A simple example of a "gauge transformation" for trial functions used in the Kohn method is presented. Under this transformation the Kohn-method answer remains invariant while the optimized value for the phase shift of the trial function becomes completely arbitrary. Thus the only important quantity may be $ktan\delta -\int \psi \mathrm{}(H-E)\mathrm{}\psi dr$, and no special significance should be attached to $ktan\delta$.

The Fourier transform $p\left(\omega \right)$ of the velocity-autocorrelation function is derived from neutron incoherent scattering results, obtained from the two liquids Ar and ${\mathrm{H}}_2$. The quality and significance of the results are discussed with special emphasis on the long-time $t^{-\frac{3}{2}}$ tail, found in computer simulations and recent theories. The available experimental data from Na, Ar, and ${\mathrm{H}}_2$ close to their normal melting points are consistent with calculations which take into account the contribution to $p\left(\omega \right)$ from the tail at low frequencies.

An analytic expression is given for screened continuum radial wave functions which extends our previous results to the case of arbitrary energy shift.

A new kind of saturation spectroscopy is discussed in which the direction and polarization of a nonsaturating probe wave is varied with respect to that of a saturating wave. Angular momenta, Landé $g$ values, and atomic lifetimes are obtained with greater ease than with earlier Zeeman laser methods. In particular, the theory is dramatically simplified.

The discharge emission spectrum in the visible and near IR from Cs or Rb vapor mixed with Xe, Kr, or Ar (of density ≳ 1 amagat) is studied. For a heavy noble gas at high density, the discharge spectrum features strong emission bands from alkali-noble-gas excited molecules correlated with the lowest $S$ or $D$ excited states, or with $P$ excited states, of the alkali atom. The emission bands are remarkably similar to the laser-excited emission bands reported previously.

It is pointed out that inclusion of the effects of higher multipole transitions leads to an asymmetry in the angular distribution of the two-photon decay spectrum of metastable hydrogen.

Inelastic electron scattering off of simple atoms is studied for collisions where the momentum transferred ($q$) from the incident electron to the atom is larger than the normal momenta of the bound electrons. We discuss the direct part of the scattering for collisions where the atom is excited to another bound state. In lowest order the second Born term, which dominates the scattering amplitude, factors into two parts. One part ($\frac{1}{q^2}$) displays a Rutherford-like scattering off the nucleus; the other factor gives the response of the atom to the presence of the impinging electron. The second Born scattering amplitudes for $1s\to 2s$ and $1s\to 2p$ electron-hydrogen scattering and $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ electron-helium scattering for large-momentum-transfer collisions are calculated.

The absolute $K$-shell ionization probabilities of Pb at very small impact parameters by 25-, 40-, and 74-MeV $\alpha$ particles are measured in an $\alpha$-x-ray coincidence experiment, using the slight inelasticity of the scattered $\alpha$ particles. Ionization probabilities are (1.9 ± 0.4) × ${10}^{-4\mathrm{}}$, (4.9 ± 1.7) × ${10}^{-4\mathrm{}}$, and (11 ± 3) × ${10}^{-4\mathrm{}}$ at 25, 40, and 74 MeV, respectively. Semiclassical calculations, using relativistic electron wave functions and corrections for Coulomb deflection effects, agree very well with the data. Possible quantitative studies of atomic distortion effects are suggested.

Close-coupling cross sections for the electron-impact parity-unfavored transition ${}_{}{}^3{}_{}{}^{}P{\left(2\mathrm{}p\right)}^2\leftarrow {}_{}{}^1{}_{}{}^{}S{\left(1\mathrm{}s\right)}^2$ in helium are calculated in an integral equation approach. At an energy 0.11 eV above threshold the present formalism yields a cross section of $1.55\times {10}^{-4\mathrm{}}{a}_0^2$ which is in good agreement with experiment. Our calculated slope at this energy is 6 × ${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$/eV against an experimental value of 4 × ${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$/eV. The present cross sections satisfy the threshold law for parity-unfavored transitions. A Born-Oppenheimer (BO) calculation is also performed, and it is found that near threshold BO cross sections are too small in comparison with experimental results. The dependence of BO cross sections on the choice of atomic wave functions is also examined.

Absolute differential scattering cross sections have been determined for single and double electron-capture collisions of 0.5- to 2.5-keV ${\mathrm{D}}^{+}$ and ${\mathrm{D}}^0$ in Cs vapor. Integration of the differential cross section over the scattering angles yielded the total electron-capture cross sections. Angular distributions were peaked in the forward direction, and the angular width increased as the particle energy decreased. Cross sections for both single and double capture processes decreased with increasing energy.

