Cross sections for the $1{}_{}{}^1{}_{}{}^{}S\to n{}_{}{}^1{}_{}{}^{}S$ ($n=2,3,4\mathrm{}$) excitations of atomic helium under proton impact are calculated with incident energy ranging from 25 to 1000 keV employing the Glauber approximation. A properly orthogonalized set of He wave functions are used. The generalized oscillator strengths for $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^1{}_{}{}^{}S$ and $1{}_{}{}^1{}_{}{}^{}S\to 3{}_{}{}^1{}_{}{}^{}S$ excitations are also calculated with these wave functions, and the results are compared with the existing theoretical and experimental data. The full Glauber scattering amplitude is separated into single-and double-scattering parts. The single-scattering amplitude is evaluated from a closed-form expression. A numerical method is employed to calculate some integrals occuring in the double-scattering amplitude. At incident energies above 500 keV, the single-scattering contribution is found to dominate the Glauber result. The effect of the double-scattering term is appreciable at intermediate energies, where it substantially lowers the cross sections from the corresponding single-scattering result. The Glauber result at intermediate energies also underestimates most of the existing theoretical and experimental cross sections, which already show a wide variation among themselves in absolute values. However, the functional dependence of the Glauber cross sections on energy is similar to that depicted by other calculations and measurements. Furthermore, the average ratio of the Glauber cross sections for $3{}_{}{}^1{}_{}{}^{}S$ and $4{}_{}{}^1{}_{}{}^{}S$ excitations at high energies show reasonable agreement with those obtained from other theories, as also from the $n^{-3\mathrm{}}$ law of cross sections.

The collision of an electron and a hydrogen atom in the presence of a laser field is studied within a previously proposed approximation (based on the space-translation approximation) for the bound states of the hydrogen atom. The Green's-function formalism is applied to derive an expression for the scattering amplitude associated to multiphoton processes. The Born-Oppenheimer approximation is obtained and numerical calculations are performed for the $1s\to 2s$ inelastic excitation. It is shown as expected that exchange effects are important only for scattering processes involving low-energy electrons.

In several recent experiments in which spin-polarized electrons were scattered from hydrogen atoms the investigators isolated the spin-exchange effects which arise in the theory from the antisymmetrization of the wave functions of the electrons. Noting the recent advances in techniques of producing and detecting polarized electrons, this paper considers the possibility of finding the terms in the effective transition operator that are spin dependent. The spin-dependent parts of the first Born term in the transverse photon and the instantaneous photon are calculated. The $1s-1s$, $1s-2s$, and $1s-2p$ scattering amplitudes are discussed specifically. A brief comparison is made of the magnitude of these effects and the accuracy of the present experiments.

Inverted Lamb dips involving infrared-radio-frequency two-photon and multiphoton processes have been observed for intracavity C${\mathrm{H}}_3$I molecules using C${\mathrm{O}}_2$ and ${\mathrm{N}}_2$O lasers. The Doppler-free resonances have been studied for radio-frequency radiation with a frequency lower or comparable to the C${\mathrm{H}}_3$I nuclear quadrupole splitting. Velocity-tuned Doppler-free resonances resulting from various coupling of the different multiphoton processes have also been detected. A dressed-molecule formalism has been applied to describe the Doppler-free resonances of the molecule dressed with the radio-frequency field. Accurate molecular constants in the ${\nu }_6$ state of C${\mathrm{H}}_3$I have been determined from the Doppler-free measurements of the ${\nu }_6\leftarrow \mathrm{O}$ vibration rotation transitions.

In the analysis of an experiment to determine the response of scintillators to relativistic heavy ions, we have discovered that the BaS${\mathrm{O}}_4$ grains (radius ∼0.5 μm), which constitute the highly reflective interior surface of our light-integration box, emit Čerenkov radiation with an index of refraction intermediate to that of crystalline BaS${\mathrm{O}}_4$ and to that of the air-crystal volume-averaged reflective coating. The small amount of radiation emitted below threshold (∼ 2% of the $\beta =1\mathrm{}$ signal) is consistent with the expected level due to Čerenkov emitting delta rays and/or to diffraction radiation with no residual scintillation.

We have calculated the photoionization cross sections for the valence levels of S${\mathrm{F}}_6$,using multiple-scattering $X\alpha$ methods for both the initial and final states. The theoretical curves are compared with measured cross sections in an attempt to complete the identification of observed photoionization peaks with theoretically predicted valence levels. We find general agreement between theory and experiment, although one notable difficulty remains.

The method of space-charge ion detection has been extended to the case of lithium. This was accomplished by the insertion of a space-charge-limited diode into a heat-pipe oven. Lithium vapor was probed with a ${\mathrm{N}}_2$ laser-pumped tunable dye laser from 7150 to 4400 Å and with a Xe arc lamp from 7500 to 2300 Å. One-through four-photon events leading to ionization were observed. The atomic transitions observed were the principal series to $n=10\mathrm{}$ and the $2s$ to $3d$, $4s$, and $4d$ two-photon transitions. The two-photon absorption signals depended upon the third and fourth powers of the light intensity, indicating a new ionization process not heretofore considered important in diode signals. This new process appears to be excitation transfer from excited-state atoms to other excited-state atoms or molecules. For the high excited-state densities achieved in this experiment, this process appears to predominate over photoionization of excited-state atoms and other collisional processes involving excited-state and ground-state species. The $B\leftarrow X$, $C\leftarrow X$, and $D\leftarrow X$ molecular transitions, investigated by previous workers, were observed here.

