$L\alpha$ x-ray-production cross sections have been measured for solid targets of ${}_{60}{}^{}{}_{}{}^{}\mathrm{Nd}$, ${}_{67}{}^{}{}_{}{}^{}\mathrm{Ho}$, and ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$ for 1.86-MeV/amu ${}_9{}^{19}{}_{}{}^{}\mathrm{F}$ and ${}_{14}{}^{28}{}_{}{}^{}\mathrm{Si}$, and 1.8-MeV/amu ${}_{17}{}^{35}{}_{}{}^{}\mathrm{Cl}$ ions as a function of the incident charge state. From the projectile-charge-state dependence of the cross sections, both direct-ionization and electron-capture contributions were extracted for a comparison to Coulomb ionization theories. The data provide supporting evidence for the theory of electron capture with a reduced binding effect. With standard fluorescence and Coster-Kronig yields uncorrected for multiple-ionization effects, the direct ionization theories did not simultaneously reproduce the projectile-$Z_1$ and target-$Z_2$ dependences of the data.

With a partial-wave interpolation method we calculate the electron bremsstrahlung energy spectra from neutral atoms with atomic number $Z=13\mathrm{} \mathrm{and} 92$ for incident electrons of kinetic energy $T_1=5\mathrm{} \mathrm{and} 10$ MeV. This is an attempt to bridge the gap between the results we have previously obtained for $T_1\le 2$ MeV and the results which can be predicted in the high-energy limit. We conclude that for light elements Born approximation modified by the Elwert factor and a form factor remains accurate, while for heavier elements the Davies, Bethe, Maximon, Olson approach is of comparable 5%-10% accuracy at these energies and continues to improve with increasing energy.

The apparent average $L$-shell ionization probabilities in $K$-shell ionizing collisions by He, C, O, and Ne ions incident on Al, Si, and Cl targets at relative velocities ranging from 2 to 8.5 have been determined from high-resolution $K\alpha$ x-ray measurements. These data, in combination with data from previous work, enabled a detailed examination of the dependence of the single $K$- plus multiple $L$-shell ionization process on projectile and target atomic number, and on relative velocity. The He-ion-on-Al data are compared with the results of binary-encounter approximation and semiclassical approximation calculations, and a general semiempirical scaling law is deduced for light-ion collisions.

Charge transfer cross sections for ${\mathrm{Li}}^{3+}$ + H, ${\mathrm{Be}}^{4+}$ + H, ${\mathrm{B}}^{5+}$ + H, and ${\mathrm{C}}^{6+}$ + H collisions are calculated for ion-impact energies from 0.025 to 200, or to 2000 (for the ${\mathrm{C}}^{6+}$ + H case) keV/amu by means of the previously proposed unitarized formula based on the distorted-wave Born approximation. The results, compared with other theoretical and experimental values, show that the present formula is very useful for impact energies from 2 to 100 keV/amu, but tends to overestimate cross sections for impact energies greater than 100 keV/amu. It is suggested that the formula can be improved by taking direct-excitation and ionization channels into consideration. A scaling rule based on the cross section obtained by means of the present method is also considered, and is applied to scaling of the experimental data.

The second and third terms of the generalized Born series are analyzed in an attempt to gain a series approximation to the differential cross section, valid through $O\left(\frac{1}{k^2}\right)$, which treats all Born terms analogously. The resulting expressions for the second and third Born terms, derived from assumptions similar to those of Glauber theory, are compared with other analyses for the case of small-angle elastic scattering of electrons by hydrogen atoms. A most notable result is that, in addition to the Glauber-like term, there is a second term of $O\left(\frac{1}{k^2}\right)$ which contributes to the real part of the third Born term. In addition, the angular range of maximum validity of the Glauber assumptions is established for inelastic collisions.

