We report measurements of Kr $K$-shell ionization cross sections for 0.5-2.0-MeV protons on ion-implanted Si(Kr) targets. Our results do not agree with earlier measurements made using gaseous Kr targets but are consistent with thin, solid-target results for other medium-$Z$ elements.

We show that the conditions of validity of the Markoff approximation for the description of cooperative spontaneous emission depend on the Fresnel number associated with the radiating system. Let $\frac{S}{\lambda L}$ be the Fresnel number, where $S$ and $L$ are, respectively, the section and the length of the radiating system, and $\lambda$ is the radiation wavelength. In the case of large Fresnel numbers, we find that the characteristic time ${\tau }_R$ of the cooperative emission of radiation must be much greater than $\frac{L}{c}$; but for small Fresnel numbers, we show that ${\tau }_R$ must be much greater than $\frac{S}{\lambda c}$.

Our recently computed differential cross sections for elastic electron scattering from the ground state of oxygen have been used to compute momentum-transfer cross sections for energies $0.136\le E\left(\mathrm{eV}\right)\le 11.02$. Leading terms from the threshold laws have been used to estimate the zero-temperature limits of the rate constants for deactivation by electron impact.

The ratio of the $L_{\mathrm{III}}$ to $L_{\mathrm{II}}$ ionization cross sections for low-energy $\alpha$ particles has been remeasured, with better experimental precision, to lower energies than our previous data. Two additional elements near gold, namely tungsten and lead, have been included. While all the elements studied deviate from PWBA calculations, the anomalous behavior of the gold and platinum ratios reported earlier is still observed.

It is well known that the spectral line shape of the narrow change signal induced at one Doppler-broadened transition by an intense laser field resonating with a second one can be extremely complex and nonclassical in form, the exact details depending on such factors as the direction of observation relative to the propagation direction of the laser field and its spatial form (traveling wave or standing wave). Nevertheless, the area under the change signal line shape, i.e. its frequency-integrated intensity, is always the same for a given laser field, and is independent of the coupling between laser and change-signal fields. A proof of this equal area property, based on quantum-mechanical transition-rate theory, is given for a three-level system composed of degenerate or near-degenerate states. The resulting expression is also applicable to line-shape calculations for experiments which study resonance fluorescence induced by intense laser or resonance radiation or other forms of excitation.

The properties of $r$-mode harmonic-oscillator coherent states are reviewed. In particular, the $\mathcal{D}$-algebra differential-operator realization of the creation and annihilation operators on the coherent states and their diagonal projectors is constructed. A homomorphism between the algebra describing $r$-field modes and the algebra describing $r$-level systems is exhibited explicitly. This homomorphism allows the projection of the multimode calculus onto the multilevel calculus. In particular, multimode coherent states and projectors can be used as generating functions for multilevel coherent states and projectors. In addition, the multilevel $\mathcal{D}$ algebra is constructed directly from the multimode $\mathcal{D}$ algebra under this homomorphism. For illustrative purposes, the $\mathcal{D}$ algebra for the diagonal coherent-state projectors for two-level atomic systems is presented explicitly in terms of a parametrization in the Bloch angles $\theta$ and $\varphi$. Two classes of applications are treated: (a) the mapping of atomic-density-operator equations of motion into phase-space equations of motion for the quasiprobability weighting function $P$; (b) the construction of equations of motion for the diagonal elements $Q$ of the density operator in the coherent states. It is shown that the solution to either equation with the appropriate initial condition gives complete statistical information for the atomic system. It is shown explicitly that the functions $P$ and $Q$ are related by a convolution integral.

Choice of light polarization should allow near-ideal self-induced-transparency (SIT) phenomena to be observed in all degenerate or nondegenerate systems. We show that the near-ideal SIT breakup observed in S${\mathrm{F}}_6$ by Zembrod and Gruhl is expected on theoretical grounds.

A generalization of the classical molecular-optics theory of the optical Kerr effect (OKE) is presented which permits a study of the effect when induced by ultrashort laser pulses. Explicit relationships between results from this general theory and often-used phenomenological equations governing the temporal behavior of the OKE are established. Numerical results are presented for the liquids carbon disulfide and nitrobenzene, illustrating in detail the temporal nature and intensity of the birefringence induced in these liquids by ultrashort laser pulses. The importance of these results is discussed in connection with a number of self-induced nonlinear phenomena arising from the OKE as well as in conjunction with the OKE shutter switched by an ultrashort laser pulse. In addition, a discussion is given of the nature of the birefringence induced by picosecond laser pulses as well as aspects of the extension of OKE photography to the subpicosecond domain.

