Absolute total emission cross sections have been measured for electron-impact excitation of He giving radiation from the $6{}_{}{}^1{}_{}{}^{}S-2{}_{}{}^1{}_{}{}^{}P$, $5{}_{}{}^1{}_{}{}^{}S-2{}_{}{}^1{}_{}{}^{}P$, $4{}_{}{}^1{}_{}{}^{}S-2{}_{}{}^1{}_{}{}^{}P$, and $3{}_{}{}^1{}_{}{}^{}S-2{}_{}{}^1{}_{}{}^{}P$ transitions. Electron energies were 50, 100, 500, 1000, and 2000 eV. Particular care was taken to make the measurements accurate and to make knowledgeable assessments of uncertainties, so that the results serve as reliable benchmarks for calibration of other excitation apparatus as well as for comparison with theory. The most accurate results are for 500-eV electron energy, where the mean uncertainty is only 3.5% high confidence level. The measured emission cross sections are modified to account for branching and cascade to give level-excitation cross sections, and results are compared with other experimental data and theoretical predictions. At 2000 eV, the measurements average 2.5% below Born-approximation calculations.

Cross sections for single- and double-electron loss (electron capture plus impact ionization) for ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{q+}$, ${\mathrm{O}}^{q+}$, and ${\mathrm{Au}}^{q+}$ incident on helium have been measured at velocities from $\sim v_0$ to $\sim 10v_0$. The charge state $q$ was varied from 1 to 21, depending on velocity and projectile. The energy and charge-state dependence of the single-loss cross section at the lower velocities is reasonably well described by the model of Olson based on Coulomb interaction between particles and classical trajectory Monte Carlo calculations. The results for ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{He}}^{++}$ at high velocities are in good agreement with earlier experimental values of Pivovar et al. and with Bethe-Born calculations of Gillespie. The double-loss cross section, which for highly charged projectiles amounts to as much as 60% of the single loss, is found to behave quite differently from the single-loss cross section, both as a function of incident charge and velocity. While single-loss cross sections at velocities between $v_0$ and $2v_0$ are almost independent of energy and proportional to $q$, the double-loss cross sections are approximately proportional to energy and to $q^2$.

The approximations used in a previous paper (I) by Tripathy and Rao for the evaluation of the matrix elements of the electron-proton and proton-proton interactions have been improved. The effect of the exponentially decaying potential-energy term on the capture cross section which had been ignored in I is also taken into consideration empirically by introducing a screening parameter. In this improved version, the departure of the capture cross section from experiment around 90 keV and above is removed, and the agreement with the experiment is found to be very good over a wide range of proton energies. Our study of the angular distributions shows dips in the differential scattering cross section similar to that of Jackson and Schiff for all energies. The behavior in angular distributions is somewhat different from that of a recent calculation by Glembocki and Halpern.

$K\alpha \alpha$ x rays have been observed for the first time in the electron-capture decay of ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$. These x rays are due to the two-electron—one-photon transition to the $K$ shell doubly ionized through $K$-shell shakeoff and shakeup during the $K$-electron capture decay. The measured $K\alpha \alpha$ x-ray energy is 11 907 ± 20 eV and the intensity ratio of $K\alpha \alpha$ x rays to $K\alpha$ x rays is (5.5 ± 1.2)×${10}^{-8\mathrm{}}$. The results are discussed and compared with theoretical calculations and other measurements.

