The authors have extended the theory of stimulated Raman scattering to include the effects of laser bandwidths, in both the transient and steady-state regimes. The case of two interacting laser beams, a pump laser and a probe (Stokes) laser, is treated. Using the phase-diffusion model for laser bandwidth, the authors demonstrate that in the absence of dispersion, the forward Raman gain is essentially independent of the laser bandwidths in the high-gain limit, while in the low-gain limit the gain coefficient is inversely proportional to the sum of the bandwidths. It is further shown that when the pump-laser bandwidth is much larger than the linewidth of the Raman medium, the stimulated Stokes output assumes the same spectrum as the pump laser in the high-gain limit. A possible interpretation of these results is discussed assuming a "phase-locking" of the Stokes phase to the fluctuations in the pump-laser phase, due to the nonlinear interaction of the two beams through the Raman medium.

Thermalized positrons in media with spatial constraints can be trapped by sinks, and annihilate with electrons into $\gamma$ quanta with characteristics that are discernibly different from those of positrons annihilating in the bulk. The dependence of the cross sections for scattering in the medium on positron velocity determines whether the fastest or the slowest particles in the velocity distribution disappear preferentially from the volume. This causes the cooling or heating of the positrons remaining in the medium. The diffusion equation is solved to derive the annihilation characteristics of positrons, with the result that diffusion heating and cooling always reduce the effective diffusion coefficient pertinent for trapping relative to that in the infinite medium. The effects on the annihilation characteristics are those of a reduced trapping rate and of an apparent initial positron population in sinks, as it is recorded by an instrument with finite time resolution. The results pertain to positronium diffusion in small gas cells, to the escape of positrons or positronium from small solids, and to the trapping of positrons by vacancies or voids in solids. They are compared with experimental results.

The photodissociation (photoabsorption) cross sections of ${\mathrm{Ne}}_2^{+}$, ${\mathrm{Ar}}_2^{+}$, ${\mathrm{Kr}}_2^{+}$, and ${\mathrm{Xe}}_2^{+}$ have been measured from 3500 to 5400 Å. The rare-gas dimer ions were produced in a drift-tube mass spectrometer, and the ${\mathrm{Kr}}^{+}$ and ${\mathrm{Ar}}^{+}$ ion laser lines were used as the photon source. The cross sections decrease monotonically with increasing photon wavelength from 3500 to 5000 Å, and then increase with photon wavelength. The cross sections have values of 1.93, 13.3, 24.8, and 29.6 × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at (3569 and 3507) Å for ${\mathrm{Ne}}_2^{+}$, ${\mathrm{Ar}}_2^{+}$, ${\mathrm{Kr}}_2^{+}$, and ${\mathrm{Xe}}_2^{+}$, respectively. The current measurements are compared with various theoretical calculations. The dependence of the ${\mathrm{Ne}}_2^{+}$ and ${\mathrm{Ar}}_2^{+}$ cross sections on the effective kinetic temperature was investigated by increasing the ion drift velocity, and was attributed to vibrational excitation of the ions.

Ab initio theoretical calculations are presented for the cross section, photoelectron angular distribution, and photoelectron spin polarization resulting from photoionization of the $6s$ electron of cesium. Starting from an initial basis of nonrelativistic Hartree-Fock wave functions, the effect of final-state spin-orbit interaction in the Breit-Pauli approximation is treated exactly. The effect of core relaxation is also examined. Our calculated results agree with recent experimental measurements of the photoionization cross section and the photoelectron spin polarization. Comparison is made with other theoretical calculations. Finally, the length form of the electric dipole interaction operator is shown to be consistent with gauge invariance when one solves for the exact eigenstates of a Hamiltonian containing spin-orbit interactions.