The excitation of a two-level active atom by a radiation field in the presence of a low-density perturber bath is studied. In particular, the collisional enhancement of the absorption cross section is investigated. Features of the absorption-line profiles are predicted on physical grounds using a dressed-atom approach and verified by detailed numerical calculations for attractive, repulsive, and Lennard-Jones-type interatomic potentials. Complete spectra of the absorption cross section both as a function of detuning and as a function of field strength are given. In the weak-field limit, the results are compared with those of traditional pressure-broadening theory and to the recent experimental results of Carlsten et al. In the strong-field limit, the results display a saturation behavior consistent with the predictions of Lisitsa and Yakovlenko.

Diatomic or polyatomic molecules in discrete molecular states imbedded in vibrational continuum(s) can be induced by available infrared laser beams to make significant transitions to the continuum(s), leading to predissociation of the molecules. These laser-induced predissociative transitions can be one of three kinds of photoprocesses studied: (i) stimulated single-photon absorption or emission of the laser photons, (ii) stimulated multiphoton absorption or emission of the laser photons, and (iii) stimulated transition without actual absorption or emission of the laser photons. The probability rates and the selection rules for these three processes are given and compared. Type I, II, and III of the above laser-induced molecular predissociation (LIMP) are defined and treated. Spectroscopic applications of these processes, such as deducing unstable electronic potential surfaces, are suggested. One such application is the locations of the potential curves of the unstable $1g\left({}_{}{}^3{}_{}{}^{}\pi \right)$ and $0^{+}g\left({}_{}{}^3{}_{}{}^{}\pi \right)$ states of diatomic halogens (${\mathrm{I}}_2$ or ${\mathrm{Br}}_2$), since LIMP of the bound states in the metastable $B{0}^{+}u\left({}_{}{}^3{}_{}{}^{}\pi \right)$ into these unstable states by process (i) is dominant. As a new mechanism of unimolecular decompositions or reactions, LIMP can open up new channels or selectively enhance particular channels of molecular decomposition with laser-field-dependent rate "constants," leading to new dissociated products or higher product yields. It provides a means of decomposing homonuclear diatoms or polyatoms in infrared-inactive modes, that are already excited in the initial discrete state.

The resonance fluorescence of a two-atom system interacting collectively with an intense driving field is studied. The first-order dispersion forces, or dipole-dipole interaction, between the atoms is included as well. The scattered-light spectrum is found to differ considerably from the single-atom spectrum even for very intense driving fields, in direct contrast with the results obtained by Agarwal et al., who studied the two-atom system but neglected the dipole-dipole interaction. The effects of collective scattering are calculated on the fluorescence spectra of idealized beams of atoms moving with uniform velocity, for a number of different number densities $〈N〉$.

The properties of the electric field gauge are compared with the radiation gauge and other "simple" gauges for problems where intense-field and/or relativistic effects are significant. Electromagnetic shifts in free-electron mass and momentum, which can be of major importance in both kinematics and dynamics when the field is intense, and which are clearly in evidence in second-order radiation-gauge formulations, do not appear in the electric field gauge in any finite order of perturbation theory. Intense-field expressions like the closed-form Volkov solution, and mass and momentum intensity parameters, are shown to be invariant in form in "simple" gauges, but find no natural expression in the electric field gauge. It is also shown that intensity effects introduce strongly spin-coupled terms even in nonrelativistic problems. For both charged and neutral bound-state systems, "crossed" vector-potential terms occur in electric field gauge which prevent separation of the Schrödinger equation into center-of-mass and relative-coordinate equations when the field intensity is high. This difficulty does not arise in the radiation gauge. These considerations inhibit the use of electric field gauge in intense-field problems.

Resonant multiphoton ionization by finite bandwidth multimode radiation is investigated without the restriction of either a "long" or a "short" correlation time of the field. By approximating the multimode radiation by a stochastic model of a chaotic field, the stochastic atomic-density-matrix equation is reduced to a tractable infinite set of differential equations. For a given bandwidth this set can be suitably truncated and numerically integrated. For large-bandwidth fields it turns out that these truncated equations constitute a systematic improvement of the method usually employed of decorrelating the atom-field variables. For zero-bandwidth fields the well-known result is recovered in that the statistical averaging of the ionization probability reduces to an average with respect to the Glauber $P$-distribution function of the chaotic field. Detailed results of numerical calculations for two-photon ionization are presented which reveal a number of new interesting features.