We report the first study of molecular-perturber-induced broadening of forbidden ground-to-Rydberg-state transitions. The ${\mathrm{N}}_2$- and CO-induced-broadening cross sections for the $3S-\mathrm{nS} \mathrm{}\left(\mathrm{nD}\right)\mathrm{}$ transitions of sodium have been measured for values of $n$, the principal quantum number of the upper state, ranging from 4 to 41. These measurements, performed using the trilevel echo technique, were accomplished at sodium and perturber densities of ${10}^{-6\mathrm{}}$ and 1 torr, respectively. The broadening rates, observed in the present experiment, differ in some respects from those observed previously with noble-gas perturbers. These differences, which presumably arise because of the presence of accessible internal degrees of freedom in the ${\mathrm{N}}_2$ and CO perturbers (and in the case of CO also because of its permanent electric-dipole moment), are most clearly displayed in $3S-\mathrm{nS}$ transitions. Previous work has shown that with noble-gas perturbers the $3S-\mathrm{nS}$ broadening cross sections display a dramatic increase at low values of $n$; they then decline at intermediate values of $n$, and at high $n$ they approach a limiting value. In the present experiment we find that the initial increase in $3S-\mathrm{nS}$ broadening cross sections with $n$ is relatively small and more gradual. For high $n$, the broadening cross sections become approximately constant. As is the case with noble-gas perturbers, the broadening of $3S-\mathrm{nD}$ transitions is generally larger than the broadening of the corresponding $3S-\mathrm{nS}$ transitions. With CO as a perturber, an unexplained irreproducibility in the broadening cross sections of high-$n$ $3S-\mathrm{nD}$ transitions is observed. One explanation has to do with the CO-induced frequency shifts being unusually large and exceeding the spectral width of our excitation lasers.

The dependence of the average $L$-shell fluorescence and Auger yields on the initial vacancy distribution is shown to be small. By contrast, the average electron yield pertaining to both Auger and Coster-Kronig transitions is shown to display a strong dependence. Numerical examples are given on the basis of Krause's evaluation of subshell radiative and radiationless yields. Average yields are calculated for widely differing vacancy distributions and are intercompared graphically for $40\le Z\le 100$ in the case of the fluorescence and Auger yields, and $12\le Z\le 100$ in the case of the electron yield. Average fluorescence and Auger yields are found to differ by less than 7% from the respective $L_3$ subshell yields in most cases of inner-shell ionization.

A variant of the trilevel-echo effect is observed and utilized to measure the effective cross section for broadening of the $3P_{\frac{1}{2}}-3P_{\frac{3}{2}}$ transition of sodium by the noble gases. The cross section measured here should be the same as the broadening cross section obtained from a direct measurement of the collisionally broadened $3P_{\frac{1}{2}}-3P_{\frac{3}{2}}$ transition linewidth (if such a measurement were possible). The new echo, the "inverted-difference-frequency" (IDF) trilevel echo, is well suited to the study of transitions between excited states of the same parity. At 400 K the measured broadening cross sections are He 115(12) ${\mathrm{\AA }}^2$, Ne 120(12) ${\mathrm{\AA }}^2$, Ar 234(23) ${\mathrm{\AA }}^2$, Kr 266(27) ${\mathrm{\AA }}^2$, and Xe 311(31) ${\mathrm{\AA }}^2$. With He as the perturber, the cross section for broadening of the $3P_{\frac{1}{2}}-3P_{\frac{3}{2}}$ transition can be calculated from measured depolarization and fine-structure-changing collision cross sections. With the other perturbers, however, collisional phase changes appear to be important. An intuitive diagrammatic technique for the analysis of echoes is applied to the IDF trilevel echo.

We calculate the contribution to elastic photon scattering from an atom due to scattering off the bound atomic electrons (Rayleigh scattering). We compare predictions resulting from our numerical evaluation of the relativistic second-order $S$ matrix in a screened central potential with other theories, particularly the form-factor approximation. We give a prescription for accurate $O(1\%)\mathrm{}$ evaluation of total-atom Rayleigh amplitudes (summed over electrons) and present sample tabulations for lead ($Z=82\mathrm{}$) for energies of experimental interest in the range from 22.1 to 2750 keV. Based on our prescription we compare elastic-scattering cross sections using Rayleigh amplitudes with selected experiments and are able to remove the large factor-of-two discrepancies previously reported.

