The collisional deactivation of the Na $5s$ and $4p$ states by collisions with ${\mathrm{N}}_2$ molecules has been studied using the method of laser-induced fluorescence. The total cross sections for the depopulation of the $5s$ and $4p$ states are 86(8) and 43(4) ${\mathrm{\AA }}^2$, respectively. The cross sections for the specific collisional transfers $5s\to 4p$, $5s\to 3d$, and $4p\to 3d$ are 32(8), 10(2), and 19(3) ${\mathrm{\AA }}^2$, respectively.

In the spirit of Firsov's theory as modified by Brice, an exact expression for the electronic stopping cross section ($S_e$) has been evaluated using analytical Hartree-Fock-Slater wave functions. Two consequences of this treatment are that (a) the individual orbital contribution to $S_e$ is obtained, (b) an ab initio calculation of Brice's $Z$ parameter is performed. In the former case conclusions are drawn about the importance of orbitals to the evaluation of $S_e$. For the latter case a comparison is made between the exact $Z$ values and Brice's values.

$K$-shell vacancy-sharing ratios have been measured for beams of aluminum, silicon, chlorine, and argon with energies between 0.7 and 16 MeV incident on solid targets of aluminum and copper, and gas targets of sulphur and argon. Values of these sharing ratios as a function of the reciprocal of the velocity of the incident ions have been observed to deviate from predicted exponential behavior under experimental conditions such that the deviations cannot be ascribed to multiple-collision effects. Results are presented for measurements of $\sigma \left(2p\sigma \right)$, the cross section for production of vacancies in the $2p\sigma$ molecular orbital, and of $\sigma \left(1s\sigma \right)$, the cross section for direct production of vacancies in the $1s\sigma$ molecular orbital, for aluminum ions with kinetic energies between 0.7 and 2.5 MeV incident on argon atoms. Comparisons are made between these measured cross sections and appropriate calculations.

A theoretical analysis of secondary electron spectra, which has previously been applied to electron-impact ionization of atoms and molecules, is applied to the experimental data on ionization of He, Ne, and Ar by protons in the 0.1-1.5-MeV energy range. The data are also compared with ab initio Born-approximation calculations. Our theoretical analysis clearly brings out expected features in the secondary-electron spectra for incident proton energies of 1 MeV and up. Inner-shell contributions and the charge transfer to the continuum process tend to obscure the appearance of a simple asymptotic behavior at lower proton energies; for a given incident energy, the analysis is simpler for atoms and molecules with lower nuclear charge.

Calculations are reported for low-energy $e$-${\mathrm{N}}_2$ scattering cross sections in the static-exchange approximation. Our approach involves solving the Lippman-Schwinger equation for the transition operator in a subspace of Gaussian functions. A new feature of the method is the analytical evaluation of matrix elements of the free-particle Green's function. Another development is the use of an analytical transformation to obtain single-center expansion coefficients for the scattering amplitude from our multicenter discrete-basis-set representation of the $T$ matrix. We present results for the total elastic and rotational excitation cross sections, and the momentum-transfer cross section, for incident electron energies from 0.5 to 10 eV. Comparison is made with other theoretical results and experimental data.

The eikonal-Born series method is used to study the imaginary part of the forward elastic-scattering amplitude for the scattering of electrons (positrons) by helium. Total cross sections are obtained by use of the optical theorem, and these cross sections are compared with recent experimental results and with optical-model predictions. This comparison shows clearly the very different convergence rates of perturbation theory in the electron and positron cases.

The partial photoionization cross sections for the four lowest-lying states of C${\mathrm{O}}_2^{+}$ have been measured with synchrotron radiation between 20 and 40 eV. The results are compared to previous photoemission measurements at discrete photon energies as well as fluorescence measurements using continuous radiation. The interrelation between photoemission and fluorescence data is discussed. The existence of four weak states of C${\mathrm{O}}_2^{+}$ with binding energies between 22 and 37 eV is verified. The dominant part of the photo-current at 40 eV is found to be associated with low-lying ionic states.

An exchange perturbation theory is developed which is identical through first order in the primitive function $G$ with the Eisenschitz-London (EL) theory. It is shown that in higher orders, $G$ is different from the EL primitive function and from the primitive functions of related theories. The function $G$ is least distorted from the zeroth-order function $F^0$, a product of functions for the subsystems when the interactions have been set equal to zero. The potential which distorts $F^0$ into $G$ is more thoroughly screened than in any other theory we have examined. We argue that this EL-type theory should be used when the unscreened interactions are strong.

