us to include a correction to the matrix element of relative order k, where k is the photon wave number. The essential feature of the low-frequency approximation, present in previous versions, is preserved here. That is, the result is expressed in terms of the physical amplitude, A, for scattering in the absence of any radiative interaction. Another potentially useful feature of the present version is that it involves angular derivatives of A, not energy derivatives, and should therefore remain valid in a region where A varies rapidly with energy.

Much of the recent activity in electron-atom and electron-molecule collision problems has been concerned with the effective use of discrete-basis-set ($L^2$) methods. In this note we study the $L^2$ expansion for a number of different operators which appear in the scattering equations in order to ascertain the performance of such approaches in model problems. The potentials used in the study were not assumed to be of short range although the solution of the scattering problem was sought over a finite region of configuration space. The results of our calculations show that the Schwinger form of the separable potential is best for the problems studied. The standard separable expansion also works well, while the $L^2$ expansion of the Green’s function is quite poor.

Cross sections for single and double ionization ${\sigma }^{i1}$ and ${\sigma }^{i2}$, the single and double electron capture to the ground state ${\sigma }^{c1}$ and ${\sigma }^{c2}$, and the ionization with electron capture to the ground state ${\sigma }^{\mathrm{ic}}$ in collisions of ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, and ${\mathrm{Li}}^{3+}$ nuclei with He atoms at nuclei energies from 0.025 to 4 MeV/amu are calculated. The independent-electron approximation is used with probabilities that are unitarized at the lower energies. Two kinds of calculations are performed: (i) The cross sections for all charge-changing processes are calculated including both the ionization and capture channels; (ii) the ionization cross sections ${\sigma }^{i1}$ and ${\sigma }^{i2}$ are calculated with neglect of the capture channel, the capture cross sections ${\sigma }^{c1}$ and ${\sigma }^{c2}$ are calculated with neglect of the ionization channel, and the cross sections ${\sigma }^{\mathrm{ic}}$ for ionization with capture are calculated with the single-electron transition probabilities obtained separately for ionization and capture. The direct-ionization calculations are based on the semiclassical Coulomb approximation, and electron capture is calculated with use of the approximation of Bassel and Gerjuoy [Phys. Rev. 113, 749 (1960)]. The calculation results show that in single and double ionization the capture to the ground state strongly affects the value of ${\sigma }^{i1}$ and ${\sigma }^{i2}$ only in collisions of He atoms with the ${\mathrm{He}}^{2+}$ nuclei whereas the ionization channel leads to a marked decrease of the cross sections ${\sigma }^{c1}$ and ${\sigma }^{c2}$ in collisions with the ${\mathrm{He}}^{2+}$ and ${\mathrm{Li}}^{3+}$ nuclei.

Total single-electron-capture cross sections for ${\mathrm{H}}^{+}$ from hydrocarbons [${\mathrm{CH}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_2$, ${\mathrm{C}}_2$${\mathrm{H}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_6$, (${\mathrm{CH}}_2$${)}_3$, ${\mathrm{C}}_3$${\mathrm{H}}_6$, ${\mathrm{C}}_3$${\mathrm{H}}_8$, ${\mathrm{C}}_4$${\mathrm{H}}_8$] and the oxide (CO, ${\mathrm{CO}}_2$, ${\mathrm{O}}_2$) and fluoride (${\mathrm{CF}}_4$, ${\mathrm{C}}_2$${\mathrm{F}}_6$, ${\mathrm{C}}_4$${\mathrm{F}}_8$, ${\mathrm{SF}}_6$) gases, as well as Ne, have been measured in the projectile energy range 0.8–3.0 MeV. For comparison at 0.8 MeV/u, electron-capture cross-section measurements for 3.2-MeV ${\mathrm{He}}^{+}$ were also made on most of these same gases. These systematic measurements display additivity failure in each ${\mathrm{C}}_{\mathrm{m}}$${\mathrm{X}}_{\mathrm{n}}$ molecular species. A simple geometrical model, used to estimate intramolecular electron-loss probabilities, allowed extraction of ‘‘atomic’’ ${\sigma }_{10}$ values for C, O, F, and S at each projectile energy. These extracted cross sections generally agreed well with total bound-state electron-capture calculations, corrected for the projectile’s energy loss and Coulomb deflection, target electron-shell binding and polarization, and relativistic effects.