A collinear reactive study of the ion-molecule system (Ar + ${\mathrm{H}}_2^{+}$, ${\mathrm{Ar}}^{+}$ + ${\mathrm{H}}_2$, Ar${\mathrm{H}}^{+}$ + H) is presented. The main emphasis was directed towards the two reactions ${\mathrm{Ar}}^{+}+{\mathrm{H}}_2(\nu =0)\to \mathrm{Ar}{\mathrm{H}}^{+}+\mathrm{H}$ and $\mathrm{Ar}+{{\mathrm{H}}_2}^{+}({\nu }^{\prime }=2)\to \mathrm{Ar}{\mathrm{H}}^{+}+\mathrm{H}$, which exhibit avoided-crossing features. It is shown that reactive transition probabilities obtained from an exact collinear treatment which incorporated a large number of vibrational states to ensure convergence are reproduced by simple reactive curve-crossing models.

In the past, variational calculations of the scattering length for scattering by a target system whose ground-state wave function is imprecisely known have suffered from numerical instabilities which severely limit their utility. The problem has recently been analyzed and the difficulty removed by the introduction of a minimum principle, not for the true scattering length, but for that of a closely connected problem. Here we report on numerical tests of this new calculational procedure. We have studied the scattering of positrons and electrons by atomic hydrogen with a trial hydrogenic ground-state wave function which is allowed to differ from the correct function. As predicted, no instability difficulties whatsoever are encountered as the trial scattering wave function and the trial target wave function are improved; apart from at most one jump for each composite bound state, the estimate of the scattering length converges monotonically.

It is shown that the interpretation of the line profile of resonant multiphoton ionization in terms of a Fano profile with a constant background can lead to difficulties. These difficulties are related to the fact that the nonresonant background may exhibit considerable structure as a function of photon frequency.

The sensitivity of high-resolution fluorescence spectroscopy has been enhanced by the detection of bursts of photons from single atoms crossing a laser beam. A tunable cw laser beam intersected a well-collimated atomic beam at right angles, and the fluorescent light was detected by an ellipsoidal collector and a photomultiplier. The passage of an atom through the beam was identified with a burst of detected photon pulses, which could be differentiated easily from the random background. For increasing burst multiplicity the spectra show improved background suppression and also significant peak narrowing. High-resolution spectra were obtained with as few as 10 atoms/sec crossing the laser beam. Statistical predictions for the case of transit-time limited signals are calculated and compared with results obtained for the Na 5890-Å and Ba 5535-Å transitions.

The authors present a detailed theoretical analysis of two-photon resonant third- and fifth-harmonic generation in metal vapors with picosecond laser pulses. These processes are described by self-consistent Maxwell-Bloch equations which take into account the effects of optical Stark shifts, multiphoton ionization, Doppler broadening, two-photon absorption, the reaction of the third-harmonic field on the fundamental, and a nonlinear index of refraction. As an example, a quantitative analysis of third- and fifth-harmonic generation in lithium vapor ($2s-4s$ transition) is presented. The limitations on energy conversion efficiency and the temporal as well as spectral characteristics of the harmonic pulses are investigated for two kinds of low-loss propagation fundamental pulses. It is shown that 90° phase-shifted fundamental pulses (zero area) are more efficient than $2\pi m$ pulses. Energy conversion efficiencies of 6.5% for third-harmonic (190 nm) and 0.07% for cascade fifth-harmonic (114 nm) pulses are predicted.

We have measured the He-, Ne-, and Ar-induced relaxation properties of the $3S-nS$ ($3S-nD$) superposition states of atomic sodium, where $n$ ranges from 5 to 20 (4 to 34). The measurements were made using the trilevel echo effect. We find that the effective collisional cross section first increases (as a function of $n$) at low $n$, and then decreases to a lower asymptotic limit at high $n$. This behavior is similar to that previously observed for the $3S-nP$ series. We also find that the difference between the collisional cross sections for $S$ and $D$ series superpositions closely approximates the inelastic collision cross sections measured elsewhere for the $d$ states. A theoretical description of the trilevel echo effect used to make the measurements is presented.

A quantum-mechanical transport equation of the Boltzmann type is proposed for the momentum-distribution function of atoms in the field of a quasiresonant traveling light wave. The physical meaning of the solution is discussed in terms of the linear momentum transferred from the photons to the atoms through a succesion of photon-scattering processes, the number of which follows a Poisson law. A connection is established with the random-flight problem. The analytical expression of the radiation-modified atomic-momentum-distribution function is derived explicitly. The first and second moments of the distribution correspond to a drift (associated with an average force) and a smearing out (associated with an anisotropic diffusion tensor), respectively. The latter effect is shown to arise from the dispersion in both the number and the direction of the scattered photons.

