Correlation due to the Coulomb interactions between electrons in many-electron targets colliding with charged particles is formulated, and various approximate probability amplitudes are evaluated. In the limit that the electron-electron, 1/$r_{\mathrm{ij}}$, correlation interactions are ignored or approximated by central potentials, the independent-electron approximation is obtained. Two types of correlations, or corrections to the independent-electron approximation due to 1/$r_{\mathrm{ij}}$ terms, are identified: namely, static and scattering correlation. Static correlation is that contained in the asymptotic, e.g., bound-state, wave functions. Scattering correlation, arising from correlation in the scattering operator, is new and is considered in some detail. Expressions for a scattering correlation amplitude, static correlation or rearrangement amplitude, and independent-electron or direct amplitude are derived at high collision velocity and compared. At high velocities the direct and rearrangement amplitudes dominate. At very high velocities, ν, the rearrangement amplitude falls off less rapidly with ν than the direct amplitude which, however, is dominant as electron-electron correlation tends to zero. Comparisons with experimental observations are discussed.

The role of structure in crossing potential-energy curves upon nonadiabatic collisions is probed by means of functional sensitivity analysis. The inelastic transition ${}_{}{}^2{}_{}{}^{}[{\mathrm{He}}^{+}+\mathrm{N}\mathrm{e}(3\mathrm{}{p}^6\left)\right]$ →${\mathrm{}}^2$Σ[${\mathrm{He}}^{+}$+Ne(3$p^5$4s)] modeled by a crossing of the corresponding diabatic potential-energy curves ($V_{11}$ and $V_{22}$) is used as an illustration. The functional derivatives δ${\sigma }_{12}$(E)/δ$V_{11}$(R), δ${\sigma }_{12}$(E)/δ$V_{22}$(R), and δ${\sigma }_{12}$(E)/δ$V_{12}$(R) of the corresponding nonadiabatic collision cross section ${\sigma }_{12}$ are calculated using the exponential distorted-wave approximation. These functional derivatives offer a quantitative measure of the importance of different regions of the potential [$V_{11}$(R) and $V_{22}$(R)] and coupling [$V_{12}$(R)] functions to the nonadiabatic collision cross section ${\sigma }_{12}$. The prominent Gaussian-like feature of the δ${\sigma }_{12}$(E)/δ$V_{12}$(R) curve in the crossing point region (R∼$R^{\mathrm{*}}$) is found to be in qualitative accord with the δ(R-$R^{\mathrm{*}}$) function idealization of the Landau-Zener-Stueckelberg (LZS) theory.

Similarly, the most prominent feature of the δ${\sigma }_{12}$(E)/δ$V_{11}$(R) and δ${\sigma }_{12}$(E)/δ$V_{22}$(R) curves occurs in the vicinity of the crossing point region where they mimic the dδ(R-$R^{\mathrm{*}}$)/dR behavior predicted by the LZS theory. The breadths of all three functional derivative curves identify a much broader region of potential function importance than the loosely defined avoided-crossing region. The region of significance is also found to increase with an increase in the total energy. This considerable sensitivity away from the crossing point along with the quantum interference structure of the functional sensitivity curves and the dynamical dependence of these sensitivities offer new insights and bring out the limitations of the intuitive pictures rooted in the LZS theory of curve crossing.

We describe the experimental observation of the resonant collisional energy transfer Na(ns)+Na(ns)+qhν→Na(np)+Na[(n-1)p]+(q○)hν which occurs when the Na atoms in a strong microwave field are tuned in energy with a static field so that the energy resonance $E_{\mathrm{ns}}$+$E_{\mathrm{ns}}$=$E_{\mathrm{np}}$+$E_{n\mathrm{-}1}$,p±mhν occurs. We describe our experimental observations and provide a detailed description of a nonperturbative theory which we have developed to explain our observations. The theory is essentially developed in terms of the resonant dipole-dipole collisions between ‘‘microwave dressed’’ atoms. Using an extension of the approach we used previously to describe resonant dipole-dipole collisions in the absence of microwaves, we are able to take into account all the coherences in the problem in a completely straightforward way.

A simple model for the resonant vibrational excitation of a molecule by electron impact is proposed in which the potential curves of the electronic states of the molecule and its resonant anion are replaced by those of linear harmonic oscillators of arbitrary frequencies and equilibrium internuclear separations. A closed-form expression for the excitation amplitude is derived. Useful recursion relations among amplitudes are obtained which allow convenient evaluation of cross sections for any inelastic or superelastic vibrational transition. The model is used to generate the cross sections for vibrational excitation of ${\mathrm{Li}}_2$ and ${\mathrm{N}}_2$ by the impact of low-energy electrons.

