The $L$-shell ionization cross sections by charged-particle impact have been calculated in the plane-wave Born approximation, using relativistic hydrogenic wave functions for the target electrons. The effects of the binding-energy increase due to penetration of the projectile and the Coulomb deflection of the projectile are taken into account. The calculated values are compared with the corresponding values obtained by other theoretical models as well as the experimental data. It is found that the present theoretical predictions are in satisfactory agreement with the experimental results for low-energy protons.

Various techniques from the field of surface science have allowed the development of a method for measuring the total absolute cross section for electron-impact-induced dissociation of a number of molecules. The technique is particularly reliable for the fluoroalkanes such as C${\mathrm{F}}_4$, C${\mathrm{F}}_3$H, ${\mathrm{C}}_2$${\mathrm{F}}_6$, and ${\mathrm{C}}_3$${\mathrm{F}}_8$. The total dissociation cross section for C${\mathrm{F}}_4$ has been measured for energies between threshold (∼ 12.5 eV) and 600 eV. The magnitude of the cross section at its maximum is 5.5×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. Less extensive data are presented for C${\mathrm{F}}_3$H, ${\mathrm{C}}_2$${\mathrm{F}}_6$, and ${\mathrm{C}}_3$${\mathrm{F}}_8$. Their cross sections at the maxima are 5.8×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, 8.6×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, and 1.18×${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$, respectively. Arguments are presented which suggest that the total dissociation cross section for each of these gases is equal to the sum of the cross sections for excitation to all electronic and ionic states, i.e., the total cross section for electronic excitation. The results are discussed from the point of view of the Bethe theory. It is concluded that the Bethe asymptotic behavior is not yet attained in the energy range of these measurements.

The nonperturbative approach developed recently by Tripathy and Rao for the study of charge transfer in proton-hydrogen collisions has been applied to the problem of positronium formation in positron-hydrogen collisions. The cross section for capture into the ground state has been calculated by partially taking into account the Coulomb distortions but neglecting the polarization effect of the target atom. The calculated cross section has a maximum at an incident energy of 10.2 eV, and as the incident positron energy increases it approaches the results of the first Born approximation (FBA) of Massey and Mohr. The calculated results for capture cross sections and differential scattering cross sections for various incident energies have been compared with those from the FBA and other theoretical calculations.

The single differential (in electron angle or energy) and total scattering cross sections for the process ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{H}}^{+}+{\mathrm{H}}^{+}+e$ are calculated as functions of the incident proton kinetic energy. The calculation is based on the first-order term of a multiple-scattering theory proposed in a previous paper. The results are compared with experiments and other theoretical values. The behavior of the ionization cross section is studied as a function of the projectile charge. This variation is shown for the ${\mathrm{He}}^{2+}$-H collision.

Converged coupled-channel calculations of $e-{\mathrm{CO}}_2$ scattering have been carried out at very low scattering energies. The results are used to show that a virtual state is present in the model static-exchange-polarization $e-{\mathrm{CO}}_2$ interaction potential used in these calculations. This result provides a possible interpretation for experimental data on total, momentum-transfer, and vibrational-excitation cross sections. A scattering length of $-6.17\mathrm{}{a}_0$ is predicted.

The energy loss straggling of a point charge penetrating a free-electron gas is reevaluated on the basis of the Lindhard dielectric constant. A systematic expansion in powers of electron velocity, introduced at an early stage, allows a slight generalization of existing results. The validity of the procedure is tested by rederivation of stopping-power expressions of Lindhard and Winther. With regard to straggling, Bonderup's formula has been partially confirmed, but a correction is found that turns out to be important in numerical applications.

The approach to electron capture developed by Chan and Eichler is combined with the optical eikonal approximation for describing the effect of the internuclear potential on the projectile trajectory. In this way, a closed-form expression is derived for the differential cross section for $1s\to \mathrm{nlm}$ capture. Numerical calculations have been performed for the reaction ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}+{\mathrm{H}}^{+}$ at collision energies of 25, 60, and 125 keV. Good agreement is obtained with the recent data of Martin et al. by using trajectories undeflected by the internuclear potential at small deflection angles and Coulomb-deflected trajectories at large deflection angles.

