The hyperfine spectrum of the Van der Waals molecule KAr is analyzed assuming an isotropic perturbation of the potassium hyperfine constant. The analysis yields the hyperfine frequency shift in KAr as a function of the internuclear separation between 9 and 18 bohr. The shift is positive at short range, $R<\mathrm{}12\mathrm{}$ bohr, and negative at longer range. The results are compared to theoretical estimates of the shift, and are used to calculate the pressure shift of optically pumped potassium in argon.

The dipole-moment derivative $\frac{d\mu }{\mathrm{dr}}$ has been calculated for LiF from available Hartree-Fock and configuration-interaction wave functions. Calculated values of $\frac{d\mu }{\mathrm{dr}}$ are not in agreement with the value determined from a measurement of the first vibrational state lifetime by Bedding and Moran. Other calculated molecular properties are also compared with the available data.

Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-$V^N$ potential.

The differential cross sections for electrons scattered by He, O, Ar, and ${\mathrm{O}}_2$ at 15 eV and by O and ${\mathrm{O}}_2$ at 5 eV have been determined using a modulated crossed-beam technique. The results for He, Ar and ${\mathrm{O}}_2$ agree well with previously published experimental and theoretical values. Measurements on ${\mathrm{O}}_2$ extend to larger back-scattered angles than previously reported. Results for O are compared with the theoretical calculations of Thomas and Nesbet. Reasonable agreement with theory is obtained at 5 eV, and while the calculations only extend to 11.0 eV, the trend in shape appears correct at 15 eV. A small-angle dip in the cross section is observed which is not predicted by the theory.

The formal development of the problem of electron-atom scattering in the presence of a laser field is considered. A time-dependent close-coupling method and a time-dependent optical-potential method are presented. With hydrogen as an example, and a weak laser tuned near the $1S-2P$ resonance, the effective long-range potentials are explicitly obtained. These potentials are time dependent, noncentral, and fall off as $r^{-n}$, where we limit ourselves to terms with $n=2, 3, \mathrm{and} 4$. They are then used to find the elastic, inelastic, and superelastic cross sections for small momentum transfer.

Static dipole polarizabilities are calculated from self-consistent-field and highly correlated wave functions for the ground states of the atoms Li through Ne. The correlation contributions to the polarizabilities are found to vary between -16% for Be and + 14% for F. The polarizabilities as obtained from the coupled-electron-pair approximation are expected to be accurate to about 2%.

Continuous x rays from a thin aluminum target produced by proton and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-ion bombardments have been measured with a Si(Li) detector over the impact-energy ranges 1-4 MeV and 3-9 MeV, respectively. The experimental results obtained were compared with theoretical predictions based on the binary-encounter approximation. Agreements are obtained both in the shape of spectra and absolute cross sections without any adjustable parameter over the entire energy range measured, but generally the theoretical calculation predicts smaller cross sections than the experimental results as the photon energy becomes higher and the bombarding energy gets lower. Energy-dependent directional anisotropy of the bremsstrahlung was theoretically estimated and compared with the experimental results measured at directions 45°, 90°, and 135° with respect to the incident beam, showing qualitative agreement.

The quantum nonperturbative analysis of Kroll and Watson for a two-level system of near-adiabatic atom-atom scattering in an intense laser-field mode is extended to treat a general multilevel system interacting with intense single- or many-field modes. A procedure for rigorously solving the adiabatic eigenvalue problem for the whole charge-field system is given. A new transition-probability formula is derived. Cross sections are calculated for the processes $\mathrm{Li}+\mathrm{H}\left(X{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}\right)+\nu \hslash \omega \to \mathrm{Li}+\mathrm{H}(A{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{} or B{}_{}{}^1{}_{}{}^{}\Pi )$ where $\nu \ge 1$. Analysis of transition in an atom due to intensity variation of a laser pulse shows that desired transition probability per pulse (e.g., ½) may be achieved by varying the pulse parameters. For this, numerical results of $\mathrm{Na}\mathrm{}\left(3s\right)+2\mathrm{}\hslash \omega \to \mathrm{Na}\mathrm{}\left(5s\right)\mathrm{}$ and of $\mathrm{Li}\mathrm{}\left(2s\right)+8\mathrm{}\hslash \omega \to \mathrm{Li}\mathrm{}\left(3s\right)\mathrm{}$ are given.

