Atomic bremsstrahlung-polarization correlations between incident electron and emitted photon are discussed for incident-electron kinetic energies in the range from 5 keV to 1 MeV. Results are reported from an exact numerical calculation in partial-wave formulation using screened potentials. It is shown that bremsstrahlung can be used as an analyzer of polarized electrons, a transmitter of polarization from electrons to photons, or a source of polarized radiation. Comparisons are made with previous work where available.

It has been shown recently that static polarizabilities can be computed efficiently by solving the multiconfigurational self-consistent-field equations for an atom in the presence of a point charge which provides the polarizing field. The formalism developed here is designed to take advantage of these calculations in the computation of dynamic polarizabilities. The approach is basically equivalent to a perturbation method in which the unperturbed state is the statically polarized atom. The transition to the time-dependent problem is effected by introducing a potential function which turns off the static field and turns on a dynamic field with the desired time dependence. The spatial parts of the time-dependent wave function are represented by linear combinations of the statically polarized configurations, without explicit reference to the orbital model.

A previously overlooked relaxation energy $R$ is introduced into the intermediate-coupling formulas of Asaad and Burhop to calculate the $\mathrm{KLL}$ Auger energies of the elements from $Z=10\mathrm{} \mathrm{to} 100$. By employing the concept of equivalent cores, together with the work of Hedin and Johansson on polarization energies of electron holes, a method was developed to estimate $R$ accurately from ground-state two-electron integrals calculated by Mann. These integrals were also used in the intermediate-coupling calculation. Agreement with experiment is excellent. A table of $\mathrm{KLL}$ Auger energies based on this work is given. These energies appear to be preferable to the older semiempirical values because they are comparable in accuracy and they have a sound theoretical basis. Their adoption for analysis of Auger spectra is suggested. The semiempirical values were based on two sets of parameters for light and heavy elements. They gave good fits only by using unrealistic values of the two-electron integrals in the intermediate-coupling equations, because the relaxation energy was omitted. In addition to predicting $\mathrm{KLL}$ Auger energies accurately, this work shows that the spin-orbit coupling constant $\zeta$ for $2p$ electrons in two-hole states is essentially the same as in one-hole states. The success of the intermediate-coupling calculations also shows that two-electron integrals in these two-hole states are accurately equal to those calculated for neutral atoms. The relaxation-energy concept can be applied to other problems.

Near-resonant charge transfer in asymmetric collisions is often dominated by long-range forces due to polarization and sometimes to ion-quadrupole interactions. These interactions can lead to regions of strong coupling at large distances. The parameters necessary for estimating the cross sections by a modified Demkov formula (for strong coupling without crossing) can be obtained from a knowledge of simple atomic properties such as ionization potentials and polarizabilities. These formulas are applied to the calculation of the cross sections for the ${\mathrm{He}}^{+}$ + K, Rb, and Cs asymmetric charge-transfer reactions and are compared with the experimental measurements of Peterson and Lorents. For these systems several inelastic channels are open and the theory predicts the relative abundances of the various excited states of He (n=2).

Cross sections, differential in emission energy and angle, have been measured for the ejection of electrons in collisions of ${\mathrm{H}}_2^{+}$ ions with molecular hydrogen. Incident-ion energies studied were 0.6, 1.0, and 1.5 MeV and electron emission was measured over the laboratory angular range of 20°-125°. Electron-emission cross sections are compared with measurements for incident protons having the same velocity as the ${\mathrm{H}}_2^{+}$ ions. Electron distributions attributable to dissociative ionization of the ${\mathrm{H}}_2^{+}$ ion are integrated to obtain the total cross section for dissociative ionization. A comparison is made between measured differential cross sections for scattering the bound electron of the incident ion and cross sections for scattering of incident free electrons.

An approximate form of the Faddeev equations has been applied to the charge-transfer process in proton-hydrogen collisions. The effect of coupling with the direct channel has been taken into account. This formalism satisfies the unitarity condition below the breakup threshold. Results for the ground-state capture cross section have been obtained with and without the inclusion of the effect of proton-proton interactions. The experimental findings for the capture cross section in the energy range 1-150 keV lie in between our two sets of results. At high incident energies our results with and without the proton-proton interaction have approached the Jackson-Schiff and Brinkman-Kramers cross sections, respectively. The differential cross sections for the capture in the forward direction have been compared with the corresponding results of other theorists. Results for the elastic cross section have also been obtained.