The effect of final-state interactions on the photodetachment cross section of negative ions in a magnetic field is discussed. Experiments on the location of the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ threshold in ${\mathbf{S}}^{-}$ as a function of magnetic field show clearly the effect of the zero-point energy of an electron in a magnetic field. The experiments also give a precise value for the electron affinity and provide information about the interaction between the atom and the detached electron.

Electron-velocity distribution functions have been calculated for electrons moving in a gas under the influence of an electric field. By assuming a differential scattering cross section such that scattering is entirely at 0° and 180°, it is shown analytically that the electron drift velocity w, the mean electron energy 〈ε〉, the transverse diffusion coefficient $D_T$, and the longitudinal diffusion coefficient $D_L$ are not, in general, determined by the momentum-transfer cross section alone. The magnitude of the errors incurred by neglecting the higher-order terms in the spherical-harmonic expansion of the velocity distribution function for this collision model are indicated. Velocity distribution functions have also been calculated for attaching gases. It is found that the velocity distribution function can be considerably altered by attachment for pure gases and gas mixtures. Consequently, any attempt to determine collision cross sections from electron-swarm measurements of w, $D_T$, and $D_L$ in attaching gases should include attachment processes in the solution of the Boltzmann equation. The magnitude of this dependence has been found to be determined largely by the ratio of the attachment collision frequency to the energy-transfer collision frequency and the velocity dependences of the momentum transfer and attaching collision frequencies.

Charge-transfer (sublevel) cross sections for ${\mathrm{He}}^{2+}$+H collisions have been calculated in the 20-eV–to–10-keV center-of-mass energy region. Both a time-independent quantum-mechanical close-coupling method (20–500 eV) and a semiclassical impact-parameter method (0.1–10 keV) were used. The close-coupling formalism is developed in terms of a molecular-state description of the ${\mathrm{HeH}}^{2+}$ system and is extended to include both radial and rotational couplings. The potentials and radial and rotational couplings for the 2sσ, 2pσ, 3dσ, and 2pπ molecular states were computed by expressing the molecular orbitals as variationally determined linear combinations of Slater-type orbitals centered at the atoms. Common molecular-electron translation factors were introduced to ensure proper asymptotic behavior of the wave functions and were found to be crucial for agreement between calculated and experimental cross sections. The usual practice of compensating for the neglect of these factors by using couplings evaluated at an atomic origin rather than at the center of mass of the nuclei is analyzed. Quantum-mechanical and semiclassical results are compatible only if Coulomb trajectories instead of straight-line trajectories are used. In particular the sublevel cross section for ${\mathrm{He}}^{+}$(2${\mathrm{p}}_{\pm 1}$) production is found to be extremely sensitive to the trajectory. At all energies above 50 eV radial and rotational couplings are about equally important. Below 100 eV cross sections fall off rapidly, and radiative charge transfer becomes the dominant process below 25 eV.

Relativistic corrections to the nonrelativistic Bethe-Bloch formula for the stopping power of matter for charged particles are traditionally computed by considering close collisions separately from distant collisions. The close-collision contribution is further divided into the Mott correction, appropriate for very small impact parameters, and the Bloch correction, computed for larger values. This division of the region of close collisions leads to a very cumbersome result if one generalizes the original Bloch procedure to relativistic energies. We avoid the resulting poorly specified scattering angle ${\theta }_0$ that divides the Mott and Bloch correction regimes by using the procedure suggested by Lindhard and applied by Golovchenko, Cox, and Goland to determine the Bloch correction for relativistic velocities.