Amplifiers based on two-photon decay channels of inverted metastable species are examined from a rate-equation and practical-feasibility viewpoint. Approximate analytical solutions, within the rate-equation approximation, predict that resonant parametric generation coupled with anti-Stokes-stimulated Raman scattering (ASRS) is a strong competitor to straight two-photon emission. Expressions for initial growth rates indicate that large linear chromatic dispersion, proper linear absorptions, and resonant enhancements can initially favor two-photon emission, but that ASRS will ultimately dominate in most practical situations if inversion depletion does not occur early. For an amplifier based on degenerate two-photon processes, this situation has led to the proposal of running the system as an odd-harmonic generator, first extracting energy via two-photon emission followed by greater-than-100% conversion to the third, fifth, seventh, etc., harmonics. This type of amplifier response has important potential applications for laser-induced thermonuclear fusion as well as for the production of coherent vacuum-uv soft-x-ray systems. An examination of practical constraints provides further analytical relationships between various physical properties of prospective metastable species. Combining these results, several two-photon schemes are pointed out. Based on current technology, atomic iodine, which is inverted to the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state, appears to be the best medium for experiments, but other materials, such as atomic oxygen, show greater promise if absolute population inversions of high-density material are created at high efficiency.

Calcium vapor has been excited by two-photon absorption of a mode-locked dye-laser pulse, and emission from a coherent superposition state of the $4s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $4s3d{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ levels has been observed using a delayed off-resonant interrogation pulse in the picosecond regime. The emission signal intensity was measured as a function of the delay time of the interrogation pulse, and showed a peak well delayed from that of the dye-laser pulse. This reflects the fact that the induced coherence is expressed by a time integral of the excitation. The emission signal was then found to decay as a result of the Doppler effect. The above process is analyzed by Bloch and Maxwell equations. This is the first reported observation of the coherence of an atomic system induced by two-photon absorption, a coherence which persists after the passage of the excitation pulse and decays inhomogeneously as a result of thermal motion. In carrying out the experiment, deformation of the input dye-laser pulse during propagation through the two-photon resonant medium was carefully avoided.

The molecular theory of the smectic $B$ and $H$ phases is extended to the smectic $E$ and VI phases by including the phenyl-phenyl interaction in addition to the dipole-dipole potential used previously. This phenyl-phenyl interaction contains quadrupole-quradrupole, dispersive, and exchange terms. The possibility of both dipolar and "herringbone" order is considered in the self-consistent-field approximation. Four phases are found, all with a two-dimensional hexagonal lattice assumed: (1) a disordered phase (smectic $B$); (2) an oriented phase in which dipoles align (smectic $H$); (3) a herringbone phase with phenyl groups ordered (smectic $E$); (4) and a herringbone phase with both phenyl groups and dipoles ordered (smectic VI). In the phases with dipolar order the director is tilted with respect to the normal to the plane. The transitions vary in order. The temperature dependence of the order parameters, entropy, and specific heat are computed.

Relative values of rate coefficients for excitation by electron collisions were determined experimentally for various transitions in Fe viii, Fe ix, and Fe x at two plasma conditions in a small $\theta$-pinch. Collisional ionization rates were also obtained for these ions. The maximum errors of the relative values of the excitation rate coefficients are estimated to be ± 30% to ± 40% and those of the ionization rates to be a factor of 1.5. Iron pentacarbonyl [Fe ${\mathrm{}\left(\mathrm{CO}\right)\mathrm{}}_5$] was used as an impurity in hydrogen or helium gases. The electron temperature and density were obtained from the analysis of scattered laser light. They were in the range 60-150 eV and ${10}^{15}$ to 2 × ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$, although this range was not available for each ion. The excitation rate coefficients were calculated by the use of the Coulomb-Born approximation. Comparison with experiment is made within each ion and also between ionization stages. A discrepancy in previous Coulomb-Born calculations is noted for the case of Fe viii.

Recent developments in the kinetic theory of time correlation functions are applied to the problem of describing spectral line broadening in a fluid. The width and shift operator of Fano's formulation for dipole radiation is expressed in terms of the solution to a few-body problem, involving the shielded interaction of a single perturber with the radiating atom. No approximations are required in this reformulation, and previous theories of neutral and Stark broadening are shown to result from systematic small-parameter expansions to low order. A plasma-parameter expansion is suggested for the Starkbroadening case under usual experimental conditions, resulting in complete shielding of the atomperturber interaction.