In an earlier paper, one of the authors gave a completely quantum-mechanical treatment of the pressure shift, due to foreign atoms, of high-series spectral lines of alkali-metal atoms. The same basic method of solving the Schrödinger equation for the system using perturbation techniques is adopted again. However, in the present paper, the center-of-mass motion is treated separately, allowing the use of more realistic distribution functions when averaging over the center-of-mass motion of the foreign atoms. By using a Boltzmann-type distribution law, it is shown that, for foreign atoms exhibiting a red shift, the observed shift decreases with increase in temperature, but no analogous result is found for atoms exhibiting a blue shift.

In proton-krypton charge-transfer collisions hydrogen is produced in the ground state and the krypton ions are preferentially populated in the ground (${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$) state when the protons are incident at about 100 eV. The preferential population of ${\mathrm{Kr}}^{+}\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)$ over ${\mathrm{Kr}}^{+}\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)$ means that the hydrogen atoms will emerge spin polarized. We have calculated the spin-polarization fraction at 100 eV as a function of impact parameter and as a function of scattering angle, and the results are reported in this paper. A comparison of these results with the results of previous calculations of proton-xenon charge transfer indicates that the latter process is more suitable for producing spin-polarized hydrogen, at least for small scattering angles.

Total and differential two-photon ionization cross sections are derived in the framework of perturbation theory, assuming a simple one-electron atomic model. It is shown that for an unpolarized target the angular distribution of the ejected electrons has the general form $\mathrm{a}+b{cos}^2\theta +c{cos}^4\theta$, whatever the quantum numbers $n$, $l$, of the initial energy level, and the state of polarization (linear or circular) of the incident radiation. The total transition rates for circularly and for linearly polarized light are quite different from each other. For an arbitrary $\mathrm{nl}$ state, the theoretically allowed maximum value of their ratio is $\frac{3}{2}$. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.

The electron-impact energy-loss spectrum of He at a scattering angle of 7° has been measured with an energy resolution of 2.7 eV full width at half-maximum using 25-keV incident electrons. A binary-encounter approximation was used to obtain the electron Compton profile from the cross-section differential with respect to both the energy loss of the incident electron and solid angle of the scattered electron $\frac{d^2\sigma }{\mathrm{dEd}\Omega }$. The electron Compton profile was corrected for interference scattering from pairs of target electrons and exchange. It was then compared to theoretical and x-ray experimental values for the Compton profile. The effects of background, multiple scattering, and energy resolution are discussed. The electron-impact and x-ray methods for measuring Compton profiles are compared.

We have measured the optical-excitation function and polarization of the 4227-Å line, using crossed electron and calcium beams, for electron energies from threshold to 1400 eV. In the high-energy region, from 100-450 times the threshold energy, we have used the Bethe theory to normalize our experimental results. An excellent signal-to-noise ratio combined with ∼0.3-eV full width at half-maximum electron-energy resolution has enabled observation of structure in the excitation function and polarization curves below 5 eV. We observed a threshold polarization limit of (98±3)%, consistent with the expected + 100%. The data are also consistent with a logarithmic approach to a high-energy polarization of - 100%.

A procedure which allows for both open and closed channels with exchange and orthogonality is formulated for a multichannel scattering process. Noniterative integral-equation theory is used to solve the coupled integrodifferential equations of the scattering problem from zero out to some transformation point where the reactance matrix is projected out to its asymptotic value by using a matrizant technique. The method is applied to a two-channel model which has some of the features of a $1s-2p$ approximation for $e$-H scattering.

The relative cross section for production of ${\mathrm{He}}^{+}$ in ${\mathrm{He}}_2^{+}$-He collisions has been measured near threshold. Convolution integrals taking account of the thermal motion of the target He atoms are numerically calculated for several forms of the threshold cross section and compared to the data. For the threshold laws considered, threshold is in the range 2.0-2.4 eV, in agreement with theoretical values of the dissociation energy of $X{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ ${\mathrm{He}}_2^{+}$. By using Liu's recent rigorous lower bound for this dissociation energy, a possible form of threshold law is obtained. The experiments also indicate that significant amounts of ${\mathrm{He}}_2^{+}$ resulting from He*-He interactions are formed in excited vibrational-rotational states of the $X{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$.

The relative elastic differential scattering cross section for the ${\mathrm{He}}^{++}$ + He system has been measured for collision energies in the range $4\le E\le 75$ eV. The experimental results have been analyzed utilizing semiclassical techniques based on a two-state model to obtain information about the intermolecular potentials for the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}$ and $E{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}$ states of ${\mathrm{He}}_2^{++}$. These results are discussed in terms of existing ab initio calculations for these two states.