In previous papers formulas for mean wave numbers and spectral widths of transition arrays have been presented. Here the method is extended to the cases ${\mathrm{nl}}^N$n’$l_{j\mathcal{’}}^{\mathcal{’}}$-${\mathrm{nl}}^N$n’’$l_{j\mathcal{’}\mathcal{’}}$ ${}_{}{}^{2\mathrm{sprime}}{}_{}{}^{}$, (${\mathrm{nl}}_j$${)}^N$ n’’$l_{j\mathcal{’}\mathcal{’}}^{2\mathrm{sprime}}$, and (${\mathrm{nl}}_j$${)}^{N+1\mathrm{}}$-(${\mathrm{nl}}_j$${)}^N$n’$l_{j\mathcal{’}}$ ${}_{}{}^{\mathcal{’}}{}_{}{}^{}$, i.e., when the spectrum exhibits several subarrays, due to the effects of large spin-orbit interactions. The first case is typical of the x-ray transitions between the internal subshells of the atom. The second and the third cases occur in the vuv and x-ray spectra of highly ionized heavy atoms. The evolution of the array 3$d^8$4s-3$d^8$4p along the isoelectronic sequence is presented as a first example of calculation, and criteria for the choice of the relevant formula are proposed. A second example is that of the 3$d^9$-3$d^8$4p array in the spectrum of tungsten. Formulas are given (in the Appendices) for the total intensities of subarrays and for the variances of the distribution of energy levels in subconfigurations of the types ${\mathrm{nl}}^N$n’$l_{j\mathcal{’}}^{\mathcal{’}}$ and (${\mathrm{nl}}_j$${)}^N$(n’$l_{j\mathcal{’}}^{\mathcal{’}}$${)}^{N\mathcal{’}}$.

Synchrotron radiation was directed at neon gas, creating ${\mathrm{Ne}}^{+}$ ions in ‘‘satellite’’ states characterized by the configurations 1$s^2$2$s^2$2$p^4$nl, in addition to the main-line final states: 2$s^{\mathrm{-}1}$ and 2$p^{\mathrm{-}1}$. Satellite features appearing in the photoelectron spectrum were studied in the near-threshold region with photon energies from 55.2 to 99.7 eV. For three of the satellite peaks, the angular-distribution-asymmetry parameter ${\beta }_i$ varies with kinetic energy in much the same way as the asymmetry parameter of the 2p line. None of the satellites have a ${\beta }_i$ like that of the 2s line. All the satellite partial cross sections ${\sigma }_i$ have a kinetic-energy dependence similar to the partial cross section of the 2p main line. However, the ${\sigma }_i$ curves are not identical, and some deviation from the 2p intensity behavior is observed. These ${\beta }_i$ and ${\sigma }_i$ results are used to confirm the previous assignments of the satellite final states in neon and to consider, in general, the energy-dependent behavior of satellites near threshold.

We report high-precision measurements of the lifetimes and collisional decay parameters of the (4$p^2$) ${\mathrm{}}^1$D and (4s5d) ${\mathrm{}}^1$D states of atomic calcium using the two-photon Hanle effect. Modification of the excited-state decay rates due to saturation of the two-photon transition is clearly observed. Spontaneous-emission rates of the possible dipole transitions from these states are deduced through branching-ratio measurements and compared with theory. The (4s4d${)\mathrm{}}^1$D lifetime is determined through observation of its exponential decay.

Fine-structure intervals have been measured for the J=(1/2), (3/2), and (5/2) levels of the doubly excited 1s2s2p ${}^4$$P^O$, and 1s2$p^2$ ${}^4$P terms of lithiumlike Ne viii, using fast-ion-beam spectroscopy in the far uv. In addition, lifetimes for the J=(1/2) and (3/2) levels of the upper term were determined, and their comparison with theory shows the importance of choosing for such levels atomic models which include magnetic interactions. Our measurement for the J=(3/2) level of 1s2$p^2$ ${}^4$P is in excellent agreement with a recent relativistic calculation and removes a previous discrepancy between measured and theoretical values for this level.