Blair et al. have given a semiclassical form for the scattering amplitude describing a proton scattered by both a $K$-shell electron and by the nuclear plus Coulomb force of the target nucleus. This form is at variance with a recent experimental result of Duinker et al. We present both simple physical arguments and a detailed theoretical analysis which establish the conditions of validity of Blair's formula. We pay particular attention to the case of resonant nuclear scattering. We find that in the case of the experiment of Duinker et al., the Blair formula is expected to hold.

The ground-state hyperfine splitting of the ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}_{}^{+}{}_{}{}^{}$ ion has been measured with a precision of 4.6 × ${10}^{-11\mathrm{}}$. About ${10}^5$ ions were confined in a rf quadrupole trap for many hours. Hyperfine pumping was achieved by a pulsed tunable dye laser and transitions between the Zeeman sublevels were induced by microwaves, locked to a primary frequency standard. The transitions were detected via changes in the ionic fluorescence perpendicular to the laser beam. The final result is $W_{\mathrm{hfs}}=8\mathrm{}037741667.69\left(0.36\right)\mathrm{}$ Hz. The uncertainty stems in about equal parts from the extrapolation to zero electric and magnetic field strength.

Multiphoton ionization of molecular nitrogen ${\mathrm{N}}_2$ is investigated by using a neodymium-glass laser. The atomic ions ${\mathrm{N}}^{+}$ and the molecular ions $\mathrm{N}_2^{}{}_{}{}^{+}$ produced during the interaction are separated by a time-of-flight analyzer and collected on the cathode of an ion multiplier. The experimental results give the values 9±1 for the nonlinear interaction order for $\mathrm{N}_2^{}{}_{}{}^{+}$ and 12±1 for ${\mathrm{N}}^{+}$, and then lead to the determination of separate probabilities of multiphoton formation of $\mathrm{N}_2^{}{}_{}{}^{+}$ and ${\mathrm{N}}^{+}$; for a flux value of 2.44×${10}^{12}$ W/${\mathrm{cm}}^2$, these probabilities are, respectively, 3×${10}^{6\pm 0.7}$ ${\sec }^{-1\mathrm{}}$ and 2×${10}^{7\pm 0.7}$ ${\sec }^{-1\mathrm{}}$. The multiphoton excitation, ionization, and dissociation processes of ${\mathrm{N}}_2$ are discussed.

High-resolution two-photon spectroscopy was applied to investigate the msns ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ Rydberg states of the alkaline-earth elements Ca, Sr, and Ba. It is shown for ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}$, and ${}_{}{}^{137}{}_{}{}^{}\mathrm{Ba}$ that the hyperfine interaction causes a level shift between odd- and even-mass isotopes. A theoretical interpretation is presented which relates the energy-level shift for odd isotopes to the singlet-triplet separation which in turn is a function of the principal quantum number, and good agreement with the experimental results is found.

The paramagnetic resonance spectrum of metastable ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ atomic nitrogen has been observed downstream from an electrodeless discharge in nitrogen-helium gas mixtures. The $g$ factors for the nine observed transitions deviate significantly from the Lande formula. Analysis of the Zeeman effect shows that the departure from Lande formula is caused by an intermediate Paschen-Back effect which occurs in magnetic fields of only a few kilogauss. The nuclear hyperfine structure has been analyzed (for the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ nucleus) and coupling parameters determined. The fine-structure interval for the ${}_{}{}^2{}_{}{}^{}P$ states has been measured to be 12 970±80 MHz.