We have measured the optical excitation functions and polarizations of the Mg resonance line (2852 Å) and of the ${\mathrm{Mg}}^{+}$ resonance lines (2796 Å, 2803 Å, unresolved) arising from ionizing excitation of magnesium atoms, for electron-impact energies from the excitation thresholds to 1400 eV. In our crossed-beam apparatus, the electron-beam energy resolution was ≈ 0.25 eV for energies below 10 eV, and the atom beam was optically thin. The excitation function of the ionic lines was normalized to that of the atomic line by relative intensity measurements. The 2852-Å excitation function, when normalized to Born theory in the high-energy limit, has a maximum cross section of $17.3\pi a_0^2\pm 3\%$ at 18.5 eV. This excitation function is graphically compared with the resonance-line excitation functions of Na, Ca, and Li previously measured in this laboratory. The 2852-Å polarization function is consistent with the theoretical threshold limit of + 100%, and has a sharp feature near 5 eV which cannot be due to cascading.

The relative excitation function for electron-impact excitation of H to yield Balmer $\alpha$ has been measured from threshold to 500-eV collision energy in a crossed-beam apparatus. The relative contributions of the $3S$,$3P$, and $3D$ states to this excitation function have been measured by modulating the electron beam and discriminating on the basis of their different lifetimes for radiative decay after excitation. The resulting set of relative $3S$,$3P$, and $3D$ cross sections has been normalized by equating the total measured Balmer-$\alpha$ cross section at 500 eV to the Born approximation. The normalized cross sections are then compared to available theories at lower energies. In contrast to virtually all known excitation cross sections of neutral atoms, which fall below the Born theory at low energies, the H ($1S\to 3D$) cross section exceeds the Born theory, apparently owing to coupling between the $3D$ and $2P$ states.

A microwave transient-response technique has been used to determine electron-neutral elastic momentum-transfer collision frequencies in argon as a function of electron energy in the range from 0.08 to 4 eV. An analytical technique has been developed for the unfolding of the monoenergetic collision-frequency data from the measured transient-response decay rate. The over-all experimental and analytical error is estimated to be less than ±25% except in the immediate vicinity of the argon Ramsauer minimum where the transient-response results may considerably overestimate the true collision frequency. The results are compared with argon collision-frequency data derived from previous dc swarm measurements and modified effective-range conversions of total elastic scattering data. The transient-response results agree well with the dc swarm data except at the Ramsauer minimum, where the transient-response data agree more closely with the modified effective-range results.

Atomic oscillator strengths have been computed by applying a Bethe-Goldstone hierarchy of variational calculations consistently to both initial and final states of a given transition. For the $1s^2{}_{}{}^1{}_{}{}^{}S\to 1s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ transitions in the He isoelectronic sequence, computed $f_l$ (length) and $f_v$ (velocity) values and the corresponding transition energies are in good agreement with the accurate $f$ values of Pekeris et al. and with observed transition energies. For the Be isoelectronic sequence, $f_l$ and $f_v$ for $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S\to 1s^{2}2s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ are in close agreement with each other if all double virtual excitations from $1s2s2p$ (with respect to $1s^{2}2s2p$ as reference configuration) are included in the variational calculations. The agreement between computed and observed transition energies is very good. Similar results have been obtained for other valence shell excitations of Be i: $2s2p{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}\to 2p^2{}_{}{}^3{}_{}{}^{}P$, $2s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}\to 2p^2{}_{}{}^1{}_{}{}^{}D$, $2s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}\to 2p^2{}_{}{}^1{}_{}{}^{}S$. The $2p^2{}_{}{}^1{}_{}{}^{}S$ state apparently lies slightly above the Be ii $2s$ threshold. The $2p^2{}_{}{}^1{}_{}{}^{}D$ state interacts strongly with the $2s3d{}_{}{}^1{}_{}{}^{}D$ Rydberg state. The oscillator strength is nearly zero for the ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}\to {}_{}{}^1{}_{}{}^{}D$ transition.

