When the resonant frequency of a moving helium-neon laser is corrected for relativistic effects, a frequency difference is predicted that varies with the direction of motion of the laser. This predicted frequency shift is shown to be in excellent agreement with the reported results of the 1964 laser experiment of Jaseja and others. The more recent work of Brillet and Hall is also analyzed in terms of this and a related effect.

A new computer program for the evaluation of matrix elements for Morse oscillators is announced. For many purposes the numerical methods used in this program are more convenient than the analytic expressions which have recently been reported.

The calculation of the radial coupling between the nuclear motion and the electronic structure which induces charge transfer at low energy is discussed, and the utility of the force operator form for computing the coupling between large configuration-interaction wave functions is demonstrated. Many properties suggest that such couplings will be useful in constructing the diabatic scattering states; the agreement with available matrix elements computed numerically is excellent.

We have calculated the decay of a metastable hydrogenic ion through the process $2S\to 1S+\gamma$, as a possible source of experiments on weak interactions in atoms. Our results are fairly exhaustive for ions with atomic number up to $Z=20\mathrm{}$ and nuclear spin $I=0\mathrm{}$. We include the effects of applied electric and magnetic fields, and of both $2P_{\frac{1}{2}}$ and $2P_{\frac{3}{2}}$ virtual states. Within this framework, only one of seven possible $P$-odd asymmetries is a likely candidate for experiment, the decay anisotropy of a polarized beam in vacuum. No viable experiments were found using the quench radiation in an electric field.

Our earlier study of the ${\mathrm{H}}^{+}$-Cs collision is extended to the lighter ${\mathrm{H}}^{+}$-alkali-atom systems. The previous one-electron projected-valence-bond approximation is further simplified and improved by the use of an effective screened Coulomb potential to represent the ${\mathrm{alkali}}^{+}$ core. This method is found to reproduce very accurately the results of a complete all-electron calculation performed on the ${\mathrm{}(\mathrm{L}\mathrm{i}-\mathrm{H})\mathrm{}}^{+}$ system. Total cross sections for charge exchange into $\mathrm{H}\mathrm{}(n=2\mathrm{})\mathrm{}$+${\mathrm{alkali}}^{+}$ are obtained from diabatic 7-state close-coupling calculations. The theoretical results nicely agree with the available experimental data for the ${\mathrm{H}}^{+}$-K and -Rb systems. On the other hand, the calculated cross section for ${\mathrm{H}}^{+}$-Na is significantly smaller than the experimental results; possible sources of this discrepancy are discussed.

A comprehensive systematic study of near-resonant charge exchange into ${\mathrm{He}}^{*}\mathrm{}(n=2\mathrm{})\mathrm{}$ levels in ${\mathrm{He}}^{+}$ -alkali-atom collisions is reported. The relevant quasimolecular properties of the ${\mathrm{}(\mathrm{H}\mathrm{e}-\mathrm{a}\mathrm{l}\mathrm{k}\mathrm{a}\mathrm{l}\mathrm{i})\mathrm{}}^{+}$ systems are obtained within the one-electron projected-valence-bond method of Kubach and Sidis. The detailed investigation of the considered systems enables one to assess the relevance of the two-state Demkov model for near-resonant charge exchange and the role of rotational coupling. The present multistate close-coupling treatment considerably improves upon the previous simplified theory of Olson and Smith and nicely reproduces the measured relative abundance of the specific ${\mathrm{He}}^{*}(2\mathrm{}{}_{}{}^{3,1}{}_{}{}^{}S,2{}_{}{}^{3,1}{}_{}{}^{}P)$ states formed by charge exchange. The calculated summed total charge-exchange cross sections generally agree with experiment for ${\mathrm{He}}^{+}$-Cs, -Rb, and -K, whereas problems remain for ${\mathrm{He}}^{+}$-Na.

Three approximate treatments of the exchange interaction in low-energy electron-molecule scattering are applied to a variety of collision systems. Static-exchange calculations for $e$-${\mathrm{H}}_2$, $e$-${\mathrm{N}}_2$, $e$-CO, $e$-LiH, $e$-HCl, and $e$-LiF collisions with scattering energies from 0.01 to 1.0 Ry are discussed, and results obtained using approximate treatment of exchange are compared with those obtained in a corresponding study in which exchange is incorporated exactly via an iterative procedure. The approximate treatments considered are orthogonalized-static, free-electron-gas model potential, and orthogonalized-model-potential procedures. The latter procedure is found to be uniformly superior to other approximate methods for all systems studied, in many cases yielding results indistinguishable from those of the exact static-exchange calculation. Strengths and weaknesses of each method are discussed.