As a first step in deriving accurate, calculable expressions for collisional redistribution of radiation, valid outside the impact regime, we present a method for calculating an accurate binary-collision density operator for an atom in the presence of a driving field and perturbers. We use projection-operator techniques to establish first the precise validity of the Markoff approximation for radiative relaxation. Using the same techniques, we show how the collisional-relaxation problem may be analyzed in a practical manner outside the Markoff approximation. The effect of correlations between radiative and collisional events is included in a consistent way, and the physical implications of these correlation effects are demonstrated for a simple example, the two-level atom with nondegenerate levels.

We apply the analysis of paper I to degenerate atomic systems and calculate the effect of correlations between an atom (the absorber) and perturbers in the binary-collision approximation. The result of our calculation is a generalized absorption profile that specifies the final state of the atom an absorption event. This profile is then related to the total intensities of Rayleigh scattering and fluorescence (redistributed radiation) from the atom. The profile is expressed in terms of collision operators that depend on the index of the multipole of the atom that is created. Some of the operators represent correlations between radiative and collisional events and cannot, except in certain limits, be expressed in terms of the usual line-broadening operators. This, of course, implies that one needs extra dynamical information, on top of that obtainable from ordinary absorption experiments, to be able to describe redistribution. Conversely, redistribution offers a probe of collisional dynamics, not given by absorption experiments, via the polarization of fluorescent light. We give practical expressions for the calculation of these operators and discuss their implications.

We present a calculation of the scattering of monochromatic radiation by a degenerate atom in the binary-collision approximation. We limit ourselves to field strengths such that $\Omega {\tau }_c\ll 1$, where $\Omega$ is the Rabi frequency for the atomic transition, and ${\tau }_c$ is the duration of a strong collision. Our calculation is not limited to the impact regime, $\Delta \omega \ll {\tau }_c^{-1\mathrm{}}$, or to the region where thermal correlations may be neglected, i.e., $\Delta \omega \ll \frac{\mathrm{kT}}{\hslash }$. (Here $\Delta \omega$ is the difference between either the incoming or outgoing photon's frequency and the atom's natural frequency.) To do this we derive an equation of motion for the correlation function, valid outside the quantum-regression regime, whose solution for practical cases is straightforward. We present solutions for the weak-field (linear-response) regime in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles created.

We have used the beam-foil technique to study the spectra of Fe XVI to Fe XX ions in the far vacuum ultraviolet range and to measure the mean lives of the upper levels of the $3s-3p$ and $3p-3d$ transitions in sodiumlike Fe XVI, the $2s^{2}2p^5{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^o{}_{}{}^{}-2s2\mathrm{}{p}^6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ resonance transition in F-like Fe XVIII, and the $2s^{2}2p^4{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-2s2p^5{}_{}{}^3{}_{}{}^{}P_2^o{}_{}{}^{}$ resonance transition in O-like Fe XIX. Deduced oscillator strengths are in good agreement with relativistic calculations. Tentative identifications are proposed for neonlike Fe XVII.

We calculate the cross section for the resonance scattering of Lyman-$\alpha$ radiation by spinless nonrelativistic hydrogen atoms in the ground state using a two-level model. A generalization of Dirac's resonance scattering theory is used together with the exact matrix elements for the electromagnetic interaction. In contrast to the usual treatments in which only the dipole approximation for the matrix elements are taken, the shift in position of the resonance is finite and has a value of 75% of the Lamb shift of the $n=1\mathrm{}$ state. Whether this latter fact is significant in renormalization calculations is left open.

Experimentally determined energy shifts of the electronic $K$ x rays in heavy muonic atoms are compared with calculations. These shifts may be caused by the incomplete screening of the nuclear charge by the muon and, in addition, by electron vacancies produced in higher shells by preceding Auger transitions. The first mechanism alone explains the experimental data within their uncertainties. This agreement and the absence of a noticeable difference between the shifts of the electronic $K\alpha$ and $K\beta$ x rays, show that the inner shells are essentially instantaneously refilled during the muonic cascade. Precision measurements of this type would give supplementary information on the initial muon distribution over $l$ states.