Absolute differential cross sections for stripping of hydrogen and deuterium atoms in nitrogen have been investigated in the energy range 0.5 to 2 keV for hydrogen and 1.03 to 4.12 keV for deuterium. The interactions were observed over scattering angles from 0 to 9°. Total cross sections for these processes were calculated by integration of the experimentally determined differential cross sections. Angular distributions were identical in shape for both ${\mathrm{D}}^{+}$ and ${\mathrm{H}}^{+}$ but different in magnitude at the same center-of-mass energy. The integrated cross sections were equal at equal velocities. The total H stripping cross sections were approximately 30% higher than those reported in previous work.

Absolute differential cross sections for the production of ${\mathrm{D}}^{-}$ and ${\mathrm{D}}^0$ + ${\mathrm{D}}_2^0$ have been determined for single and double electron-capture collisions into dissociative states by 1.0- to 5.0-keV ${\mathrm{D}}_2^{+}$ in Cs vapor. Integrations of the differential cross sections over the angles yield the total cross sections for the production of ${\mathrm{D}}^{-}$ and ${\mathrm{D}}^0$ + $\mathrm{D}_2^{}{}_{}{}^0$. A theory has been developed of the angular distributions of dissociation fragments resulting from electron capture into dissociative states of diatomic molecular systems. Predictions are made that the angular distribution $\frac{d{\sigma }_f}{d\omega }$ of any fragment $f$ should scale as $E_i^{}{}_{}{}^{-1\mathrm{}}\frac{d{\sigma }_f}{d\omega }=f\left(E_i{\theta }^2\right)$, where $E_i$ is the incident energy of the diatomic molecular ion. The observed distributions fit this scaling law. An interesting structure is found at 23.5 keV ${\mathrm{deg}}^2$, which yields information about the dependence of the electron-capture cross section on the internuclear separation of the incident molecular ion during the interaction time.

The role of electron-electron interaction beyond the restricted Hartree-Fock approximation, particularly the exchange core polarization effect, is shown to be crucial for explanation of the experimentally measured hyperfine interaction in the ($1s^{2}2s;{}_{}{}^2{}_{}{}^{}S$) state of the lithium like stripped fluorine atom (${\mathrm{F}}^{+6\mathrm{}}$). Results are presented for the entire series of such atoms from ${\mathrm{Li}}^0$ to ${\mathrm{Ne}}^{+7\mathrm{}}$ and for the excited ($1s^{2}3s;{}_{}{}^2{}_{}{}^{}S$) and ($1s^{2}2p;{}_{}{}^2{}_{}{}^{}P$) states of ${\mathrm{F}}^{+6\mathrm{}}$. The significance of the trends in these hyperfine constants is discussed. A prediction is made of the hyperfine constant in the ground electronic state of sodium like ${\mathrm{Ca}}^{+9\mathrm{}}$, which is amenable to time-of-flight measurements.

The three-body bound-state problem with Coulomb forces is solved in the Feshbach-Rubinow approximation. Analytical expressions for the ground-state energy and wave function are obtained, and numerical results are presented for heliumlike atoms.

The absolute cross section for production of atomic Balmer $\alpha$, $\beta$, and $\gamma$ radiation by dissociative electron collisions with molecular hydrogen and molecular deuterium has been measured from threshold to 540 eV. Also measured are some absolute cross sections for the excitation of a few molecular lines. All of the cross sections for dissociation show some structure just above threshold. Below this structure, dissociative excitation is interpreted as proceeding through both predissociation and direct dissociation via a bound state above the dissociation limit of the molecule. Above this structure, dissociation proceeds through production of the unbound doubly excited ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ states of ${\mathrm{H}}_2$. It is also argued that excitation of these doubly excited states is the major channel for production of excited atomic states in addition to being the major channel for production of protons by electron collisions with the molecule. Indeed its relative contribution increases with an increase of the principal quantum $n$. This contribution follows an inverse power law of 5.0 ± 0.5. Dissociation via the bound states depends on $n$ with an inverse power law of 6.5 ± 1.0. The cross sections for production of excited deuterium atoms were found to be less than those for production of excited hydrogen atoms in the corresponding states, and the ratio varied from ∼ 0.5 below 30 eV to ∼ 0.82 at high energies, again indicative of three competing processes for dissociative excitation of the molecular target gas.

A Glauber approximation to the scattering amplitude for the direct inelastic scattering of structureless charged particles by ion targets is derived and applied to inelastic scattering by hydrogenlike ions with arbitrary nuclear charge. The $1s\to nlm$ Glauber scattering amplitudes are evaluated in closed form as simple sums of Meijer $G$ functions. The asymptotic behavior of these amplitudes is examined for both large and small momentum transfers, and for the limit of infinitely large nuclear charge.