The $L_{23}-M_{4,5}{M}_{4,5}$ principal and satellite Auger spectra are synthesized for atomic Cu and compared to the measurements in solid Cu. It is found that the $L_2-L_3{M}_{4,5}$ Coster-Kronig rate is significantly different in intermediate coupling from its value in $j-j$ coupling. With intermediate coupling and matrix elements obtained with a Cu-ion potential (with an $L$-shell hole), the synthesized satellite spectra do not agree with the Cu measurements, but do agree with the measurements on Zn, when the energy scale is suitably contracted. With $L_2-L_3{M}_{4,5}$ matrix elements obtained with a neutral-atom Cu potential, the synthesized Cu spectra are in quantitative agreement with the measurements. However, in this case the calculated Cu $L_2$ linewidth is significantly larger than the measured values. All the required transition-rate expressions in intermediate coupling are presented.

Positions, widths, and oscillator strengths for the $2s-2p$ "shape" resonance and the lowest Feshbach resonance in the ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ spectrum of ${\mathrm{H}}^{-}$ have been computed via the method of complex coordinates. The dc Stark broadening of the shape resonance has been determined giving a quantitative estimate of the effects of plasma microfields on the resonance and explaining the negative observational results of Ott et al. [Phys. Rev. A 12, 2009 (1975)].

A crossed ion-laser beam apparatus has been used to obtain ${\mathrm{Cs}}^{-}$ and ${\mathrm{K}}^{-}$ cross sections for photodetachment into the ground (${}_{}{}^2{}_{}{}^{}S$) and first excited state (${}_{}{}^2{}_{}{}^{}P$) of the neutral atom in the photon energy range near the threshold for production of ${}_{}{}^2{}_{}{}^{}P$ neutrals. A total cross section is determined from the cross section for production of neutral atoms and the partial cross sections are obtained from the cross section for production of photoelectrons transmitted through a low-pass kinetic-energy filter. The filter characteristics are determined empirically and the discrimination between ground-and excited-state detachment channels is approximately 1000. It is apparent from the data that the detachment channels are strongly coupled in the threshold region, a result attributed to long-range forces between the detached electron and the neutral atom. The data are compared with a semiempirical multichannel photodetachment model developed by Lee; the model is quite successful in its prediction of the energy-dependent cross section for production of Cs ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ from knowledge of the previously measured ${\mathrm{Cs}}^{-}$ total photodetachment cross section. We have produced an approximate fit to the ${\mathrm{K}}^{-}$ data with this model. The following electron affinities have been determined: for Cs, 0.4715(3) eV, and for K, 0.50147(10).

Theoretical estimates are proposed for the profiles of the central components of Lyman-$\alpha$ lines for conditions where Stark effects caused by high- and low-frequency fields are more important than fine-structure splitting. An experiment-theory discrepancy of a factor ∼2 for hydrogen Lyman-$\alpha$ lines is removed by allowing also for electron-produced low-frequency fields.

Absolute cross sections for pair production by photons incident on targets of aluminum, iron, copper, tin, and lead were measured using the internal-source method. The measurements were made for the 1.119- and 2.6145-MeV $\gamma$ rays in the decays of ${}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$ and ${}_{}{}^{228}{}_{}{}^{}\mathrm{Th}$, respectively, and also a composite cross section was measured for the mixture of the 1.1732- and 1.3325-MeV $\gamma$ rays in the decay of ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$. The results are in general agreement with the theoretical predictions of Øverbø and those of Tseng and Pratt, and clearly demonstrate the importance of accounting for electron screening of the nuclear Coulomb potential in the calculations.

A theory is developed to describe the interplay of vibrational relaxation and luminescence occurring simultaneously in a molecule, in terms of a master equation involving true sinks of probability. Specifically, the basic equation is the Montroll-Shuler equation augmented by the addition of sink terms which can be nonlinear as well as linear in the vibrational energy. These terms describe radiative and nonradiative decay and expressions for the former are derived explicitly in terms of Franck-Condon factors. Exact solutions in terms of known functions are obtained in the linear case for several physically motivated initial vibrational distributions, viz., $\delta$-function, Boltzmann, Poisson, and Laguerre. Two perturbation schemes are developed to analyze the nonlinear case, one of which is useful for small nonlinearities and the other for arbitrarily large nonlinearities but for low temperatures. Illustrative applications of the theory include the exact calculation of time- and frequency-resolved emission spectra (linear decay calculation) and the perturbation analysis of quantum yields in the presence of strongly energy-dependent nonradiative transitions (nonlinear decay calculation).