Physical effects associated with change in angular momentum (in particular, $s\to p$ transitions) caused by collision-induced excitation at a level crossing in kilovolt-energy ion-atom or atom-atom scattering are investigated. The component of angular momentum involved in this effect is that perpendicular to the plane of collision. The excitation of $p_{-}$ states ($\Delta L_{\perp }=-1\mathrm{}$) and $p_{+}$ states ($\Delta L_{\perp }=+1\mathrm{}$) can be distinguished experimentally by the emission of right-handed (RHC) and left-handed (LHC) circularly polarized photons emitted in a direction perpendicular to the collision plane. It is shown that the reduced differential scattering cross sections ${\rho }_{\mathrm{RHC}}$ and ${\rho }_{\mathrm{LHC}}$, measured in coincidence with detection of the designated photon, are shifted with respect to one another by an amount $\Delta \tau$, where $\Delta \tau =\frac{2\theta \left(\frac{d\tau }{\mathrm{db}}\right)}{D}$. Here $\theta$, $\frac{d\tau }{\mathrm{db}}$, and $D$ are, respectively, the angular velocity of trajectory motion, derivative of the deflection function, and slope of the ground-state-excited-state energy difference, all calculated at the level crossing. It is suggested that the more appropriate measurements to make experimentally are ${\rho }_{\mathrm{RHC}}$ and ${\rho }_{\mathrm{LHC}}$, rather than the Stokes parameter $P_3$. The effect should be able to provide an experimental determination of the slope of the energy difference at the level crossing. Calculations have been made on the Li-Ne, ${\mathrm{Mg}}^{+}$ -He, and ${\mathrm{Mg}}^{+}$-Ar collision systems. The shifts $\Delta \tau$ between ${\rho }_{\mathrm{RHC}}$ and ${\rho }_{\mathrm{LHC}}$ at 1-keV incident energy are 17.4 keV deg for Li-Ne, 5.1 keV deg for ${\mathrm{Mg}}^{+}$-He, and 4.3 keV deg for ${\mathrm{Mg}}^{+}$-Ar systems. The shifts increase in direct proportion to the square root of the incident energy in keV. They are easily measurable even at energies below 1 keV.

Differential elastic and total reaction cross sections for electron scattering on hydrogen at 100 eV are obtained in a one-channel calculation using a momentum-space optical potential. Wave functions in reaction space are represented by the extreme screening approximation for the continuum and the Born approximation for discrete excitations. Exchange amplitudes are evaluated throughout. Total cross sections for discrete excitations and ionization are well reproduced by individual parts of the potential. The shape of the elastic angular distribution and the total reaction cross section are within experimental error. The absolute elastic cross sections are 24% below the present experimental determination.

One-photon $K{L}_{2,3}^n$ ($n=1,2\mathrm{}$) radiative electron rearrangement ($K{L}^n$ RER) x-ray transitions have been observed in sodium, magnesium, and aluminum metals following electron-impact excitation. The structure of the $K{L}^n$ RER transitions has been separated from the $\mathrm{KLL}$ and $K{L}_{1}V$ radiative Auger (RA) structure and their intensity relative to the $K{L}_{2,3}^n-L_{2,3}^{n+1\mathrm{}}$ transitions has been determined. No significant discrepancy between the experimental and calulated $K{L}^1$ RER branching ratios has been found in contrast to recent ion-impact results of Jamison et al. for aluminum and silicon. Our $K{L}^2$ RER results also agree with theoretical predictions.

A many-electron theory for electric-quadrupole transitions is proposed. Correlated length and velocity results are evaluated for the transitions Li I $2s\to 3d$, $2p\to 3p$; Cs I $6s\to 5d$, Ti III $3d^2{}_{}{}^3{}_{}{}^{}F\to 3d^2{}_{}{}^3{}_{}{}^{}P, 3d4s{}_{}{}^3{}_{}{}^{}D$; Cu II $3d^{10} {}_{}{}^1{}_{}{}^{}S\to 3d^{9}4s{}_{}{}^1{}_{}{}^{}D$; C III $2s^2{}_{}{}^1{}_{}{}^{}S\to 2p^2{}_{}{}^1{}_{}{}^{}D, 2s3d{}_{}{}^1{}_{}{}^{}D$, and Zn I $4s^2\to 4s4d{}_{}{}^1{}_{}{}^{}D$, and found to be in good agreement. For Cs I, relativistic effects were also large.