We study three ways in which two-photon ionization, at high light intensities and near an intermediate-state resonance, may be described. We calculate the instantaneous ionization rate, the total ion count, and a saturable rate constant. We find that the total ion count, which is the experimentally interesting quantity in most cases, is very closely modelled by our saturable rate constant. The instantaneous ionization rate bears no useful relation to the total ion count in many cases. In comparing these three descriptions of ionization we have included the effects of detuning from resonance, finite light bandwidth, finite intermediate-state lifetime, and light intensity; we have varied all of these parameters independently over several orders of magnitude. Our conclusions are in good agreement with, and extend the findings of, Ackerhalt and Shore

We have studied theoretically and experimentally the dynamic behavior of a nonlinear Fabry-Perot interferrometer filled with a Kerr medium. The Fabry-Perot responses ranging from extremely transient to quasi-steady-state in various modes of operation are considered. The experimental results are in excellent agreement with theory. It is shown that the quasi-steady-state operation requires not only a medium response time much smaller than the cavity round-trip time, but also a characteristic time of the input intensity variation several hundred times larger than the cavity round-trip time. Even in the quasi-steady-state limit, optical switching is often featured by overshoot and ringing after switching. The switching speed is limited by the cavity buildup time.

A relatively simple method for calculating the properties of a paraxial beam of electromagnetic radiation propagating in vacuum is presented. The central idea of the paper is that the vector potential field is assumed to be plane-polarized. The nonvanishing component of the vector potential obeys a scalar wave equation. A formal solution employing an expansion in powers of $\frac{w_0}{l}$ is obtained, where $w_0$ is the beam waist and $l$ the diffraction length. This gives the same result for the lowest-order components of the transverse and longitudinal electric field of a Gaussian beam that was derived by Lax, Louisell, and McKnight using a more complicated approach. We derive explicit expressions for the second-order transverse electric field and the third-order longitudinal field corrections.

We investigate, theoretically, fluctuations in coherent steady-state pulses in a nonlinear swept-gain amplifier. In the superradiant steady state, we predict large energy and power fluctuations which are found to be largely independent of the magnitude of the fluctuating force.

For a pencil-shaped extended medium with Fresnel number equal to 1, we have quantum mechanically derived a description of the initiation of superfluorescence in terms of Maxwell-Bloch equations with a fluctuating source due to the zero-point fluctuations of the vacuum field. By the introduction of classical behavior, these equations are extended to include nonlinear behavior due to decreasing atomic inversion. The principal assumption in the derivation is that the main features of superfluorescence are governed by the interaction of atoms with field modes inside two small solid angles around the pencil axis. The delay ${\tau }_D$, defined as the time at which the mean-squared tipping angle of the collective Bloch vector attains the value 1, turns out to be given by ${\tau }_D=\left(\frac{{\tau }_R}{4}\right){\left[\ln {\left(2\mathrm{}\pi N\right)}^{\frac{1}{2}}\right]}^2$, where ${\tau }_R$ is the radiation time for collective decay and $N$ is the number of atoms. The corresponding effective initial tipping angle roughly equals $\frac{2}{{\mathrm{}\left(N\right)\mathrm{}}^{\frac{1}{2}}}$. A Fokker-Planck equation is derived to describe the statistics of the initial development of the tipping angle. The variance $\Delta {\tau }_D$ of the delay of the superfluorescence pulse satisfies approximately $\Delta {\tau }_D=\frac{2.3}{\ln N}$. A brief comparison with previous treatments of superfluorescence is given.

A quantum statistical analysis of a two-photon laser is presented in a generalization of the one-photon laser. A two-photon loss mechanism is assumed by taking detailed-balance considerations into account. The expressions for the photon statistical distribution exhibit the exact influence of the Doppler parameter and other relaxation parameters. In addition, the photon statistics can be studied as a function of the detuning. Threshold conditions for the laser action are noticed. The peak photon number and half-width of the photon distributions are obtained. It is found that the photon distribution can be written as a ratio of the one-photon laser-photon distribution to the Poisson distribution for photons.

Anisotropy in the velocity and attenuation of longitudinal ultrasound was studied for the first time in a stable smectic-$B$ liquid crystal ($\beta$-methyl-butyl-methoxybenzylidene amino cinnamate). Anisotropy in the velocity was found to be consistent with the predictions of the Martin-Parodi-Pershan hydrodynamic theory in both smectic-$A$ and -$B$ phases, but was significantly smaller than when measured in the same material by Brillouin scattering. Furthermore, strong dispersion was observed near the smectic-$A$—smectic-$B$ phase transition for sound propagating perpendicular to the symmetry direction.

Anisotropic ultrasound propagation was studied in a magnetically aligned monodomain smectic-$A$ liquid crystal (di-$n$-decyl azoxy methyl cinnamate). A large attenuation was observed near the isotropic-smectic-$A$ phase transition. The anisotropy in the sound velocity was found to be in agreement with the predictions of hydrodynamic theory, and no dispersion was found in the frequency range used (4-12 MHz). The temperature dependence of the physically meaningful elastic constants was determined. The anisotropy in the attenuation was also measured. Unlike the velocity anisotropy, no intermediate minimum was observed.