We have investigated theoretically and experimentally the contribution of double scattering to the depolarized scattering intensity. This work was motivated by a recent molecular scattering theory calculation of Oxtoby and Gelbart, who found that the intensity of the depolarized light scattered by a fluid near the critical point arises primarily from successive independent scattering events; however, the dependence of the depolarization ratio on sample size predicted by Oxtoby and Gelbart cannot be directly tested, since they considered an impractical geometry, a small illuminated sphere concentric with a large spherical scattering volume. We have calculated for a practical scattering geometry the depolarized intensity due to double scattering by simply integrating over all possible double scattering events. Although our measurements were performed on a fluid near the critical point, our calculations apply to any system which has a differential scattering cross section with an angular dependence given by the dipole intensity distribution, $\sigma ={\sigma }_0{sin}^2\phi$, where ${\sigma }_0$ depends on the properties of the scattering system and $\phi$ is the angle between the polarization vector of the incident light and the direction of propagation of the scattered light. (The scattering integrals that we have derived can also be straightforwardly evaluated for a system whose cross section has a different angular dependence.) In the scattering geometry considered here a vertically (V) polarized focused laser beam illuminates a parallelepiped sample volume, which is viewed at a 90° scattering angle by a detector which is in the horizontal plane. Our principal theoretical result is that the ratio of the intensity of the horizontally (H) polarized component of the doubly scattered light, $I_{\mathrm{VH}}^d$, to the (total) intensity of the vertically polarized component of the scattered light, $I_{\mathrm{VV}}$, should be given by $\frac{I_{\mathrm{VH}}^d}{I_{\mathrm{VV}}}=\frac{1}{4} \pi {\sigma }_{0}S$, where $S$ is the height of the sample seen by the detector; $S$ is assumed to be small compared to the horizontal dimensions of the sample. There is an additional "collision-induced" contribution to the depolarized intensity which we have not calculated, but if the sample height $S$ is greater than the laser-beam diameter, this contribution will be dependent of $S$. Thus the prediction is that plots of the measured depolarization ratio $\frac{I_{\mathrm{VH}}^d}{I_{\mathrm{VV}}}$ (which includes both the double scattering and collision-induced contributions) as a function of $S$ will be straight lines with slopes given by $\frac{1}{4}\pi {\sigma }_0$. We have measured the depolarization ratio for xenon as a function of sample height, wavelength, and temperature, and the results are in agreement with the predictions of the double-scattering theory [except very close to the critical point where higher-order scattering is important, i.e., the theory is applicable for $\frac{(T-T_c)}{T_c}\gtrsim {10}^{-3\mathrm{}}$]. We conclude that depolarization ratio measurements may be generally useful in determining absolute scattering cross sections for a variety of scattering systems. Refinements of the technique are suggested which would make possible absolute cross-section measurements of high accuracy even for systems which are not strong scatterers.

We study the static and dynamical correlations of density fluctuations in a classical one-component plasma (OCP), in the framework of thermodynamic fluctuation theory and linearized hydrodynamics. First we show that the fluctuations of the local electric field stabilize the OCP against density fluctuations, even when the compressibility becomes negative for $\Gamma \gtrsim 3$, where $\Gamma$ is the usual plasma coupling parameter. Then, following closely the work of Mountain, we compute the dynamical structure factor in the hydrodynamic limit and show that the thermal Rayleigh peak vanishes in the long-wavelength limit, in agreement with recent molecular dynamics results. The shear and bulk viscosity coefficients $\eta$ and $\zeta$ are calculated for large $\Gamma$ in the framework of the "generalized hydrodynamics" formalism, using the known short-time expansion of the correlation functions. The coefficient $\eta$ is found to exhibit a minimum as a function of $\Gamma$ and $\zeta$ is found to be negligible compared to $\eta$ in the OCP.

We show that, by virtue of the linewidth reduction provided by counter-propagating beams, it is possible to use the optical Stark shift to sweep a two-photon resonance through the sum frequency of the applied light while simultaneously satisfying the conditions required for optical adiabatic rapid passage. Consequently, the application of a near-resonant pulse of light can result in complete population inversion of a two-photon transition.

A rigorous result obtained using the theory associated with dilatation analytic potentials is that by performing a complex coordinate rotation, $r_j\to r_j{e}^{i\theta }$, on a Hamiltonian whose potential involves only pairwise Coulombic interactions, one can show that when $\theta =\frac{\pi }{2}$, no complex eigenvalues (resonances) appear whose energies have a real part greater than the total ionization energy of the atomic system. This appears to conflict with the experimental results of Walton, Peart, and Dolder, who find resonance behavior above the total ionization energy of the ${\mathrm{H}}^{--}$ system and also the theoretical stabilization results of Taylor and Thomas for the same system. A possible resolution of this apparent conflict is discussed and a calculation to check its validity is proposed.

The lifetime of the metastable ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of Mg has been remeasured by a dye-laser excitation technique. The metastable state was populated by an intense pulse of 4571-Å radiation from a flashlamp-pumped dye laser, and the decay of the population was monitored by observing the absorption of 5173-Å resonance radiation from a Mg discharge lamp. The measured value for the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ lifetime is 4.5 ± 0.5 msec.