Absolute total cross sections for producing ${\mathrm{H}}^{+}$, ${\mathrm{H}}^{-}$, $e^{-}$, ${\mathrm{N}}_2^{+}$, and ${\mathrm{O}}_2^{+}$ have been measured for H+${\mathrm{N}}_2$ and H+${\mathrm{O}}_2$ collisions from 50-eV to 3-keV hydrogen-atom energy. The experimental techniques used, when combined with classical differential-scattering calculations, also allowed determinations of the absolute large-angle-scattering differential cross sections for ${\mathrm{H}}^{+}$ production. The experimental and theoretical procedures are reviewed, and the results are compared, where possible, with the data of other investigators.

The closed-form, separable-expansion expression of Belyaev, Wrzecionko, and Irgaziev for the two-body $T$ matrix is studied numerically for the case of a Yukawa potential. The method shows good convergence for the elastic scattering amplitude at intermediate energies, yielding results almost identical to Glauber's eikonal method.

The experimentally determined intensities of x rays due to muonic and pionic atoms formed in gaseous and liquid helium are analyzed. The analysis is based largely, though not entirely, on some estimates of Auger rates. A discussion of Stark transitions, some estimates of the time required to slow a recoiling mesonic atom after it ejects an electron from a nearby atom in liquid helium, and a brief discussion of kaonic x-ray intensities are also employed. It is concluded that an $\alpha {\mu }^{-}$ or an $\alpha {\pi }^{-}$ atom in liquid helium probably becomes temporarily bound to a helium atom during its cascade to the $1s$ state. More specifically, it is argued that the relatively intense muonic $K\gamma$ line in gas, the relatively faint muonic and pionic $K\gamma$ lines in liquid, and the anomalously high $\frac{K\beta }{K\alpha }$ intensity ratio for pions in liquid indicate that molecular ions are probably formed in liquid but not in gas by $\alpha {\mu }^{-}$ and $\alpha {\pi }^{-}$ atoms with $n=4\mathrm{}$.

The presence of coherent electromagnetic radiation has a profound effect on the Compton scattering of x rays from electronic systems. Here, two electronic systems are considered—bound electrons in atoms and an electron gas. The scattering cross section is expressed in terms of a power series in even derivatives of the double integral of the electronic-momentum distribution function over ${\overrightarrow{\mathrm{p}}}_{\perp }$, the planar momentum vector perpendicular to $\overrightarrow{\mathrm{k}}$, the momentum transfer to the electron. It is shown that the effect offers an important experimental technique for measurements of details of electronic-momentum distribution in the scattering system.

Using the beam-foil technique, we have measured the decay times of the resonance lines $2p^6{}_{}{}^1{}_{}{}^{}S-2\mathrm{}{p}^{5}3s{}_{}{}^{1,3}{}_{}{}^{}P$ of Ne i-like Cl viii and Arix. We compare our results with theoretical values of the absorption oscillator strengths of these transitions and those of lighter ions of the isoelectronic sequence. We have partially resolved the Na i-like satellite spectra and suggest some identifications based on relativistic Hartree-Fock calculations. Some new observations of transitions between $n=3\mathrm{}$ and $n=4\mathrm{}$ levels of the Ne i-like ions are reported.

Compton profiles of Ne, Ar, and Kr are calculated from ground-state energies and wave functions with full correlation contributions included. The latter is carried out by regarding atoms as inhomogeneous interacting electron-gas systems using the Kohn-Sham self-consistent scheme in the local-density approximation. The calculated values are brought closer to the experimental values from Hartree-Fock results. There are numerical problems for large atoms.

The lifetimes of the $3{}_{}{}^1{}_{}{}^{}S$, $3{}_{}{}^1{}_{}{}^{}D$, $4{}_{}{}^1{}_{}{}^{}D$, $4{}_{}{}^1{}_{}{}^{}F$, and $5{}_{}{}^1{}_{}{}^{}F$, states of He have been determined experimentally to be 54.5±0.8, 16.7±0.8, 36.4±1.2, 67±10, and 142±20 nesc, respectively. The measurements were made at several incident electron energies using a pulsed-electron time-delayed-coincidence technique.