The complex-rotation method has been applied to investigate autoionization states of the positronium negative ion ($e^{-}{e}^{+}{e}^{+}$). Only the singlet $S$ states are considered, but both the lowest resonance below the $n=2\mathrm{}$ and $n=3\mathrm{}$ positronium thresholds are calculated. Using the Hylleraas-type wave function with 161 terms, the resonance parameters (position and width) are determined by the complex-rotation method. The higher members of the resonances are estimated by the stabilization method but no width and "shift" are provided. In addition, by varying the mass of the positron from $1m_e$ (electron mass) to $\infty$, we are able to investigate the lowest resonance for systems ranging from ${\mathrm{Ps}}^{-}$ to ${\mathrm{H}}^{-}$. From this analysis, the lowest resonance for other three-body systems ($e^{-}{\mu }^{+}{e}^{-}$, ${\mu }^{-}p{\mu }^{-}$, ${\mu }^{-}d{\mu }^{-}$, ${\mu }^{-}t{\mu }^{-}$) are deduced.

An examination is made of the relation between line-integral representations of the scalar and vector potentials for the electromagnetic fields and line-integral representations of the polarization and magnetization fields due to an aggregate of charged point particles. The connection between the two types of representation is to be found in the Lagrangian that describes the interaction of the fields with the particles. This can be expressed completely in terms of the charge and current densities coupled to the scalar and vector potentials or partially (though sometimes completely) in terms of the polarization and magnetization fields coupled to the electric and magnetic induction fields. It is shown that the integration paths for the polarization and magnetization fields are determined by those for the scalar and vector potentials and by the motion of the charged particles; the integration paths are in general curvilinear and emanate from a moving reference point. It is also shown that altering the reference point or the integration paths amounts to a gauge transformation of the potentials and causes a similar "gauge" transformation of the polarization and magnetization fields. The results obtained here reduce in special cases to some given previously by other authors.

The electron momentum distribution for molecular hydrogen is calculated from an explicitly correlated Gaussian wave function corresponding to the total energy of - 1.17442 a.u. and accounting for 99.9% of the correlation energy. The high-accuracy Compton profile obtained confirms the results of recent high-energy electron-impact spectroscopy measurements of Lee, but disagrees in the region of very small momentum with earlier x-ray Compton-scattering data.

We describe a spectroscopic method combining saturated absorption and Zeeman optical pumping. A weak expanded monochromatic laser beam creates a velocity-correlated orientation in an atomic level without optical saturation. A polarization-modulated counterpropagating detection beam provides signals related to simple atomic observables. Combination with magnetic resonance techniques is described. We have applied this method to metastable states of Ne, with nuclear or electronic orientation. Effects of velocity-changing, depolarization (Kastler- or Dehmelt-type pumping) or metastability exchange collisions are discussed.

Multiphoton free-free transitions are detected in the scattering of electrons on argon atoms and on hydrogen molecules in the presence of an intense pulsed C${\mathrm{O}}_2$ laser field. The authors present measurements for several values of the incoming electron energy, the electron scattering angle, and the angle between the laser polarization vector and the electron momentum transfer. All observations are in qualitative agreement with a recent theoretical model based on a low-frequency approximation.

An analysis of the temporal behavior of the image of a moving object in a simple imaging system is presented which explicitly takes into account the finite transit time of the light propagating from the object to the image plane. This analysis, which places no restrictions on the magnification of the imaging system or on the spatial shape or extent of the object, uncovers a number of novel and highly unorthodox phenomena hitherto unforeseen. Of particular significance, in the case where the object velocity $v_o$ and the magnification $M$ satisfy $\frac{\mathrm{}(M+1\mathrm{})\mathrm{}{v}_o}{c}>1\mathrm{}$, is the finding that a single object gives rise to two simultaneous images which move antiparallel to one another away from a common point in the image plane. One of these images displays a normal, forward time dependence, while the other image exhibits a time-reversal character resulting in the anticausality in the observed temporal behavior of the object and of time-dependent or causal events associated with it. The theory is developed to include the imaging of arbitrary, three-dimensional objects. The important case where the object is stationary but has a time-dependent intensity distribution is also examined and it is shown, in this case as well, that anticausal behavior can be observed in the image plane under quite general conditions. The ramifications of this work for high-speed photography in general are discussed, and numerous illustrations are given of the image behavior in time for moving objects of simple geometrical shapes.