Potential-energy curves and coupling matrix elements have been calculated for the CsH and Cs${\mathrm{H}}^{+}$ systems. The potentials and coupling terms were employed in the coupled equations where the nuclear motion is described classically to obtain the energy dependence of the cross sections for energies 0.1-3.0 keV. The cross sections so obtained were: $Q_{+0\mathrm{}}$ for the reaction ${\mathrm{H}}^{+}$ + Cs → H + ${\mathrm{Cs}}^{+}$, $Q_{+m}$ for ${\mathrm{H}}^{+}+\mathrm{Cs}\to \mathrm{H}\mathrm{}\left(2s\right)+{\mathrm{Cs}}^{+}$, $Q_{-0\mathrm{}}$ for ${\mathrm{H}}^{-}$ + ${\mathrm{Cs}}^{+}$ → H + Cs, and $Q_{0-}$ for $\mathrm{H}\mathrm{}\left(1s\right)+\mathrm{Cs}\to {\mathrm{H}}^{-}+{\mathrm{Cs}}^{+}$. The CsH potential-energy curves were also used to estimate the ionization cross sections $Q_{\mathrm{i}\mathrm{o}\mathrm{n}-\mathrm{C}\mathrm{s}}$ for ${\mathrm{H}}^{-}+\mathrm{Cs}\to {\mathrm{H}}^{-}+{\mathrm{Cs}}^{+}+e$ and $Q_{\mathrm{i}\mathrm{o}\mathrm{n}-\mathrm{H}}$ for ${\mathrm{H}}^{-}+\mathrm{Cs}\to \mathrm{H}+\mathrm{Cs}+e$, and to yield an upper-limit cross section $Q_{m-}$ for the reaction $\mathrm{H}\mathrm{}\left(2s\right)+\mathrm{Cs}\to {\mathrm{H}}^{-}+{\mathrm{Cs}}^{+}$. Semiempirical calculations were employed to obtain the deactivation cross section $Q_{\mathrm{mg}}$ for $\mathrm{H}\mathrm{}\left(2s\right)+\mathrm{Cs}\to \mathrm{H}\mathrm{}\left(2p\right)+\mathrm{Cs}$ where the product $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ rapidly radiates to $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$. At 0.5 keV the theoretical cross sections obtained were $Q_{+0\mathrm{}}=1.2\mathrm{}\times {10}^{-14\mathrm{}}$, $Q_{+m}=5.5\mathrm{}\times {10}^{-15\mathrm{}}$, $Q_{-0\mathrm{}}=1.5\mathrm{}\times {10}^{-14\mathrm{}}$, $Q_{0-}=8.2\mathrm{}\times {10}^{-16\mathrm{}}$, $Q_{\mathrm{i}\mathrm{o}\mathrm{n}-\mathrm{C}\mathrm{s}}=1.3\mathrm{}\times {10}^{-15\mathrm{}}$, $Q_{\mathrm{i}\mathrm{o}\mathrm{n}-\mathrm{H}}=2.9\mathrm{}\times {10}^{-15\mathrm{}}$, $Q_{\mathrm{mg}}=8.1\mathrm{}\times {10}^{-15\mathrm{}}$, and $Q_{m-}\le 4\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. For the reactions where experimental data is available, the theoretical cross sections are in satisfactory agreement with experiment except for $Q_{0-}$, where the theoretical values are approximately a factor of 5 larger than the experimental values.

A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close coupling with respect to vibrational degrees of freedom but adiabatic-nuclei with respect to rotation. In addition, this theory can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated. Explicit formulas for all these cross sections are given. The theory is applied to low-energy $e$-${\mathrm{N}}_2$ scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the ${\Pi }_g$ partial wave. The contribution of remaining partial waves can be obtained directly from the adiabatic-nuclei approximation. The close-coupling calculation for the ${\Pi }_g$ wave is carried out, and we find that it does give rise to the substructure as well as the gross structure of the 2.4-eV resonance. When this amplitude is combined with the adiabatic amplitudes, we can compute absolute values of all cross sections of interest. In particular we find that vibrational excitation cross sections are about twice as large as previously inferred. The momentum-transfer cross section can also be computed, and it too reveals substructure within the gross structure resonance.

