The recently introduced Jacobi or $J$-matrix techniques for quantum scattering are developed to include the construction of exact analytic matrix elements of regular and Coulomb partial-wave zeroth-order and full Green's functions. Very simple results obtain for the unperturbed Green's functions, while full Green's functions require a single diagonalization of an $N\times N$ Hamiltonian matrix, where $N$ is the number of basis functions coupled by the matrix truncated potential. In an application of the $J$-matrix Green's functions to the theory of atomic dynamic polarizabilities, the analytic result for hydrogen is derived, and it is shown how more general systems may be treated in a way which is superior to the usual $N$-term variational approach. In an application to error bounds for phase shifts, we show how the full Green's functions can be used to demonstrate the absence of false pseudoresonances in $J$-matrix scattering calculations, and bound the possible errors in computed phase shifts.

The production of $K$ vacancies has been measured for target and projectile atoms in Ne-Al and Ar-Al, -Cl, -Ti, -Cr, -Fe, -Ni collisions at energies ranging from 0.75 to 16 MeV. The results have been examined in terms of the $K$-vacancy-sharing theory of Meyerhof. Agreement between theory and experiment is generally good, although there is some indication of deviations at low energies.

$L$-shell and individual x-ray production cross sections for 8-36-MeV oxygen ions on thin solid targets of Ce, Pr, Sm, Eu, Dy, and Ho are measured and compared with predictions of theories of direct Coulomb ionization. In comparing theory and experiment, we use, with reasonable justification, fluorescence yields, Coster-Kronig yields, and radiative widths obtained from single-hole initial configurations. The theoretical treatment which provides the best overall fit to the data is the plane-wave Born approximation with corrections for Coulomb deflection of the projectile and increased binding of the target electrons. The effects of multiple ionization are examined through measurement of x-ray energy shifts as measured with Si(Li) detectors and by vacuum crystal-spectrometer measurements of $L$ x-ray spectra produced by 3-MeV proton and 25-MeV oxygen-ion bombardment of a thick La target.

We have investigated the electron-ion three-body collisional-radiative recombination for electron temperatures below 4000 °K using the Mansbach-Keck rates of electron-impact-induced transitions between hydrogenic energy levels of high principal quantum number. At such temperatures and for a wide range of electron densities, the statistical recombination process is simultaneously governed by collisional and radiative transitions between excited levels near the ionization limit, where many atomic and molecular systems possess a hydrogenic energy-level structure. In order to also take into account radiative transitions, we have numerically solved a system of coupled equations, describing the quasi-steady-state populations of 100 bound levels. These equations are expressed in, and solved for, the first differences between the reduced population densities $\rho \mathrm{}\left(p\right)\mathrm{}$, which improves the computing precision and establishes the location of the "bottleneck" in the recombination sequence. Our results are consistent with the following approximation for the collisional-radiative recombination rate coefficient (in ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$): ${\alpha }_{\mathrm{cr}}=1.55\mathrm{}\times {10}^{-10\mathrm{}}{T}^{-0.63\mathrm{}}+6.0\mathrm{}\times {10}^{-9\mathrm{}}{T}^{-2.18\mathrm{}}{\mathrm{}\left[e\right]\mathrm{}}^{0.37}+3.8\mathrm{}\times {10}^{-9\mathrm{}}{T}^{-4.5\mathrm{}}\mathrm{}\left[e\right]\mathrm{}$, where the electron temperature $T$ is in °K and the electron density [$e$] is in ${\mathrm{cm}}^{-3\mathrm{}}$; the first and last terms describe purely radiative and collisional recombination, respectively, and the second term results from the complex interplay of collisional and radiative processes. Agreement with experimental data is reasonable.

The ${\mathrm{Ar}}^{+}$ + ${\mathrm{N}}_2$ collision is studied at energies from 1.0 to 3.0 keV and in an angular range between 0 and 4.0 deg. The energy-loss spectra of the scattered ions demonstrate the presence of elastic scattering and inelastic processes arising from vibro-rotational excitation of the ground electronic state of ${\mathrm{N}}_2$, electronic excitation of the target with concomitant vibro-rotational excitation, and target ionization. Studies of the angular dependence of these processes suggest that (a) the collisions involve the entire molecule and are thus not adequately described in terms of a binary collision model, (b) electronic and vibrational excitation occur via mechanisms which exhibit negligible coupling, and (c) electronic excitation of ${\mathrm{N}}_2$ is due predominantly to the $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}\to X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ transition as evidenced by observation of the onset of dissociation at larger scattering angles. The probability of charge exchange in ${\mathrm{Ar}}^{+}$ + ${\mathrm{N}}_2$ and ${\mathrm{N}}^{+}$ + ${\mathrm{N}}_2$ collisions is also investigated and shows an angular behavior very similar to that found in ${\mathrm{He}}^{+}$ + ${\mathrm{N}}_2$. Inelastic scattering results for ${\mathrm{He}}^{+}$ + ${\mathrm{N}}_2$ are reported.