The wave function for an electron in combined Coulomb and uniform magnetic fields is expanded in oblatespheroidal angle functions. The resulting Schrödinger equation for the radial function is solved for the energy levels by means of two different adiabatic approximations, which yield rigorous lower and upper bounds on the lowest exact energy levels for each symmetry state of the system. Results are presented for the level and binding energies of hydrogenic $1s$, $2s$, and $2p$ levels for magnetic fields in the range ${10}^7\le B\lesssim {10}^{11}$ G and compared with results of other authors. These results indicate that the present adiabatic approximation methods employing spherical symmetry may be expected to give reliable results for energies of low-lying hydrogenic levels for magnetic fields in the range $0\le B\lesssim {10}^9$ G.

The Fredholm method for solving linear integral equations can yield a unitary solution for a Schrödinger equation of an evolution operator. Explicit results are derived in the simple case of an atomic system undergoing transitions towards a continuum of constant density of states after the application of a constant perturbation.

In this paper I calculate the leading transition amplitudes for a single-photon-double-excitation process which is dominated by long-range correlation effects. The process examined is an excitation of a Rydberg atom with the inner core in an $S$ state and the outer electron in essentially a hydrogenic state $n$ to another $S$ inner-core state and the outer electron in another hydrogenic state $n^{\prime }$. We find the leading contribution comes from terms in which the photon is received by the inner core. The excitation of the outer electron is done in intermediate states. The transition amplitude factors into a part entirely dependent on the inner core and a part which is a simple hydrogenic matrix element for the outer electron. The form of the amplitudes suggest that the coefficient to the hydrogenic matrix element be called a "transition polarizability."

We report ab initio calculations of Auger transition rates for hydrogen fluoride, using Hartree-Fock molecular orbitals from finite-basis Slater-type-orbitals calculations. Continuum orbitals are calculated as spherical waves in the single-center expanded-molecular potential. Results show reasonable agreement with experiment and with previous calculations for neon. The effect of final-state configuration mixing is discussed, as well as the use of perturbation theory for improving the continuum orbitals.

The equation describing perturbed motion of a nonlinear oscillator is studied by a Hamiltonian formalism and by computer mapping. Other physical situations, including the motion of a charged particle in the field of two plane waves, the destruction of magnetic surfaces in a tokamak, and the bounce motion of a charged particle trapped in a magnetic field, can be described by the same equation. Theory predicts the regions of stochastic instability of orbits in a good agreement with computer calculations.

An analytical semiclassical expression is derived for the two-photon transition in a three-level system under the influence of two pulsed fields. We study the Autler-Townes doublet as a function of the time dependence of the field amplitudes and the relaxation widths of the levels. The time variations of the field amplitudes cause shifts in the doublet and modify the radiative decay widths of the levels. The validity of the treatment extends into the intermediate-intensity regime.

The simultaneous oscillation of two standing waves in a solid-state laser is considered. An exact solution in terms of continued-fraction expansion is derived. This method enables one to consider high-intensity fields. Two distinct regimes are treated: a weak-coupling regime and a strong-coupling regime, depending on the intensities of the two modes. The effects of spatial inhomogeneity are stressed in the two different ranges of operation. The gain function turns out to be the sum of two parts: the first one includes gain saturation and the second one derives from the direct coupling of the two modes. The dispersionlike behavior of this latter term is discussed as a general result of nonlinear interactions. The amplification of a small-amplitude mode in presence of a strong one is interpreted in terms of a hyper-Rayleigh effect.

The theory of optical Bloch equations with stochastic coefficients is discussed in detail. It is shown that Bloch equations with stochastic fields lead to multiplicative stochastic processes for which exact solutions can be obtained. The steady state and the transient regimes of the phase-diffusion model of the laser bandwidth are treated, and exact solutions of Bloch equations are obtained. The case of fluctuation due to collisions is also discussed. A simple stochastic model of radiation-induced collisions is presented. For each stochastic model of incoherences formulas for the longitudinal and transverse lifetimes are derived exactly. It is shown that the finite bandwidths of light or the collision incoherences do not, in general, have a simple additive effect in atomic equations of motion.