The impact-parameter dependence of the probability for production of target $K$ x rays has been measured for oxygen projectiles on copper and for carbon and fluorine projectiles on argon at scaled velocities near 0.5. The O-on-Cu data were taken for 1.56-, 1.88-, and 2.69-MeV/amu O beams incident upon thin Cu foils. A thin Ar-gas target was used for 1.56-MeV/amu C and F beams, permitting measurements to be made for charge-pure ${\mathrm{C}}^{+4\mathrm{}}$, ${\mathrm{C}}^{+6\mathrm{}}$, ${\mathrm{F}}^{+9\mathrm{}}$ and ${\mathrm{F}}^{+5\mathrm{}}$ projectiles. Ar and Cu $K$ x rays were observed with a Si(Li) detector and scattered projectiles with a collimated surface-barrier detector. Comparison of the shapes of the measured $K$-vacancy-production probability curves with predictions of the semiclassical Coulomb approximation (SCA) shows adequate agreement for the O-on-Cu system. For the higher ratio of projectile-to-target nuclear charge ($\frac{Z_1}{Z_2}$) characterizing the C-on-Ar and F-on-Ar systems, the SCA predictions are entirely inadequate in describing the observed impact-parameter dependence. In particular, they cannot account for large probabilities found at large impact parameters. Furthermore, the dependence of the shapes on the projectile charge state is found to become pronounced at larger $\frac{Z_1}{Z_2}$. Attempts to account for this behavior in terms of alternative vacancy-production processes are discussed.

We present cross sections for the excitation of the two lowest ($b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $a{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$) triplet states of molecular hydrogen by electron impact for incident electron energies ≤ 20 eV. The cross sections are calculated using the distorted-wave approximation with the inelastic transition density obtained in the random-phase approximation. An efficient expansion technique using Gaussian basis functions allows us to avoid numerical integrations and to treat accurately the noncentral nature of the scattering process with full allowance for electron exchange. The sum of the two triplet cross sections is found to be in good agreement with the experimental cross section for dissociation of ${\mathrm{H}}_2$ into 2H.

The method of polarized pseudostates has been used to calculate cross sections for the elastic scattering of electrons by atomic oxygen. These pseudostates are added to the close-coupling expansion to give a polarization potential in agreement with experimental values of polarizability. The resulting elastic cross sections are in good agreement with other theoretical calculations as well as with experiment for energies up to 10 eV. The reactance matrices obtained in this calculation have been used to calculate collision strengths for fine-structure transitions in the ground-state ${}_{}{}^3{}_{}{}^{}P$ term for electron temperatures above 5000° K.

Incoherent x-ray scattering factors have been calculated for Li through Ne by integrating over Compton profiles calculated using the impulse approximation. Analytic expressions for the impulse-approximation Compton profiles (IACP) were derived from Clementi-Hartree-Fock (HF) analytic wave functions. Both experimental and theoretical HF electron binding energies were used in the numerical computation of the IACP inelastic scattering factors. These IACP scattering factors are compared with results obtained from the Waller-Hartree (WH) theory using HF atomic wave functions and a configuration-interaction (CI) wave function. Differences of as much as a factor of 2 are found at low scattering angles between the IACP and WH results calculated from HF wave functions. At low scattering angles the IACP results are in closer agreement with WH scattering factors calculated from the CI wave function than those computed from HF functions. A realistic possibility for obtaining more accurate inelastic scattering factors is demonstrated by direct integration over Compton profiles than can be computed from the WH scheme.

Assuming the necessity of basis sets more general than one-particle function products, a new procedure is proposed for approximating the solution of the Schrödinger equation in order to eliminate the factorial-rate increase in the number of terms that generally arise when a trial function not constructed from one-particle function products is used. The handling of the spin is discussed under the assumption that the Hamiltonian is spin-free and the explicit spin dependence in the wave function is not needed.