We consider the correlation of two particles on a sphere interacting via various repulsive forces: a Coulomb repulsion, a Gaussian, and a $\delta$ function. This "rigid-bender" picture with Coulomb repulsion provides a schematic model of intrashell angular correlation in doubly excited two-electron atoms. We examine energy levels and reduced densities $\rho \left({\theta }_{12}\right)$ for states corresponding to shells $n_1=n_2=2,3,4\mathrm{}$. Energy levels for fully converged states fall into remarkable rovibrator patterns, as found in the corresponding three-dimensional case by Kellman and Herrick. The rovibrator nature of the states is directly reflected in plots of $\rho \left({\theta }_{12}\right)$, which reveal both collective rotations and vibrations and even the influence of centrifugal distortion. A minimal basis ($l_{max}=n-1\mathrm{}$) is inadequate to represent angular correlation in the higher-energy states of each shell. The repulsive Gaussian potential, which is finite at ${\theta }_{12}=0\mathrm{}$, shows the onset of independent-particle shell-model behavior in higher-energy states. Comparison of the Coulomb case with the delta-function potential exhibits the degree to which kinematics governs wave-function character.

The spectrum of resonance fluorescence and the second-order correlation function are calculated for a system of two identical two-level cooperative systems interacting via the dipole-dipole interaction. The results are valid for arbitrary incident-field strengths and for atomic separations much less than the resonant wavelength. The intensity of the sidebands at the Rabi frequency is diminished by the dipole interaction, whereas that of the sidebands at twice the Rabi frequency is enhanced. Both the cooperative behavior and the dipole-dipole interaction act to diminish the photon antibunching, as shown by the second-order correlation function.

Doubly excited states of ${\mathrm{H}}^{-}$ lying below the hydrogenic $N=3\mathrm{} \mathrm{and} 4$ thresholds are investigated in hyperspherical coordinates. Adiabatic potential curves are calculated using the recently developed analytical channel functions and approximate resonance energies, and their classifications are described. It is found that the present classification differs from the recent work by Gailitis for ${}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_{}^e{}_{}{}^{}$ states. Angular correlations for doubly excited states below $\mathrm{H}\mathrm{}(N=2\mathrm{})\mathrm{}$ and $\mathrm{H}\mathrm{}(N=3\mathrm{})\mathrm{}$ thresholds are also investigated for ${}_{}{}^{1,3}{}_{}{}^{}S_{}^o{}_{}{}^{}$, ${}_{}{}^{1,3}{}_{}{}^{}P_{}^o{}_{}{}^{}$, and ${}_{}{}^{1,3}{}_{}{}^{}D_{}^e{}_{}{}^{}$ symmetries. States belonging to different channels are found to have a high degree of different angular correlations.

Photon echoes have been employed to measure the relative broadening rates of the lithium $D$ lines perturbed by the noble gases. We find that, for each noble-gas perturber, the $D_1$-line and $D_2$-line photon-echo-relaxation rates are identical. Our results are compared with those obtained in line-shape studies of pressure broadening.

In an optical radio-frequency double-resonance experiment on N${\mathrm{O}}_2$ optical saturation resonances are observed. These resonances appear superimposed on the normal magnetic resonance spectrum. With increasing laser light intensity they change the resonance spectrum considerably. We present a model to describe the observed saturation phenomena: The resonances are attributed to the interaction of two optical photons and at least one radio-frequency photon with the molecule. The theory shows that saturation resonances appear in the population and in the coherence of the dressed-molecule levels in agreement with the experimental results.

We have made 17 new high-precision measurements of the $\mathrm{nF}-\mathrm{nG}$ intervals ($n=5,6\mathrm{}$) of neutral ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ using the microwave-optical method. The rms one-standard-deviation experimental uncertainty for the transitions reported here is 188 kHz (14 ppm). The new measurements agree with the predictions of a least-squares fit to previous experimental data, and are up to 40 times more precise. The $\mathrm{nF}-\mathrm{nG}$ manifold is now known experimentally to better than 1 MHz for all values of the quantum numbers. The precision of the experimental measurement exceeds that of the best currently available theory by approximately three orders of magnitude.