The two-dimensional dispersion relation for the free-electron laser is derived in the cold-beam limit. It is found that the forward wave has the largest growth rate, but the backward wave has the greatest spatial amplification rate. For $\frac{k_{0}v}{{\omega }_p}>{\gamma }^{\frac{-3\mathrm{}}{2}}+{\gamma }^{\frac{-1\mathrm{}}{2}}$, the free-electron laser is unstable at all angles with the low-frequency waves being absolutely unstable.

The theory of the Stark shift of hydrogen ground-state hyperfine levels has been tested at the 2.4% level of accuracy in a hydrogen maser. The quadratic-Stark-shift coefficient for the hyperfine-transition frequency was experimentally found to be $\left|\delta \nu \mathrm{}\right|=8.448\left(206\mathrm{}\right)\mathrm{}\times {10}^{-14\mathrm{}}$ Hz ${\mathrm{}(\mathrm{V}/\mathrm{m})\mathrm{}}^{-2\mathrm{}}$, where the electric field was perpendicular to the axis of quantization. The quoted uncertainty corresponds to one standard deviation. The uncertainty has contributions from the statistics of the data and from systematic effects. A number of possible sources of systematic error or unwanted frequency shifts has been tested. The theoretically predicted coefficient $\left|\delta \nu \right|=8.236\mathrm{}\times {10}^{-14\mathrm{}}$ Hz ${\mathrm{}(\mathrm{V}/\mathrm{m})\mathrm{}}^{-2\mathrm{}}$ is in reasonable agreement with the present experimental result.

The power spectrum of the light scattered by a two-level atom in the presence of a coherent continuous-pulse-train driving field is analyzed. Separate expressions for the coherent and incoherent components of the spectrum are obtained. The coherent part of the spectrum consists of a series of spikes (delta functions) which are displaced from the optical carrier by multiples of the pulse repetition frequency. The incoherent spectrum can have fixed peaks at these same frequencies plus sidebands equally spaced on opposite sides of these fixed peaks. That is, the spectrum consists of a series of triplets. The special case of a two-mode driving field is treated numerically and graphs of spectra are presented.

A canonical transformation, which diagonalizes the single-mode radiation Hamiltonian in the rotating wave approximation, is exploited to dress a two-level atom by the strong monochromatic driving field in the resonance fluorescence phenomenon. Langevin equations of motion are obtained for dressed atomic operators, and their solutions yield the amplitude of waves scattered into the fluorescence field. The power spectrum of the scattered field is obtained from the first-order correlation functions between dressed atomic operators. The results of the present treatment are compared with others, and advantages and disadvantages of the present method are discussed.

A density-matrix calculation of the line shape for an optically pumped coupled three-level system subjected to two traveling wave-laser fields with Gaussian intensity profiles is presented to third-order in perturbation theory. A closed-form expression for the line shape in the extreme transit-time limit is obtained. The line shape of the narrow resonance (Raman-type processes) is found to be an exponential function of the detuning, with half-width at half maximum ${\Delta }_{\mathrm{HWHM}}^{\left(\mathrm{Hz}\right)}\simeq 0.98\left(\frac{u}{2\pi D}\right)$ ($D$ is the intensity $\frac{1}{e}$ diameter and $u$ is the thermal speed). The saturation intensity is also modified by the transit rate ${\gamma }_t=\frac{\sqrt{2}u}{D}$ (rad/sec).

Broadband continuum radiation on the order of one erg per 100 ${\mathrm{cm}}^{-1\mathrm{}}$ and extending several thousand angstroms outside the gain curve of a Nd: glass laser has been observed and theoretically analyzed to be consistent with an electronic phase modulation process brought about by an intensity-dependent nonlinear index of refraction in the active medium of the mode-locked laser. Possible sideband pulse powers may approach 1 MW for 100 ${\mathrm{cm}}^{-1\mathrm{}}$ linewidth. Temporal and spatial synchronization of the sideband and 1.06-μm laser pulses is verified and utilized when the pulses are optically mixed in a nonlinear ammonium dihydrogen phosphate crystal to extend the region of the intense ultrashort continuum to higher frequencies.