The total cross section for pair production in the field of atomic electrons (triplet production) is considered in detail. A discussion of the relevant theoretical papers is presented; the more familiar cross section for pair production in the Coulomb field of the nucleus serves for comparison. The effect of exchange and $\gamma -e$ interactions, atomic binding, and radiative corrections are all considered. Earlier expressions for the recoil distribution have been simplified considerably. Numerical values for screening corrections, exchange and $\gamma -e$ contributions, and total cross sections are given. Comparison is made with experimental cross sections for pair production on hydrogen and deuterium.

An exact Green's function is constructed for the one-electron Schrödinger equation using a central potential obtained from a piecewise linear approximation to $-rV\left(r\right)\mathrm{}$ of Herman and Skillman. With the Green's function two- and three-photon ionization cross sections are calculated for $\mathrm{He}\mathrm{}\left(1s\right)\mathrm{}\left(2s\right)\mathrm{}{}_{}{}^1{}_{}{}^{}S$, ${}_{}{}^3{}_{}{}^{}S$, and the alkali metals, and compared to other calculations and experiments. Resonances in the cross sections occur at model eigenvalues rather than experimental energy levels. It is demonstrated that the resonances can be made to occur at experimental values either by simple shifts in the wavelength scale, by adjusting the ionization energy in the calculation, or by including the eigenvalue differences in a finite sum. However, as these are perturbation-theory calculations and not applicable at very high intensities or on resonance, only the wings of the resonance structure are included in the calculation.

The existence of Hohenberg-Kohn—like density-functional theorems in momentum space is demonstrated. Invoking principles employed by Levy to construct universal variational density and density-matrix functionals in position space, it is found that (1) there exists a universal variational functional for the one-electron reduced density matrix in momentum space, and (2) for any given external potential, there exists a proper variational functional for the one-electron momentum-space probability density.

The photoionization cross section of Xe $5p^5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}6p(J=0\mathrm{})\mathrm{}$ is calculated near threshold. We use a $\mathrm{jjJM}$-coupling scheme to describe the excited-state spectrum of xenon. By transformation from $\mathrm{jj}$ to $\mathrm{LS}$ coupling, one set of cross-section results is obtained using bound and continuum orbitals generated in the Hartree-Fock approximation. Another set of cross-section results is obtained using orbitals generated in the Dirac-Fock approximation. The difference in the two sets of results, which represents the contribution from relativistic effects, is found to be as much as 25% at certain energies. On the other hand, differences in the cross-section results which arise from the choice of electromagnetic field gauge are found to be as much as 75%.

We report high-resolution spectroscopy of the $D{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $D^{\prime \prime }{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and $B^{\prime \prime }{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ states in ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$, performed in absorption in the vicinity of 83 nm. Predissociative widths as narrow as 0.3 ${\mathrm{cm}}^{-1\mathrm{}}$ have been measured, and profile analyses based on the theory of Fano are performed on these predissociated states. The importance of overlap integrals in the predissociation of $B^{\prime \prime }$ is shown, and the absorption cross section $\sigma =(7.2\mathrm{}\pm 0.7)\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ for the $B^{\prime \prime }\leftarrow X(2,0)\mathrm{}$ is determined. Anomalous behavior observed in the $D\mathrm{}(v=5\mathrm{})\mathrm{}$ states of ${\mathrm{D}}_2$ is analyzed in terms of an accidental perturbation by the $D^{\prime \prime }\mathrm{}(v=0\mathrm{})\mathrm{}$ states.

Cusp conditions are derived for eigenfunctions of many-electron systems for the coalescence of more than two particles.

Fine structures in the $\mathrm{nd}{}_{}{}^2{}_{}{}^{}D$, $n=4,5\mathrm{}$ and $\mathrm{nf}{}_{}{}^2{}_{}{}^{}F$, $n=4,5,6\mathrm{}$ levels in Be ii have been measured, using fast-beam, level-crossing spectroscopy. The results, accurate to within ${10}^{-3\mathrm{}}$, point to small deviations from a hydrogenic fine-structure splitting due to correlation effects involving the $1s^2$ core for the $\mathrm{nf}{}_{}{}^2{}_{}{}^{}F$ levels.