The authors consider a system comprised of a collection of identical two-level atoms interacting with the electromagnetic field in the dipole approximation and with an externally applied steady-state coherent driving field. The atoms are considered to interact with each other only via the electromagnetic field and are assumed to be contained within a volume much smaller than a resonance wavelength. The system is treated as a quantum-statistical ensemble in the rotating frame, rotating at the carrier frequency of the externally applied coherent field. The Hamiltonian in this frame is explicitly time independent and the exact analog of a spin temperature is defined. The thermodynamic-Green's-function method is used to determine the thermodynamic equilibrium properties of the system in the rotating frame. This results in a nonlinear relation between the applied field and the field in the volume containing the atoms. The expression is a nonlinear function of the effective or "spin" temperature as well, and has the form of a first-order phase transition with the macroscopic atomic polarization as order parameter. In the low-"spin"-temperature limit, and for perfect tuning, the expression reduces to the exact form of the nonlinear relation for optical bistability derived by Bonifacio and Lugiato and relating the incident and transmitted fields for atoms in a ring cavity in the mean-field approximation. The results contain absorptive as well as dispersive contributions. These results predict essentially different behavior as a function of off tuning compared with behavior predicted by others using statistical steady-state models far from thermodynamic equilibrium. In the limit of zero value for the applied field amplitude, the results reduce to the conditions for the well-known second-order superradiant" phase transition. The condition for the existence of the second-order phase transition is shown to depend on the cavity tuning and the photon escape rate. The authors also show why, in light of the experiments in optical bistability, this second-order phase is difficult to observe.

The authors have experimentally examined the height dependence of the Rayleigh linewidth in C${\mathrm{O}}_2$ at $T-T_c=0.001\mathrm{}°$C. The results are compared with the predictions of the mode-mode coupling, decoupled mode, and dynamic-droplet theories of the critical point. Linewidth data are more easily described by the decoupled-mode theory than by other models.

The critical behavior of the refractive index $n$ of three critical mixtures, nitroethane-isooctane (N-I), isobutyric-acid-water (I-W), and triethylamine-water (T-W), has been investigated u$\stackrel{\mathrm{`}}{\mathrm{s}}$ing a very sensitive and reliable interferometric method which enables gravity effects to be ignored. An accuracy $\frac{\delta n}{n}\simeq 4\times {10}^{-7\mathrm{}}$ has been obtained in the range $T-T_c=5\mathrm{}\times {10}^{-4\mathrm{}}-20\mathrm{}°$C [$t=\frac{(T-T_c)}{T_c}=1.7\mathrm{}\times {10}^{-6\mathrm{}}-7\mathrm{}\times {10}^{-2\mathrm{}}$]. All anomalies can be interpreted in terms of density or specific-heat anomalies. Thus, for the first time in binary fluids, the $\alpha$ exponent could be accurately determined, and was found very close to the renormalization-group (RG) value (${\alpha }_{\mathrm{RG}}=0.110\mathrm{}\pm 0.003$ for $n=1\mathrm{}$ and $d=3\mathrm{}$, to be compared with ${\alpha }_{\mathrm{N}-\mathrm{I}}=0.10\mathrm{}\pm 0.02$, ${\alpha }_{\mathrm{I}-\mathrm{W}}=0.12\mathrm{}\pm 0.05$, and ${\alpha }_{\mathrm{T}-\mathrm{W}}=0.113\mathrm{}\pm 0.005$). In the T-W system, the nonanalytical corrections are sufficiently high to allow, also for the first time, the critical exponent $\Delta$ to be determined accurately. The experimental value ${\Delta }_{\mathrm{T}-\mathrm{W}}=0.50\mathrm{}\pm 0.03$ is in good agreement with the value obtained by RG theory ($\Delta =0.493\mathrm{}\pm 0.007$). The amplitude values of the diverging part are in agreement with the two-scale-factor universality and allow the universal constant $X={\left(R_{\xi }^{+}\right)}^3$ to be determined, here also in agreement with the RG values [$X_{\mathrm{I}-\mathrm{W}}=(2.0\mathrm{}\pm 0.2)\times {10}^{-2\mathrm{}}$, $X_{\mathrm{RG}}\simeq 1.76\times {10}^{-2\mathrm{}}$]. In the systems studied here, the regular variation was found to be close to ideal variation, suggesting that the mixing anomaly is due mainly to the critical behavior of the specific heat. In addition, we review the results for other systems which have been studied by density, volume, thermal diffusivity, and specific-heat measurements. Although the data are not generally very accurate or reliable, they all support the same general conclusions derived from the analysis of the present data.