Total deactivation cross sections for collisions of metastable H ($2{}_{}{}^2{}_{}{}^{}S$) on He and Ar have been measured in the energy range 0.1-3000 eV. At low collision energies an apparatus designed to utilize time-of-flight techniques was used, while at the high energies an apparatus that employed beam-attenuation techniques was used. The cross sections are found to be on the order of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ at the lowest energies and decrease slowly to approximately ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at the highest energies. The experimental data were analyzed to obtain information about the difference in potential energies, $\Delta V\left(R\right)\mathrm{}$, between the two ${}_{}{}^2{}_{}{}^{}\Sigma$ molecular states arising from the $\mathrm{H}\mathrm{}(n=2\mathrm{})\mathrm{}$+He and Ar separated atoms. Our analysis also shows that the dominant deactivation mechanism of $\mathrm{H}\left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S\right)$ at energies less than 500 eV is excitation to $\mathrm{H}\left(2\mathrm{}{}_{}{}^2{}_{}{}^{}P\right)$, which rapidly radiates to the ground state.

$K$-shell x-ray production cross sections for thin targets of selected elements Ti to Sb have been measured for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ ions in energy steps of 0.2 MeV/amu in the range from 1.0 to 5.0 MeV/amu. Comparisons of the cross-section data for the lighter elements ($Z_2\le 28$) to the plane-wave Born approximation (PWBA) and the PWBA corrected for binding energy and Coulomb deflection show that the data are best represented at the lower energies by the corrected PWBA and approach the PWBA at the higher energies. When approximate relativistic corrections are made to the theories for the heavier elements studied, the same general trend is observed. Calculation of the ratio $R=\frac{\sigma \left(Z_1\right)}{Z_1^2\sigma (Z_1=1)}$ supports the inclusion of binding energy and Coulomb defection corrections to the PWBA at the lower ion energies. The corrections to the PWBA, while improving the fit to the data, underestimate the cross sections by 10-100% in all cases. The $\frac{K\beta }{K\alpha }$ ratios are found to be in good agreement with theoretical estimates assuming single-hole ionization.

The interaction in the ($p^{+}$, H) collision system is examined in terms of the exact ${\mathrm{H}}_2^{+}$ and H electronic states. The nonadiabatic interactions between the ${\mathrm{H}}_2^{+}$ electronic states which asymptotically go to the $n=1\mathrm{}$ or $n=2\mathrm{}$ atomic states are calculated together with the corresponding translational contributions. The question concerning the choice of the space-fixed and rotating atomic bases is investigated in relation to the long-range interactions. The adiabatic-diabatic question is discussed in connection with the noncrossing rule and dynamic correlations between the separated and united atomic states. With the aid of the calculated interactions, the "coupling hypothesis," which states that the nonadiabatic transitions are directly correlated with the closest approach of the electronic state energies, is examined. The characteristic features of the radial and rotational couplings are discussed in a phase-interference model.

The scattering length $A$ characterizes the zero-energy scattering of one system by another. It was shown some time ago that a variational upper bound on $A$ could be obtained using methods, of the Rayleigh-Ritz type, which are commonly employed to obtain upper bounds on energy eigenvalues. Here we formulate a method for obtaining a variational lower bound on $A$. Once again the essential idea is to express the scattering length as a variational estimate plus an error term and then to reduce the problem of bounding the error term to one involving bounds on energy eigenvalues. In particular, the variational lower bound on $A$ is rigorously established provided a certain modified Hamiltonian can be shown to have no discrete states lying below the level of the continuum threshold. It is unfortunately true that necessary conditions for the existence of bound states are not available for multiparticle systems in general. However, in the case of positron-atom scattering the adiabatic approximation can be introduced as an (essentially) solvable comparison problem to rigorously establish the nonexistence of bound states of the modified Hamiltonian. It has recently been shown how the validity of the variational upper bound on $A$ can be maintained when the target ground-state wave function is imprecisely known. Similar methods can be used to maintain the variational lower bound on $A$. Since the bound is variational, the error in the calculated scattering length will be of second order in the error in the wave function. The use of the adiabatic approximation in the present context places no limitation in principle on the accuracy achievable.