An analytically tractable extended asymptotic model for the response properties of weakly bound anions (small detachment energy $E$) is proposed and the $2^l$-pole polarizability, the sum rules, and the photodetachment cross section determined by the model are computed analytically. The model is based on the following two assumptions: (1) The alkali-anion valence orbital ${\Psi }_{0,\gamma }\mathrm{}\left(r\right)\mathrm{}$ may be approximated by its asymptotic form ${\Psi }_{0,\gamma }\mathrm{}\left(r\right)\mathrm{}\sim {\mathrm{Nr}}^{-1\mathrm{}}{e}^{-\gamma r}$, as $r\to \infty$, where $N$ is a normalization factor and $\gamma ={\mathrm{}\left(2E\right)\mathrm{}}^{\frac{1}{2}}$. (2) The alkali-anion $l$-wave continuum states are approximated by analytic eigenstates determined by a one-parameter $r^{-2\mathrm{}}$-type pseudopotential. The pseudopotential parameter $\lambda$ is chosen to reproduce an appropriately defined representative $l$-wave electron-alkali phase shift. For the case of zero pseudopotential ($\lambda =l$), the model reduces to one successfully applied to the hydride anion. Dipole polarizabilities and photodetachment cross sections determined from the model for ${\mathrm{Li}}^{-}$, ${\mathrm{Na}}^{-}$, and ${\mathrm{K}}^{-}$ are compared with the numerical results of Moores and Norcross. Agreement is typically within 10-15% if the pseudopotential ($\lambda \ne l$) is included.

An exchange perturbation theory is developed which yields in infinite order the same primitive function $F$ that is found in infinite order with the Hirschfelder-Silbey (HS) theory. The perturbation equations are identical to the HS equations only through first order. This is because the perturbing potential in our theory is not the bare interaction potential of the HS theory, but rather that potential screened by a nonlocal potential. The screening is the weakest that we have found in studying the equations satisfied by primitive functions, which are least distorted from products of the functions for the subsystems when the interactions have been turned off. We argue that this HS-type theory is best used when the interactions are weak.

We have used the ion-beam method with a gas-jet target to measure the radiative lifetimes of three laser levels ($4p{}_{}{}^3{}_{}{}^{}P$, $4p^{\prime }{}_{}{}^3{}_{}{}^{}D$, $4p^{\prime }{}_{}{}^1{}_{}{}^{}F$) and two other levels of ${\mathrm{Cl}}^{+}$. The levels and lifetimes in nanoseconds are: $4p{}_{}{}^3{}_{}{}^{}P$, 11.6±0.6; $4p^{\prime }{}_{}{}^3{}_{}{}^{}D_3^{}{}_{}{}^{}$, 8.7±0.9; $4p^{\prime }{}_{}{}^1{}_{}{}^{}F_3^{}{}_{}{}^{}$, 12.7±0.6; $4p^{\prime }{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, 5.0±0.6; and $4p^{\prime \prime }{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, 6.7±1.3.

We solve the problem of two discrete quantum levels which are coupled by a time-dependent radio-frequency pulse $W\left(t\right)=V\left(t\right)\mathrm{} e^{i\nu t}$, where the envelope function is of a form suggested by Rosen and Zener: $V\left(t\right)=V_{0}sech\left(\frac{\pi t}{T}\right)$. When a level damping constant $\gamma$ is included, in the manner of Bethe-Lamb theory, the solutions show new features which are not expected on the basis of a sudden-approximation theory, where $V\left(t\right)=\mathrm{const}$ over the pulse duration $T$. Various transient effects such as "ringing" are not present in the extended Rosen-Zener solution; these effects are related to the large impulsive forces at the step discontinuities in the sudden approximation. The final-state level amplitudes can be quite different depending on the size of the pulse rise time $T$ as compared with the system Bohr period $\frac{1}{\omega }$. Our results allow a continuous and quantitatively exact comparison between the extremes of the sudden ($\omega T\ll 1$) and adiabatic ($\omega T\gg 1$) approximations. A model of a "quasisudden" step function is also constructed, and remarks are made on the validity of a certain conjecture by Rosen and Zener.

Pattern-recognition techniques are applied to the classification of atomic spectral transitions using hydrogen as a model system. Certain of the transitions have been randomly selected and treated as unclassified lines. Training of the known data at the 100% level has been achieved. Prediction of $n_1$ is 95.8%, while predictions of transitions of the type $n_1$, $l_1\to l_2$ and $n_1$, $l_1\to l_2$, $J_1\to J_2$, are 83.4% and 66.67%, respectively. Using similar techniques, two unknown transitions in neutral atomic sodium have been classified.

Curium energy levels have been classified according to configuration using pattern-recognition techniques. Four features—energy level, Landé $g$, $J$, and isotope shift—have been used to describe each level. Forty levels have been assigned with high probability based on consistent results obtained by various pattern recognition techniques. This represents an increase of 9% for even levels and 19% for odd levels. In addition, 14 levels have been assigned to one of two possible configurations. Pattern recognition in general, as applied to atomic energy-level classification, is discussed.