The frequency distributions of the first six Lyman lines of hydrogenlike carbon, oxygen, neon, magnesium, aluminum, and silicon ions broadened by the local fields of both ions and electrons are calculated for dense plasmas. The electron collisions are treated by an impact theory allowing (approximately) for level splittings caused by the ion fields, finite duration of the collisions, and screening of the electron fields. These calculations are fully quantum mechanical and include the full Coulomb interaction. Ion effects are calculated in the quasistatic, linear-Stark-effect approximation, using distribution functions of Hooper and Tighe which include correlation and shielding effects. Theoretical uncertainties from the various approximations are estimated, and the scaling of the profiles with density, temperature, and nuclear charge is discussed. A correction for the effects caused by low-frequency field fluctuations is suggested.

An exact lower bound for the correlation energy of a three-dimensional classical one-component plasma (OCP), based on Mermin's inequality for the structure factor and a trivial inequality for the pair correlation function, is generalized to the cases of $d$-dimensional OCP's with $d$-dimensional Coulomb interaction where $d=1,2, \mathrm{and} 3$. For $d=1\mathrm{}$ and $d=3\mathrm{}$, this lower bound gives values close to the known exact values and the results of numerical experiments, respectively. In the case of $d=2\mathrm{}$, where the interaction potential is logarithmic, this lower bound improves upon the known one in the domain $\frac{e^2}{T}<25.0\mathrm{}$, $e$ and $T$ being the charge and the temperature in energy units.

The authors analyze the connection between the theory of stochastic processes and quantum mechanics. It is shown that quantum mechanics is not equivalent to a Markovian diffusion process as claimed in recent papers. The origin of a possible confusion about this question is clarified. The authors further demonstrate that there does not even exist a non-Markovian process equivalent to quantum mechanics.

Nuclear-magnetic-resonance measurements of the proton-spin relaxation for water in biological cells are known to exhibit a multiexponential decay. A theory, based on the diffusion equation using the bulk diffusivity of water, is developed to explain this phenomenon. It is shown that multiexponential decay arises simply as a consequence of an eigenvalue problem associated with the size and shape of the cell and that this multiexponential decay can only be observed for samples whose size is of the order of a biological cell. As an example, the theory is applied to a previously published data for rat gastronemius cells. Excellent agreement is obtained, and furthermore, the size of the cell is calculated by fitting the theory to the experiment.

Lyapunov characteristic numbers are used to estimate numerically the Kolmogorov entropy of an isolated one-dimensional self-gravitating system consisting of $N$ plane parallel sheets with uniform density. It appears that the Kolmogorov entropy increases linearly when the number of degrees of freedom is greater than or equal to 2.

We prove that a spin-½ charged particle moving in a plane under the influence of a perpendicular magnetic field has ($N-1\mathrm{}$) zero-energy states, where $N$ is the closest integer to the total flux in units of the flux quantum. The ($N-1\mathrm{}$) independent wave functions are calculated explicitly. The result, which is extremely simple to prove, is an example of the Atiyah-Singer index theorem when applied to the Euclidean two-dimensional Dirac equation.

The quantum-mechanical virial theorem for scattering of a particle by a central force is expressed in terms of Wigner's definition of time delay, $\tau =\frac{2\hslash d\eta }{\mathrm{dE}}$. By using semiclassical approximations, the quantum-mechanical virial is transformed into the classical virial and $\tau$ becomes exactly the classical delay time.