Photoelectron angular distributions have been studied in resonant multiphoton ionization of barium via J=0 states, in the region where the 6sns ${\mathrm{}}^1$$S_0$ Rydberg series interacts strongly with the 5d7d ${\mathrm{}}^3$$P_0$ doubly excited state. This interaction is dominantly quadrupole and is localized around n=18. The data analysis reveals spin-orbit coupling and strong channel mixing in the continuum.

The Mössbauer resonance absorption line in solids is of narrow, natural width. In viscous liquids the linewidth is broadened by diffusion. In many biological systems—whole cells, membranes, or proteins—at temperatures above the freezing point of the internal water, a superposition of broad and narrow lines is observed. Here, the Mössbauer spectral shapes expected in this new ‘‘phase’’ of proteinic matter are calculated. The calculation is based on the assumption that the unfrozen conformational degrees of freedom of the macromolecules can be described in terms of damped harmonic oscillators acted upon by random forces. The known classical correlation functions for harmonically bound particles in Brownian motion are utilized to calculate the Mössbauer spectra. The theory predicts the following: a spectrum which can be approximated by a superposition of a narrow and a broad line; and a sharp decrease in the total resonance absorption as a function of temperature and asymmetric quadrupole doublets in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ spectra, even when the Debye-Waller factor is isotropic but the damping frequencies are anisotropic. The presented formulas, with only minor changes, are also applicable to the description of neutron quasielastic scattering from systems in which nuclei diffuse in restricted geometries: bound diffusion on surfaces, lamellar systems, ionic polymers, biopolymers, and membranes. Finally, calculated spectra are compared to recent experimental Mössbauer spectra, and the agreement is outstanding. The spectral shape of particles participating in both bound translational and free rotational diffusion is also calculated.

The physical processes leading to laser-induced breakdown of argon in the flux range ${10}^9$${<10\mathrm{}}^{12}$ W/${\mathrm{cm}}^2$ have been analyzed. A model has been developed to predict breakdown thresholds which includes multiphoton ionization of ground-state atoms and electron-impact excitation of 4s and 4p states of Ar followed by photoionization of these states. Important processes that occur when the electron concentration exceeds ${10}^{14}$ ${\mathrm{cm}}^{\mathrm{-}3}$, such as three-body recombination, dimer formation, dissociative recombination, photodissociation, and photoionization of the excited molecular and/or atomic species formed, have been included in a late-time breakdown model in order to determine the channels through which the laser energy is deposited in the gas. Experiments have been carried out with use of a frequency-tripled neodymium-doped yttrium-aluminum-garnet beam with 15-ns pulse length, yielding a breakdown threshold of 3×${10}^{10}$ W/${\mathrm{cm}}^2$ at p=1 atm in good agreement with model predictions. Comparison of theoretical thresholds and thresholds reported in the literature for pulse lengths in the range 0.4–500 ns is presented.

We discuss relations between different jump processes used by us and other workers for the description of external electromagnetic field fluctuations. We show that the shot noise, the random telegraph signal, and the Poisson process are examples of a general class of fluctuations described by the relevant Burshtein-Chapman-Kolmogorov-Smoluchowski equation. We establish general conditions for which all these processes lead to the same atomic response in strong field-atom interactions.

The linewidths and energies of 4d holes (main lines in x-ray photoelectron spectra) are calculated for a number of elements in the range ${}_{70}{}^{}{}_{}{}^{}\mathrm{Yb}$ to ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$, with use of nonrelativistic atomic many-body theory. The nonrelativistic Hartree-Fock frozen-core approximation for one-electron wave functions and Auger energies gives very good agreement with experiment. In the case of 4s and 4p holes, the Auger (in particular, super-Coster-Kronig) energies have to be calculated with inclusion of relaxation and relativistic effects. Combined with frozen-core, nonrelativistic one-electron wave functions, this gives good agreement with experimental energies and widths for 4s and 4p holes in ${}_{80}{}^{}{}_{}{}^{}\mathrm{Hg}$. In conclusion, it is very important to include the effects of two final-state holes on the Auger electron, as well as the polarization response which screens the Auger emission matrix element. This latter effect is largely equivalent to the so-called exchange interaction between the Auger electron and the final-state holes.