Based on a fundamental and simple treatment, selected calculations are performed of differential and total cross sections of multiphoton free-free transitions. The emphasis is on high values of the radiation field intensity such that the amplitude $v_0$ of the classical electron oscillatory velocity is equal or larger than the incoming velocity $v_i$. A variety of new information is obtained which gives a useful insight into various aspects of both the current theory and the physics of multiphoton free-free transitions. The calculations concern the following: (i) total cross sections in parallel and perpendicular geometry for both multiphoton emissions and absorptions, (ii) the breakdown of a known sum rule, (iii) the comparison of exactly calculated total cross sections with those based on widely used simplifications, and (iv) the investigation of the role of the range of scattering potential. Under particular conditions, the classical aspects of the elementary process (the interaction with the field) are found to affect the collision event and its characteristic parameters in a very peculiar way. The most interesting and new results are obtained when $v_0$≥$v_i$ and ${\mathrm{v}}_0$∥${\mathrm{v}}_i$.

A quantum-mechanical treatment of the degree of polarization of photofragment fluorescence in the case where two dissociative electronic states of different symmetry with the same limit are excited coherently is presented. This results in an interference effect which depends both on the photoabsorption probability amplitudes in the different excited states as well as on the phase differences of their vibrational wave functions at large distances. Oscillations of the polarization ratio as a function of the photon energy are predicted. Applications to some simple cases involving a diatomic molecule initially in a ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }$ state are presented. The case of ${\mathrm{Ca}}_2$ is discussed. The role of fine (or hyperfine) structure, and in particular the case of unresolved fluorescence is treated. The classical model in terms of oscillating electric dipole moments properly averaged over the initial orientations of the molecule is presented and allows the interpretation of the quantum results.

The polarizability and photoemission cross section and asymmetry parameters for the 1${\pi }_u$ level of acetylene (${\mathrm{C}}_2$${\mathrm{H}}_2$) has been given previously in the time-dependent local-density approximation. In this work real-space pictures of the time-dependent potentials are given for acetylene demonstrating metalliclike screening except for energies near the previously reported autoionization resonance in the 1${\pi }_u$ cross section of acetylene. The character of the on-resonance screening is understood in terms of underlying molecular orbitals participating in the resonance. The differential partial cross sections for the 1${\pi }_u$ level are discussed in terms of the screening potentials. In general, the effect of dynamic screening is to cause the angular distribution of the outgoing photoelectrons to be enhanced in the direction of the external field.

The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated state a and a second state b of an atom. We assume the density matrix ρ of state a initially has only diagonal elements given by 〈m‖ρ‖m〉=C+${\mathrm{Dm}}^2$ where C and D≠0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area).

For spatially uniform laser pulses, these signals are periodic functions of the laser fluence. When the laser is completely speckled, we show that the signal is well approximated by a Lorentzian curve. This latter case is of considerable experimental interest since most pulsed dye lasers have poor transverse mode structure which can readily be converted into a statistically well-defined speckle pattern. The oscillator strength of the transition between states a and b is found using (1) the fluence half-width of the ‘‘depolarization curve,’’ the Lorentzian-like dependence of the fluorescence polarization on the laser pulse fluence, (2) the detuning of the laser from the transition frequency ${\omega }_{\mathrm{ab}}$, and (3) some known constant factors which depend on the angular momenta of states a, b, and f. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption line shape and also to the temporal and spatial profile of the laser pulse. It yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.

A detailed analysis is made for the bound 5$p^6$→5$p^5$ns,nd levels observed in the photoabsorption of ${\mathrm{Ba}}^{2+}$. A multichannel quantum-defect theory approach, with ab initio calculations for some of the parameters, is used to describe periodic enhancements in intensity associated with interchannel mixing. Qualitative agreement between experiment and theory requires the inclusion of plasma-broadening effects to account for the apparent increase in strength of the higher n levels.

The relativistic photoionization cross sections from ${\mathrm{ns}}_{1/2}$,${\mathrm{np}}_{1/2}$,${\mathrm{np}}_{3/2}$ subshells, in the high-energy limit, have been analytically obtained. The main effects of screening enter through their effects on bound-state normalizations and energy levels. To estimate further effects, the screened potential at small distances is analytically described by a power-series expansion in the small distance r. For this high-energy-limit situation, both bound and continuum wave functions are expanded in power series for small r. The bound-free transition cross sections are then calculated analytically. Our results show that, beyond the known screening effect described by normalization factors, the screening effect enters the cross sections primarily through the change in bound-state energy and is otherwise not too sensitive to the expansion coefficients of the potential. The formulas contain no explicit n dependence. Comparisons with existing finite-energy numerical results indicate that ratios, though not absolute values, of cross sections attain their high-energy limits relatively early. Using Poincaré’s theorem, all the photoionization results may be analytically continued to the high-frequency region of the spectrum of electron bremsstrahlung. Screening is dominated by the ‘‘extra’’ screening (namely, the screening which is not described by the known ‘‘normalization screening’’) except in the very tip region (a few eV above threshold), where normalization screening is much more important. The extension to positron bremsstrahlung is also discussed.

We present detailed experimental results for the resonance structure of atomic Ca in the region of the 3p threshold, from 26 to 40 eV, as manifested in the partial cross sections of the 4$s^{\mathrm{-}1}$ and 3$p^{\mathrm{-}1}$ main photoelectron lines and several of their satellites, including satellite–to–main-line branching ratios. We also present partial photoionization cross sections for the 4$s^{\mathrm{-}1}$, 3$p^{\mathrm{-}1}$, and 3$s^{\mathrm{-}1}$ main lines up to 120 eV photon energy. Finally, we give a qualitative, theoretical discussion of the resonance structure and decay mechanisms, and compare the measured 4s, 3p, and 3s photoionization cross sections with theoretical results within the framework of random-phase approximation and many-body perturbation theory.