The three previous calculations of this process yield differing results for the transition rate. We show the relations between them and difficulties with each of them. One difficulty is that the finite spatial extent of the laser field has been omitted. It is also found that a laser field, which is sufficiently intense to be labeled ultrastrong, makes the electron move relativistically so that it becomes necessary to use Volkov states to describe the electron in the laser field. The transition rate is obtained, with the use of a C${\mathrm{O}}_2$ laser as an example, and it is found that the transition rate rises as the laser intensity rises. This is a consequence of the use of relativistic kinematics and is not true nonrelativistically.

Saturation effects in coherent anti-Stokes Raman scattering (CARS) spectroscopy are discussed. The discussion is limited to Raman-resonant CARS (${\omega }_l-{\omega }_s\simeq {\omega }_{21}$, where ${\omega }_{l,s}$ are the frequencies of the pump fields with powers $P_{l,s}$, and ${\omega }_{21}$ is the frequency of the Raman transition $|1\mathrm{}〉\to |2\mathrm{}〉$) with the possible addition of a one-photon resonance (${\omega }_l\simeq {\omega }_{31}$ is the frequency of the electronic transition $|1\mathrm{}〉\to |3\mathrm{}〉$). For these cases we show that the CARS polarization ${\mathcal{p}}_{\mathrm{CARS}}$ is proportional to the off-diagonal density-matrix element ${\rho }_{21}$. In order to determine ${\rho }_{21}$, we use Laplace transforms to solve the Bloch equations for the effective two-level system $|1\mathrm{}〉$ and $|2\mathrm{}〉$ when ${\omega }_l$ is far from resonance, or for the three-level system $|1\mathrm{}〉,|2\mathrm{}〉$, and $|3\mathrm{}〉$, when ${\omega }_l\simeq {\omega }_{31}$. The steady-state expression for ${\mathcal{p}}_{\mathrm{CARS}}$ in the former case gives ${\mathcal{p}}_{\mathrm{CARS}}\propto P_l{P}_s^{\frac{1}{2}}$ at low powers and ${\mathcal{p}}_{\mathrm{CARS}}\propto P_l^0{P}_s^{\frac{-1\mathrm{}}{2}}$ at high powers. In the three-level system, we show that when the pressure is low and at least one field is weak, the slow time dependence of ${\rho }_{21}$ must be considered. When one field is strong and the other weak, the CARS spectrum is Stark split. When $P_l$ is high, for example, ${\mathcal{p}}_{\mathrm{CARS}}\propto P_l^0{P}_s^{\frac{1}{2}}$ for ${\omega }_s\simeq {\omega }_{32}$ and ${\mathcal{p}}_{\mathrm{CARS}}\propto {\left(P_l{P}_s\right)}^{\frac{1}{2}}$ when ${\omega }_s\simeq {\omega }_{32}\pm V_{13}$ where $V_{13}$ is the one-photon Rabi frequency for the $|1\mathrm{}〉\to |3\mathrm{}〉$ transition. The Wilcox-Lamb approximation is used to reduce the three-level Bloch equations to rate equations containing one- and two-photon terms. When the fields are so weak that both one- and two-photon terms are small compared to the decay terms, the usual expression for ${\mathcal{p}}_{\mathrm{CARS}}$ is reproduced. If only the direct two-photon processes are important, the effective-two-system results are reproduced. When both fields are intense and nearly resonant, the steady state is rapidly achieved. The results for the case where one field is much stronger than the other are essentially the same as those for one strong and one weak field. When the fields are of comparable strength, ${\mathcal{p}}_{\mathrm{CARS}}\propto P_l^{\frac{1}{2}}{P}_s^0$ for ${\omega }_l\simeq {\omega }_{31}$ and ${\omega }_s\simeq {\omega }_{32}$, and the CARS spectrum is split into five components.