Interruption of the hyperfine interaction during electron spin-exchange collisions shifts the hydrogen-atom ground-state $\Delta m_F=0\mathrm{}$ hyperfine transition frequency in proportion to the spin-exchange collision rate and to the average time $T_D$ during which the exchange interaction interrupts the hyperfine interaction. Measurements of the thermal average $T_D$ for hydrogen-hydrogen collisions at 308 °K in an atomic hydrogen maser confirm the predictions of a semiclassical theory and a numerical estimate using straight-line collision trajectories. Measurements of much longer $T_D$ for hydrogen-atom collisions with ${\mathrm{O}}_2$, NO, and N${\mathrm{O}}_2$ molecules are consistent with the formation of long-lived intermediate complexes during some collisions.

The production of vacancies in the inner and outer shells of the target and projectile have been studied in ${\mathrm{Ne}}^{i+}$ + Ne collisions in the incident energy range of 45 keV to 2.2 MeV through the observation of $K$ x rays and Auger electrons. Data are given for incident charge states $i=0, 1, \mathrm{and} 2$. Parameters necessary for the analysis of collision kinematics were extracted from previous data and used to investigate these effects on the observed Auger spectra. The kinematic line broadening in the Ne collisions is shown to obscure the peak structure characteristic of the multiple ionization states. The centroid energies and average energy widths of the Auger groups, together with absolute intensities, are reported as a function of the ${\mathrm{Ne}}^{i+}$ energy and electron emission angle for both target and projectile. After kinematic corrections, it is found that target and projectile Auger-electron emission are isotropic to within ± 10% and that the $K$ vacancy created is equally shared between the target and projectile. The average number ${\overline{n}}_A$ of electrons removed from the $L$ shell simultaneous with the $K$ vacancy production is estimated from the centroid Auger-electron energies and compared with previously measured data. It is found that ${\overline{n}}_A$ increases with the ${\mathrm{Ne}}^{+}$ energy from ∼2.5-3.6 over the energy range studied. Absolute cross sections for x-ray and Auger-electron production are reported with an accuracy of about ±15%, and mean fluorescence yields are determined from these cross-section data. The fluorescence yield increases with incident ${\mathrm{Ne}}^{+}$-ion energy, and is consistent with the observed degree of $L$-shell ionization. Total $K$-vacancy production cross sections agree well with available calculations below 200 keV, but the theoretical results underestimate the cross sections at higher energies. This reflects a breakdown of the two-state approximation made in the calculation. Information regarding the coupling of outer-shell molecular orbitals in the entrance channel is extracted from the comparison of the measured data and previous calculations.

An extension of projectile-electron spectroscopy to keV-energy alkali-metal beams has permitted the first observations of the energies of a number of optically forbidden core-excited autoionizing states of the alkali metals. For example, we have located the $\left(1s2\mathrm{}{s}^2\right){}_{}{}^2{}_{}{}^{}S$ and the $\left(1s2\mathrm{}{p}^2\right){}_{}{}^2{}_{}{}^{}D$ states of Li which lie at 56.31±0.03 eV and 61.04±0.03 eV, respectively, above the ground state. Energies for theoretically less-well-established doublet and quartet states in Na, ${\mathrm{Mg}}^{+}$, and K are also presented.

The electron-impact dissociation cross sections of the ${\mathrm{H}}_2$ molecule have been calculated for the processes leading to $\mathrm{H}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ and to $\mathrm{H}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ by means of the Born-Rudge and Born-Ochkur methods. In addition to direct excitation to the repulsive $b{}_{}{}^3{}_{}{}^{}{\Sigma }_u_{}^{+}{}_{}{}^{}$ state for the first process, cross sections are also computed for excitation of the discrete levels of the $a{{}_{}{}^3{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$, $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $d{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and $e{{}_{}{}^3{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ states in order to account for cascades. These two mechanisms are found to be of equal importance. The second process is found to proceed mainly through excitation of the $B^{\prime }{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ state except near the threshold where $e{{}_{}{}^3{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ is an important contributor. The theoretical cross sections are in reasonably good agreement with experimental data for the first process. The cross sections of the second process account for nearly two-thirds of the measured cross sections of $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$-atom production by electron impact. The difference is attributed mainly to predissociation and dissociative excitation through the doubly excited states.