The $L$ and $M$ x rays of Pb were observed with a Si(Li) detector of 190-eV resolution for a 6-keV x-ray line. Absolute shell-ionization cross sections were derived and compared to plane-wave-Born-approximation (PWBA) and binary-encounter-approximation (BEA) predictions. The agreement between theory and experiment was generally good for both cross sections and x-ray ratio predictions. For proton energies less than 3 MeV the $\frac{L\alpha }{L\beta }$ and $\frac{L\alpha }{L\gamma }$ ratios display deviations that are qualitatively predicted by both theories but only absolutely reproduced by the PWBA result for $\frac{L\alpha }{L\beta }$. The $\frac{L\alpha }{\mathrm{Ll}}$ ratio exhibits a minimum in the proton energy range 0.5-3.0 MeV that is not predicted by a single-ionization-state process.

Model potential calculations are presented of the ground-state potential curves and overlap dipole moments of the alkali-metal-atom—inert-gas-atom pairs LiHe, NaHe, LiNe, and NaNe. The coefficients of collision-induced absorption are evaluated for LiHe and NaHe at temperatures of 300 and 1000 °K using both quantum-mechanical and classical theories. The classical approximation accurately reproduces the quantum-mechanical results.

Using the beam-foil technique, we have observed zero-field quantum beats in the intensity decays of transitions from the $1snp{}_{}{}^3{}_{}{}^{}P$ terms ($n=2, 3, 4, 5$) in ${}_{}{}^{6,7}{}_{}{}^{}\mathrm{Li}$ ii, and deduced the magnetic hyperfine coupling constant for each isotope for the $2p {}_{}{}^3{}_{}{}^{}P$ terms. Preliminary values for these coupling constants are $A(1s2p{}_{}{}^3{}_{}{}^{}P, {}_{}{}^6{}_{}{}^{}\mathrm{Li}ii)=0.091\mathrm{}\pm 0.001$ ${\mathrm{cm}}^{-1\mathrm{}}$ (2.73 GHz), $A(1s2p{}_{}{}^3{}_{}{}^{}P, {}_{}{}^7{}_{}{}^{}\mathrm{Li}ii)=0.239\mathrm{}\pm 0.002$ ${\mathrm{cm}}^{-1\mathrm{}}$ (7.17 GHz). The measured fine structures agree with recent calculations within a few percent.

Utilizing the first Born approximation and an eikonal/closure approximation plus Bethe's generalized-oscillator-strength (GOS) formalism, we evaluate $s$- and $p$-shell ionization of Ne and Ar. Partial-wave contributions to the GOS are calculated using an analytic independent-particle model (IPM) whose parameters have been established in previous work on excitation GOS's. For single ionization of Ne and Ar shells ($K$ shell excepted), total cross sections and cross sections differential in the energy of the secondary electron are calculated for electron-impact energies near threshold to 10 keV. The eikonal/closure approximation which is developed in detail for large atoms differs from the Glauber theory by not assuming sudden passage of the projectile in which the time dependence of the bound electron and the energy transfer to the projectile may be neglected. In the single-scattering limit, the theory produces a simple factor multiplying the usual Born approximation amplitude, which leads to improved agreement with experiment at low energy.

The ground-state wave function for a quantum electron gas is approximated by $\psi =\Phi D$, where $D$ is the ground-state ideal-gas wave function and $\Phi =\exp [-(\frac{1}{2}\left)\Sigma {i<j}^{}u\left(r_{\mathrm{ij}}\right)\right]$. Three-body correlation functions in the energy are approximated so that the energy is a functional of only pair-correlation functions. The variational principle is applied by utilizing the functional derivative of the pair-correlation function with respect to $u\left(r\right)\mathrm{}$. The three- and four-body correlation functions in the functional derivative are approximated in a consistent manner. Use of the Kirkwood superposition approximation for the many-body correlation functions in the functional derivative gives unphysical results. A new approximation to the functional derivative is obtained by using the convolution approximation for the many-body terms. This gives a reasonable result for the asymptotic form of the wave function. The hypernetted-chain functional derivative combined with the convolution approximation for the energy gives the same asymptotic form. When the random-phase approximation to the energy is used with the Gaskell-Broyles-Sahlin-Carley functional derivative, the equation may be solved analytically, giving the same result obtained by Gaskell. The asymptotic form is the same as the two previous methods, namely, $u\sim \left(\frac{e}{\hslash }\right)\frac{{\left(\frac{m}{\pi \rho }\right)}^{\frac{1}{2}}}{r}$.

It is shown that the radius of curvature $R^{\prime \prime }$ of the photon echo is related to the radius of curvature $R$ of the first pulse and $R^{\prime }$ of the second pulse by $\frac{1}{R^{\prime \prime }}=\frac{2}{R^{\prime }}-\frac{1}{R}$ and yields a focusing effect for the photon echo.