An eikonal formalism is developed to calculate corrections due to screening to the exactly solvable case of the unscreened Coulomb field. The high-energy Sommerfeld-Maue wave functions are used, and, by construction, the unscreened case is reproduced exactly for all coordinate space. The modification caused by screening is found to be multiplicative, and it appears as a phase factor $\exp \{\mp \mathrm{iZ}{e}^2(\frac{E}{p}\left)\ln \right[p(r\pm z)]-i(\frac{E}{p})\times \int {\pm \infty }^{z}V(\rho , \xi )d\xi \}$, where $p$ is a large momentum, $E$ is the corresponding relativistic energy, and $V$ is the screened Coulomb field. Our approximate high-energy wave function is given by one formula for all coordinate values, without any need to introduce partial waves, is easy to calculate numerically, and is shown to satisfy a second-order differential equation to a very good accuracy practically in the whole space. For example, the outgoing solution satisfies an appropriate equation to an accuracy better then 3% in a very large region of cylindrical variables $\rho \ge 0.1$, $z\le 2p$, which expands with increasing $p$.

This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the $n=3\mathrm{}$ state by electron bombardment. By coherence is meant that the density matrix describing the atom after the collision has off-diagonal matrix elements in the field-free basis. The differential cross section for producing Balmer-$\alpha$ photons at 90° to the electron beam is calculated as a function of an applied longitudinal electric field. The off-diagonal elements show up as a dependence of the observed light on the directions of the electric field. Theoretical results based on the Born approximation are compared with an experiment at 200 and 500 eV. It is pointed out that this method for measuring relative phases of scattering amplitudes can be generally applied and is not restricted to $n=3\mathrm{}$ excitation of hydrogen.

The character of the ionic beam downstream from the foil in a beam-foil experiment depends on whether the incident particle entering the foil is atomic or molecular. In this paper it is demonstrated how incident molecules affect charge-state distributions, beam-particle scattering, charge exchange, excitation functions, mean lives and transition probabilities, alignment, and linear straggling after the foil. The possibility of exploiting certain molecular effects for further study is also discussed.

We have used the beam-foil interaction mechanism to populate highly excited states in lithium by passing 300-keV ${\mathrm{Li}}^{+}$ ions through 8-μg/${\mathrm{cm}}^2$-thick carbon foils. The energies of the electrons emitted via autoionization were analyzed. By moving the foil along the beam axis, prompt and delayed electrons due to decays of Lii and Liii states were identified. These spectra are interpreted with the help of detailed theoretical calculations. The excitation energies of the $\mathrm{LiI}\left(1s2\mathrm{}{s}^2\right){}_{}{}^2{}_{}{}^{}S_{}^e{}_{}{}^{}$ and $\mathrm{LiII}\mathrm{}\left(2s2p\right)\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}P_{}^o{}_{}{}^{}$ terms were determined to 0.5% accuracy. We have observed decays of doubly excited Liii states above the $n=2\mathrm{}$ threshold. On the basis of our theoretical estimates, we assign a peak in the high-energy portion of the spectra as due to deexcitation of triply excited $\mathrm{LiI}2s^{2}2p$ and $2s2p^2$ configurations.

A simple theoretical method for calculating radiative capture cross sections is proposed. Applying the quantum defect theory, the radiative capture process and the tip bremsstrahlung process are treated together on the same footing. An application to radiative capture of 50-keV electrons by ${\mathrm{Au}}^{+49\mathrm{}}$ ions is presented.

The ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$ doubly excited states of ${\mathrm{Ar}}^{-}$ are formed by charge exchange of ${\mathrm{O}}^{-}$ and ${\mathrm{H}}^{-}$ ion beams with argon. Measurements of the angular distribution of autodetached electrons from these states yield the relative populations of the $M_J$ magnetic substates for the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state. A drop in the cross section for the formation of both $J$ states is seen near 1.5 keV for ${\mathrm{H}}^{-}$ -on-Ar exchange collisions.

Cross sections have been measured for the differential (in angle) scattering of 15-keV ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^0$ in targets of He, Ar, ${\mathrm{H}}_2$, and ${\mathrm{N}}_2$. Separate cross sections are presented for scattering projectiles in the singly charged (${\mathrm{H}}^{+}$), neutral (${\mathrm{H}}^0$), and negatively charged (${\mathrm{H}}^{-}$) states; scattering angles range from 0.5 to 10 deg. Summing these constituent cross sections we arrive at a "total" cross section for scattering all projectiles into a particular angle. This "total" differential cross section is compared with predictions using a simple screened Coulomb potential; for the molecular targets the cross section is taken to be twice that for the corresponding atom. For ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^0$ impact on He and ${\mathrm{H}}_2$ the measured cross section agrees with the predicted value; in these cases the effect of screening is negligible. For ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^0$ impact on Ar and ${\mathrm{N}}_2$ the measurements agree fairly well with the screened Coulomb calculation at angles up to 1.5 deg and then fall lower than the predictions at larger angles; theory and experiment differ by a factor of two at 10 deg in one case. For all cases considered the formation of scattered ${\mathrm{H}}^{-}$ ions occurs in less than 2% of the collision events.