The absolute cross section for photoionization of atomic oxygen from the $2p^4{}_{}{}^3{}_{}{}^{}P$ ground state of ${\mathrm{O}}^0$ to the $2p^3{}_{}{}^4{}_{}{}^{}S$ ground state of ${\mathrm{O}}^{+}$ has been measured at five narrow wavelength intervals between 89.8 and 76.2 nm. The cross section near the $2p^3{}_{}{}^4{}_{}{}^{}S$ threshold is 4.5 Mb ± 7%. Recent calculations by Taylor and Burke, and by Pradhan and Saraph are in reasonable agreement with this work. The dipole-length results of Taylor and Burke (4.1 Mb) are in better agreement with the experiment than their dipole-velocity results (3.2 Mb).

We have measured the profile of the 4471-Å line of Hei at electron densities $n_e=3\mathrm{}\times {10}^{15}, {10}^{16}, \mathrm{and} 3\times {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$ in plasmas of different chemical composition. We have observed a smearing of the central dip of the line varying with the inverse square root of the reduced mass of the radiator-perturber system. A comparison with a calculation using ion dynamics at $n_e=3\mathrm{}\times {10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$ shows a better agreement for the dip intensity than with the usual quasistatic ion calculations.

Analytic expressions previously derived for neutral atoms permit the accurate prediction of inner-shell nonrelativistic dipole photoeffect cross sections for positively charged atomic ions. The simple dependence of these cross sections on nuclear charge $Z$ and ionic charge $Z_i$ results from scaling properties of self-consistent central potentials in the interior of the atom. Comparisons are made with numerical calculations of the same cross sections.

We present a theory of Stark splitting in doubly resonant three-photon ionization (three-level system) with nonmonochromatic fields. The asymmetry of the peaks of the resonance curve due to Stark splitting is shown to be reversed when the laser bandwidth is larger than the width of the atomic transitions of the resonant states. It is further shown that ionization as well as the probe field have a significant effect on the features of the splitting. Similar effects are found with monochromatic fields in the presence of an additional level near the initial level (four-level system). The results of the analysis are in general qualitative agreement with existing observations.

Anomalous modes of electronic-spin relaxation of optically pumped Rb atoms observed in He and Ne buffer gases may result from the modification of the Rb hyperfine interaction, induced by the formation of Rb-He and Rb-Ne Van der Waals molecules. Isolation of anomalous effects also resolves disagreements in cross sections previously reported for the spin relaxation of Cs in Ne.

The time dependence of the polarized and unpolarized parts of the secondary-radiation intensity, $I_{\mathrm{p}}$ and $I_{\mathrm{up}}$, and the time-dependent degree of polarization $P\left(t\right)\mathrm{}$ are calculated. A method is based upon the Feynman-diagram technique which is extended to enable the calculation of the reduced-density matrix element. It is found that, for the step excitation, $P\left(t\right)\mathrm{}$ does not show a simple exponential decay. Especially in the off-resonance case, $P\left(t\right)\mathrm{}$ shows oscillatory behavior. In the case of pulse excitation, $I_{\mathrm{up}}$ takes its maximum value after the excitation pulse has been turned off, and in the long-time limit it decays with the radiative-damping rate. In contrast to $I_{\mathrm{up}}$, $I_{\mathrm{p}}$ quickly responds to the excitation pulse and shows rapid exponential decay with the transverse-relaxation rate. It is also found that, contrary to the nondegenerate case, the total intensity of the secondary radiation does not exhibit simple exponential decay with the radiative-damping rate.

The minimization of the uncertainty relation $2\Delta x\Delta p\ge \hslash$ characterizes the coherent states. The spincoherent states of Radcliffe minimize the uncertainty relation $2\Delta \left(\overrightarrow{\mathrm{J}}·\overrightarrow{\mathrm{u}}\right)\Delta \left(\overrightarrow{\mathrm{J}}·\overrightarrow{\mathrm{v}}\right)\ge \left|〈\overrightarrow{\mathrm{J}}·\overrightarrow{\mathrm{w}}〉\right|$ (where $\overrightarrow{\mathrm{u}}$, $\overrightarrow{\mathrm{v}}$, $\overrightarrow{\mathrm{w}}$ form an arbitrary orthonormal basis), but this property does not characterize them. Here, we analyze that situation and suggest an alternative to restore the parallelism.