The reduction of quantum noise in homodyne experiments on squeezed radiation is explained as the reduction of quantum noise of measurement at the modulated frequencies. The quantum noise measured by the spectrum analyzer is given by the Fourier transform of the intensity fluctuations correlation function. The zero line which represents the ‘‘quantum limit’’ is the quantum noise of measurement of the local oscillator radiation, and it is proportional to the square root of the laser intensity.

General expressions are derived for various quantities that characterize the far field generated by any fluctuating localized current distribution that is statistically stationary, at least in the wide sense. In particular, expressions are derived for the cross-spectral density tensors of the electromagnetic field, for the coherence matrix and the Stokes parameters, for the degree of polarization, and for the degree of coherence of the far field in terms of the cross-spectral density of the transverse part of the source current. The analysis is illustrated by considering radiation from a fluctuating linear current source.

Making use of numerical collision simulations, we have examined the stability of the bistable solitary-wave solutions (predicted earlier by Kaplan [Phys. Rev. Lett. 55, 1291 (1985) and IEEE J. Quant. Electron. QE-21, 1538 (1985)]) to the generalized nonlinear Schrödinger equation for a wide range of nonlinear functions f(I), I being the intensity. Gradations of stability have been observed, ranging from absolute instability through ‘‘weak’’ solitons to ‘‘robust’’ solitons. For all models studied, it was found that dP/dδ¯<0 guarantees unconditional instability while dP/dδ¯>0 is a necessary condition for the existence of weak and robust solitons. Here P is the energy of the solitary pulse and δ¯ is a propagation parameter. Sufficiency conditions for robustness of the soliton have also been suggested. We have further demonstrated that it is possible to construct physically realistic nonlinear models f(I) for which robust bistable solitons exist.

Experimental evidence for a subcritical Hopf bifurcation in a NMR laser device is presented and compared with a two-dimensional model of a laser with a phase-locked injection signal. Computer results from numerical integration of the Bloch-Kirchoff-type laser equation are discussed. The use of the Hopf bifurcation for the experimental determination of laser parameters is described.

The description of an electromagnetic field of complicated statistics with noise, coherent, and squeezed features are discussed using the nondiagonal coherent-state representation of the density matrix and the normally ordered characteristic function derived therefrom. The quantity 〈($a^{\mathrm{°}}$${)}^n$$a^n$〉 which plays a central role in the theory of many-photon processes is found for this field. Particular cases with dominant coherent signal, noise, or squeezing are discussed. It is found that the ratios 〈($a^{\mathrm{°}}$${)}^n$$a^n$〉/(〈$a^{\mathrm{°}}$a〉${)}^n$ for the coherent, the chaotic, and the strongly squeezed vacuum states are 1, n!, and (2n-1)!!, respectively. The value of 〈($a^{\mathrm{°}}$${)}^n$〉 related to the anomalous coherence function is considered. It is found that the noise does not influence 〈($a^{\mathrm{°}}$${)}^n$〉.

It is suggested that the light-cone coordinate system is the natural language for the Lorentz-covariant phase-space representation of quantum mechanics. The localized light wave is discussed as an illustrative example. It is shown that the unitary transformation of a localized light wave from one Lorentz frame to another can be achieved through its covariant phase-space representation.

A time-resolved study of the relaxation times of the third-order susceptibility for the optical Kerr effect in ${\mathrm{CS}}_2$ and nitrobenzene was made by degenerate four-wave mixing using 5-ns pulses from a broadband laser. In the case of ${\mathrm{CS}}_2$ we observed both subpicosecond (∼0.2 ps) and picosecond (∼2 ps) relaxation times for the susceptibility tensor element of ${\chi }_{\mathrm{xyyx}}^{\mathrm{}\left(3\right)\mathrm{}}$ and ${\chi }_{\mathrm{xxxx}}^{\mathrm{}\left(3\right)\mathrm{}}$ both at 553 and 623 nm. The observed relaxation times agree with those obtained utilizing subpicosecond pulses. The relaxation times of nitrobenzene could not be measured because the shorter relaxation time is shorter than the resolution time and the longer one is longer than that of ${\mathrm{CS}}_2$.

We derive a general diffusion equation for the density of an atomic vapor immersed in a buffer gas and irradiated by nearly resonant light. The combination of velocity-selective excitation with state-dependent rates of velocity-changing collisions then gives rise to a drift term, and at the same time the diffusion tensor becomes anisotropic and intensity dependent. Both the effect of light-induced drift and diffusive pulling of atoms by the light are described by this diffusion equation in a consistent and correlated fashion.

The theory of a correlated-emission free-electron laser is developed for the case where the electron beam is initially in a coherent superposition of two pure momentum states. A strong correlation between the two laser modes is found under certain requirements on the electron beam and the relative phase diffusion coefficient can vanish.