The first Born approximation calculation of Kroll and Watson is extended by a time-dependent eikonal calculation. The resulting amplitude returns to their first Born approximation in the extreme limit of a weak scattering potential or small momentum transfer. In the ultrastrong-field limit, the total cross section reduces to the field-free eikonal result.

The maximum and high-energy loss side of the Bethe ridge, obtained from high-energy electron-impact spectroscopic observations with 25-keV electrons, has been interpreted in terms of an effective Compton profile, $J_{\mathrm{eff}}(q, K)$ defined in terms of the absolute generalized oscillator strength (GOS) $f(K, E)$ as $J_{\mathrm{eff}}(q, K)=\left(\frac{2K^3}{E}\right)f(K, E)$, where $q$ is $\frac{(E-K^2)}{2K}$ with $K$ the momentum transfer and $E$ the energy loss. It is well known that for He and ${\mathrm{H}}_2$ this effective profile for constant $q$ approaches the x-ray Compton profile in the limit of large $K$ for fixed but large incident-electron energy. We report here the discovery of plateaus in the envleope of $J_{\mathrm{eff}}(q, K)$ for constant $q$ with increasing $K$, in addition to the x-ray profile limit, for target systems containing more than one shell. In the cases of ${\mathrm{N}}_2$ and Ne, an additional plateau is observed which is associated with the outer-shell electrons because the maximum of the Bethe ridge has not yet reached the energy-loss region of core or $K$-shell excitations. This additional plateau makes it possible to define an effective outer-shell Compton profile. In the case of argon, two plateau regions are observed before the Bethe ridge reaches the $K$-shell contributions and effective profiles are defined for the $M$ and $M$- plus-$L$ shells. Comparisons with theory suggest that the cumulative-shell Compton profiles agree with direct theoretical computations utilizing the x-ray formula but including only contributions from the shell(s) in question at the 5% accuracy level. On the other hand, computations of the GOS using explicit final-state ion wave functions agree with our experiments at the (1-2)% level.

Stationary bounds are obtained on the $K$ matrix, which is characterized by eigenphase shifts and mixing parameters that describe the scattering process. It is assumed that the incident particle is distinguishable from the target particles, and that if there are any open channels apart from the ground state, they are excitation channels. The new development is the omission of the requirement that the wave functions and energies of the target states associated with open channels be known exactly. A stationary lower bound is obtained by using the close-coupling approximation and forming a stationary bound on the matrix potential which arises in that approximation. Stationary upper and lower bounds are obtained by the development of stationary upper and lower bounds on the full (exact) optical-model potential; the effects of virtual rearrangements can be included in the latter approach. The stationary bounds derived are rigorous if the calculation is sufficiently accurate so that the bounds on the tangent of each eigenphase lie on the correct branch. This requirement exists in much the same way as in earlier work, which provided calculable bounds only when the target wave functions are known precisely. It is not a new feature of the present paper, whose principal concern is the extension of this earlier work to cases where such precise information about the target is lacking.

A model for calculating the dissociative ionization cross sections of diatomic molecules is developed. The activated state for dissociative ionizations is modeled to occur via the ejection of a bound electron and an excitation of another bound electron. This process is described by successive two-electron scatterings in the first Born and the binary-encounter approximations. Comparison of calculated cross sections with available experimental data for five diatomic molecules (${\mathrm{H}}_2$, CO, ${\mathrm{N}}_2$, NO, and ${\mathrm{O}}_2$) shows good agreement with incident-electron energies above 200 eV.

An eikonal approximation has been used to investigate the elastic positron-hydrogen-molecule scattering problem. The effective potential used here includes the static as well as the polarization potentials. The spherical and the nonspherical parts of both potentials are taken into consideration. The results have been obtained from 0.1 to 50 eV. The results for the elastic cross section are found to be very close to the experimental findings below the positronium-formation threshold. The effect of the polarization potential is found to be appreciable even up to 50 eV.