The main purpose of this paper is to study the behavior of the atomic fluctuations and the spectrum of the light transmitted by an absorptive bistable device. To this end we develop an approximation scheme based on the so-called system-size expansion and apply it to the quantum-mechanical Langevin equations for the atomic fluctuation operators. The Bonifacio-Lugiato mean-field equations for bistability are derived from the lowest-order approximation to the system-size expansion, while the atomic correlation functions result from the next-higher-order expansion. The calculated spectrum of the transmitted light exhibits line narrowing near the bistable thresholds, discontinuous formation of sidebands along the high-transmission branch of the device, and hysteresis effects.

Effects of multiphoton ionization on third-harmonic generation in phase-matched Na and Xe mixtures have been investigated using a mode-locked Nd: YAG laser with a pulse duration of 28 psec and peak-power densities up to 3 × ${10}^{12}$ W/${\mathrm{cm}}^2$. Analytical expressions accounting for refractive-index changes due to the depletion of neutral Na atoms and the plasma formation are presented which are used to estimate the wave-vector mismatch created by the multiphoton ionization of Na. The multiphoton-ionization probability $W$ for Na has been obtained from measurement of the number of ions formed by the focused laser beam: $W=6.8\mathrm{}\times {10}^{-49\mathrm{}}{I}_0^5$ ${\sec }^{-1\mathrm{}}$ at $\lambda =1.064\mathrm{}$ μm, where $I_0$ is the field intensity in W/${\mathrm{cm}}^2$. A time-dependent calculation using the value of $W$ obtained shows that multiphoton ionization of Na atoms brings about advancing and shortening of the third-harmonic pulse at high input intensities. The experimental results for the third-harmonic generation are in good agreement with calculated results which incorporated the effects of ionization. A comparison of the ionization effects with the quadratic Kerr effect is also presented.

The question of how the light output of a laser and its fluctuations depend on the optical-cavity length at a given frequency is investigated theoretically for a laser oscillating in a single Gaussian mode. The treatment is quantum mechanical, and is based on the Scully-Lamb laser model, except that a perturbation expansion is used and possible cooperative atomic effects are included. It is shown, with the help of some reasonable approximations, that the probability distribution of the photon-occupation number can be cast into a form that is similar to the Scully-Lamb formula, but with coefficients that depend on cavity length in a more complicated way. Curves are presented that illustrate the behaviòr and should lend themselves to experimental test.

The first-order correction due to space-charge effects to the small-signal gain of a free-electron laser is calculated classically. For a current density of ${10}^2$ A/${\mathrm{cm}}^2$, an interaction length of 1 m and an electron beam energy of 20 MeV, the maximum small-signal gain is reduced by about 0.5% while for ${10}^3$ Amp/${\mathrm{cm}}^2$, it is reduced by about 5%. The reduction is proportional to $\frac{{\left(\frac{{\omega }_{p}L}{c}\right)}^2}{{{\gamma }_0}^3}\equiv S$, where ${\omega }_p$ is the electron plasma frequency, $L$ is the interaction length, $c$ is the velocity of light, and $m{c}^2{\gamma }_0$ is the initial electron energy. $S=0.092\mathrm{}$ in the former case and 0.92 in the latter.

The normally ordered correlation function and the power spectrum (cross spectral tensor) of a thermal radiation field existing inside and outside a one-dimensional optical cavity which transmits radiation at one of its end surfaces are calculated on the basis of a multimode formulation of the field developed in a previous paper. The correlation function is found to consist of a series of trigamma functions resulting from retarded correlations due to reflections at the cavity end surfaces. The power spectrum is a product of the Planck distribution and the mode functions of the universe which have a periodic factor with the period being equal to the cavity mode separation. For the purpose of obtaining a description of the cavity which allows one to deduce its thermal noise property, a form of fluctuation-dissipation theorem is derived which connects, in a one-dimensional space with arbitrary structure, the normally ordered correlation function with the admittance for the electric field probed by a current. Application of this theorem to the model cavity leads to an explicit and simultaneous description of the fluctuation and dissipation associated with all the cavity modes. The dissipation is shown to be due to radiation of electromagnetic energy into the free space. The above relation is reduced, under the assumption of high cavity quality factor and of single-cavity-mode selection, to that of a Markovian noise associated with a single decay constant. The consistency of these results with the field commutation relation is examined.

Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in ${\mathrm{Al}}_2$${\mathrm{O}}_3$: ${\mathrm{Cr}}^{3+}$ (ruby) with the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after $Q$-switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.