Relative and absolute populations of 19 levels in beam-foil—excited neutral helium at 0.275 MeV have been measured. The singlet angular-momentum sequences show dependences on principal quantum number consistent with $n^{-3\mathrm{}}$, but the triplet sequences do not. Singlet and triplet angular-momentum sequences show similar dependences on level excitation energy. Excitation functions for six representative levels were measured in the range 0.160 to 0.500 MeV. The absolute level populations increase with energy, whereas the neutral fraction of the beam decreases with energy. Further, the $P$ angular-momentum levels are found to be overpopulated with respect to the $S$ and $D$ levels. The overpopulation decreases with increasing principal quantum number.

A systematic study of $L$ x-ray production and $L$-subshell ionization by MeV electron impact has been made. Cross sections were measured for 14 elements from Ba ($Z=56\mathrm{}$) to ($Z=83\mathrm{}$) at electron bombarding energies of 1.04, 1.39, and 1.76 MeV. Within the error limits there is no dependence on the electron energy. At all energies, measured $L$ x-ray production cross sections exhibit a gradual increase with atomic number. For the heavier elements, typical average values for the $L\alpha$, $L\beta$, and $L\gamma$ group are 70, 55, and 9 b, respectively. $L$-subshell ionization cross sections were derived from the $L\alpha$, $L\beta$, and $L\gamma$ x-ray production cross sections with the use of theoretical $L$-subshell fluorescence yields, Coster-Kronig yields, and radiative branching ratios. The total $L$-shell ionization cross section drops from 1200 b at Ba ($Z=56\mathrm{}$) to 380 b at Bi ($Z=83\mathrm{}$) with individual $L$-subshells contributing roughly in proportion to their electron number. The measured cross sections are in good agreement with the predictions of the binary-encounter collision model of Gryziński.

Using simple scaling laws based on the adiabatic approximation, Meyerhof and co-workers have compared experimental data on $K$-vacancy production cross sections for symmetric collisions of heavy atoms and ions, with ab initio calculations of cross sections for direct impact ionization of hydrogen atoms by slow protons, done in this laboratory. It is shown here that the relative magnitudes and energy dependences of such cross sections can be understood using a simplified model theory; dominant features are determined by the oscillatory exponential factors associated with momentum and energy loss by the heavy particles, rather than the electronic-coupling matrix elements.

Relative elastic differential cross sections for electrons scattered from ${\mathrm{H}}_2$ have been measured for angles between 3 and 130 deg and electron energies between 100 and 1000 eV. The data agree very well with the first Born theory by Ford and Browne, and Liu and Smith for angles larger than 30 deg; however, strong deviations are found in the small-angle range. This discrepancy is discussed from the point of view of charge-cloud polarization and its adiabatic limit. It was found that the cross sections have not yet reached the adiabatic limit at 100 eV. The differential cross sections are integrated, and the total elastic cross sections are determined. The present values continue smoothly to the results of Truhlar et al. and are compatible with those of Ulsh, Wellenstein, and Bonham.

Recently developed analytic methods, which reduce the Glauber amplitude for charged-particle-neutral-atom collisions to a one-dimensional integral representation involving modified Lommel functions, are used to evaluate the cross sections for the direct excitation of $3{}_{}{}^1{}_{}{}^{}D$ and $4{}_{}{}^1{}_{}{}^{}D$ states of helium by electron impact with incident energies from 40 to 1000 eV. It is shown that the Glauber amplitudes can be written in terms of three generating functions: One of these has already been derived by Thomas and Chan; the detailed reduction of the other two is given in this paper. Comparison is made with the Born, Ochkur, and Woollings-McDowell approximations. The polarization fraction of the 6678-Å helium line emitted in $e^{-}$+He collisions is also calculated in the Glauber approximation. The agreement between theory and experiment is less than satisfactory in the entire energy region.

The cross section for production of excited Ne ions with double $K$-shell vacancies is measured by observing the Auger electrons from the decay of these states. A Ne-gas target is bombarded by 1-2-MeV/amu N, O, and F projectiles in various incident charge states. The $K$-shell Auger hypersatellites are observed only for bare nuclear projectiles. The projectile charge-state dependence, projectile $Z$ dependence, and energy dependence of the cross section suggest $K$-shell electron exchange as a production mechanism.

Cross sections for pure rotational excitation ($J=1\mathrm{}\to 3$) in ${\mathrm{H}}_2$ are reported at electron energies $E_0$ of 15 eV to 100 eV at scattering angles $\theta$ of 115°, 3 to 40 eV at 20°, and at 40 eV at angles between 10° and 135°. It is found that for intermediate $E_0$ the probability of pure rotational excitation at high $\theta$ is greater than that for elastic scattering. Moreover, this probability is found to decrease slowly with $E_0$, having a value at its peak (at 4 eV) which is only ∼ 20 times that at 100 eV.