The clustering of ${\mathrm{N}}_2$ to ${\mathrm{Li}}^{+}$ has been studied experimentally using a drift tube at a gas temperature of $318K$. The gas pressure was varied between 0.5 and 1.5 Torr, and $\frac{E}{N}$ (the ratio of the uniform electric field strength in the drift region to the neutral number density) was varied between 9 and 24 Td (1 Td=${10}^{-17\mathrm{}}$ V ${\mathrm{cm}}^2$). Under these conditions, the major reactions are ${\mathrm{Li}}^{+}+{\mathrm{N}}_2+{\mathrm{N}}_2\underset{k_{12}}{\stackrel{k_{21}}{\rightleftarrows }}{\mathrm{Li}}^{+}·{\mathrm{N}}_2+{\mathrm{N}}_2 \mathrm{and} {\mathrm{Li}}^{+}·{\mathrm{N}}_2+{\mathrm{N}}_2+{\mathrm{N}}_2\underset{k_{23}}{\stackrel{k_{32}}{\rightleftarrows }}{\mathrm{Li}}^{+}2{\mathrm{N}}_2+{\mathrm{N}}_2$ The rate coefficients and the mobilities of ${\mathrm{Li}}^{+}$·${\mathrm{N}}_2$ and ${\mathrm{Li}}^{+}$·2${\mathrm{N}}_2$ were deduced by comparing measured arrival-time profiles of the ions with profiles generated by an analytical drift-tube model developed for three interreacting ion swarms. We find that the association rate coefficient $k_{21}$ decreases from 2.0×${10}^{-30\mathrm{}}$ ${\mathrm{cm}}^6$/sec at $\frac{E}{N}=9\mathrm{} \mathrm{Td}\mathrm{to} 1.7\times {10}^{-30\mathrm{}}$ ${\mathrm{cm}}^6$/sec at $\frac{E}{N}=24\mathrm{}$ Td, the collisional-dissociation rate coefficient $k_{12}$ increases from 0.7×${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec at $\frac{E}{N}=9\mathrm{}$ Td to 1.6×${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec at $\frac{E}{N}=24\mathrm{}$ Td, and the collisional-dissociation rate coefficient $k_{23}$ increases from 4.8×${10}^{-13\mathrm{}}$ ${\mathrm{cm}}^3$/sec at $\frac{E}{N}=9\mathrm{} \mathrm{Td}\mathrm{to} 1.6\times {10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec at $\frac{E}{N}=24\mathrm{}$ Td. Adequate fits could be obtained with values of $k_{32}$ from 1.6 to 3.0 (×${10}^{-29\mathrm{}}$) ${\mathrm{cm}}^6$/sec; a median value of 2.2×${10}^{-29\mathrm{}}$ ${\mathrm{cm}}^6$/sec at all values of $\frac{E}{N}$ was used to obtain the above values of the other rate coefficients. The reduced mobility (and its standard deviation) for ${\mathrm{Li}}^{+}$ in ${\mathrm{N}}_2$ was found to be 3.87±0.13 ${\mathrm{cm}}^2$/V sec; for ${\mathrm{Li}}^{+}$·${\mathrm{N}}_2$ in ${\mathrm{N}}_2$, 2.04±0.12 ${\mathrm{cm}}^2$/V sec; and for ${\mathrm{Li}}^{+}$·2${\mathrm{N}}_2$ in ${\mathrm{N}}_2$, 1.96±0.12 ${\mathrm{cm}}^2$V sec.

The adiabatic-nuclei theory of electron-molecule scattering is extended to account for electronic excitation of the target. The approximate expressions for the wave function and the scattering amplitude are derived from a formally exact expansion in terms of the fixed-nuclei, electronic-scattering solutions. The formalism treats molecular-bound and continuum states on an equal footing. We also propose a modified expression for the adiabatic-scattering amplitude which is expected to have an increased range of validity near excitation thresholds.

We introduce an analogy between the theory of autoionizing states as described by Fano and the theory of certain states ("pseudo-autoionizing states") of an irradiated atom. These "pseudo-autoionizing states" are used to obtain a number of qualitative results concerning resonant multiphoton ionization probabilities for several experimental arrangements. This method makes clear the importance of nonresonant processes in determining resonant multiphoton ionization line shapes.

A relativistic source-field approach in radiation theory is examined and is shown to predict the radiative corrections which normally require second quantization of electromagnetic fields. The connection between this approach and conventional quantum electrodynamics is pointed out and discussed. For most practical situations, the source-field effects are negligible, and semiclassical radiation phenomena are described by the relativistic wave equation which we derive from the total Hamiltonian. This wave equation is then transformed to an exact multipolar form which is suitable for application to many radiation problems. Its nonrelativistic limit is obtained and interaction terms are interpreted.

A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a $c$ number. It is thus proved quite rigorously and generally that the use of a $c$-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.

Absorption spectra of high-density pure krypton and xenon gases, in the wavelength range 118-150 nm and the density range 1-80 amagat, exhibit a red shift of all the atomic lines. The shifts are interpreted by taking into account the high-density interactions with the help of the local field correction of Lorentz introduced in classical dispersion theory.

An expansion formula for Stark effect transition probabilities is derived in terms of field-free (spherical) transition probabilities. Expansion coefficients are squares of Clebsch-Gordan coefficients from the SO(4) = SU(2) × SU(2) description of the hydrogen atom. The method provides new sum rules for Stark transitions which explain regularities in previous calculations. Accurate formulas for average Stark transition probabilities obtain from application of the method to an empirical model for field-free transition probabilities. The approximation permits estimation of Stark lifetimes in the large-$n$ regime.

In the present work, probabilities of emission (absorption) of nuclear $\gamma$ radiation in molecules are calculated. In this process, molecular vibrations are excited and deexcited because of recoil of the nucleus. For vibrationally excited molecules, the existence of vibrational satellite shift is opposite in sign, and it allows compensation for the misalignment of the absorption and emission lines. The parameters (width, intensity, sign) of narrow frequency-tuned resonances of $\gamma$ radiation with the molecules excited by laser emission in a low-pressure gas are calculated. The contributions of vibrational anharmonicity and rotation-vibration interaction are discussed.