An exact solution is given for the canonical model equations describing the electromagnetic fields on a free-electron-laser amplifier comprised of a high-quality relativistic electron beam propagating along the axis of a helical pump magnetic field. The case of a cold beam is analyzed in detail and it is shown that, depending upon the parameters, one can have gain when the system is stable, owing to constructive spatial interference of modes, or exponential gain when it is unstable. Gain curves, line shapes, and linewidths are presented for conditions of reported and planned experiments. Reasonable agreement is found with the reported experiments.

Experiments on light absorption in DNA solutions in the region of 260 nm demonstrate specific multiple sharp oscillations of $\frac{\mathrm{dA}}{\mathrm{dT}}$ vs temperature $T$, $A$ being the optical density. A one-dimensional Ising model with a long-range polyspin interaction in an inhomogeneous "magnetic field" is used to present a quantitative description of these oscillations. An explicit analytical formula, derived in the paper, provides a surprisingly good agreement between the theory and experiments. It also alows one to obtain from these experiments important information about the sequence of the "magnetic fields," which represents the DNA component sequence. This is demonstrated by an example of a particular DNA. The long-range interaction in the Ising model implies a phase transition. Its nature is shown to depend crucially on well-defined properties of the DNA sequence.

The authors consider a one-dimensional classical system with an interaction potential $v\left(r\right)=C_R{e}^{-{\gamma }_{R}r}-C_A{e}^{-{\gamma }_{A}r}$, where $C_R$, ${\gamma }_R$, $C_A$, and ${\gamma }_A$ are positive parameters. The evaluation of the partition function for this model system is reduced to an eigenvalue problem for a second-order partial differential equation, which is solved by means of the adiabatic approximation. A Van-der-Waals-type equation of state is obtained.

In order to obtain multiplet energies and therefore energies of excited states of atoms and molecules, the local-density theory of Hohenberg, Kohn, and Sham has recently been extended to give the lowest energy of a specified angular momentum and spin symmetry. It is explained why this method does not work if the exchange correlation functional is taken to be symmetry independent. Instead it is shown how the local-density theory can be used to estimate the energies of states of mixed symmetry and how the multiplet splittings are obtained from these estimates. The new method is tested on light atoms and the local-density theory with exchange only reproduces the Hartree-Fock results within 0.1 eV. With correlation included, the error in the local-density approach is typically a factor of 3 less than in the Hartree-Fock approach.

In this work an explicit formula is obtained for the population probabilities of the excited levels of the various charge states in an optically thin plasma. The plasma is assumed to be in a complete steady state, i.e., time independent and homogeneous. First, a recursive expression is obtained for the partial densities of the various charge states in the plasma. This expression is used to get an implicit algebraic expression for the population probabilities of the excited states, which is finally solved for low electron densities to yield an explicit, and simple, expression for the population probabilities. Simplified formulas for H-like ions and a few numerical examples are also presented.

In this work a few things are done: (i) the results of the previous work are compared to the work of McWhirter and Hearn and analytical expressions are derived for their $r_0$ and $r_1$ coefficients, (ii) new validity criteria are proposed for the local-thermodynamic-equilibrium and corona-equilibrium models, and (iii) a numerical example is given.

The methods of information theory are applied to the problem of describing the transport of internal energy along a linear harmonic chain in a stationary state. It is shown that the average energy flux along the chain is a constant of the motion which can be directly incorporated into the canonical formalism. The classical probability distribution in phase space is constructed and used to evaluate the partition function in the thermodynamic limit. Thermodynamic relationships between the undetermined multipliers and the given information are explicitly determined, as are the singlet- and pair-distribution functions in configuration and momentum space and the correlation of the momentum of a specific particle in time. For a given system energy there is an upper bound for the mean rate of energy transport. As this limit is closely approached, both the range and duration of correlations become large. This behavior, as well as some other features of the model, is reminiscent of that near a critical point.

The degree to which gravity-induced density gradients influence the determination of the critical exponent $\eta$ from light scattering experiments on simple fluids is carefully examined. As the critical temperature is approached from above, the scalling of the angular distribution of the scattering breaks down. Best fits of the angular distribution by a theory which properly scales yield apparent values of $\eta$ which depend on temperature. In experiments where $\eta$ is inferred indirectly by applying hyperscaling to measurements of $\gamma$ and $\nu$, there is an accessible region of reduced temperature where gravity systematically alters the results.

Some inconsistencies are pointed out for the observed lack of perpendicular heating in the paper of Gentle, Leifeste, and Richardson.

The absence of $T_{e\perp }$ as the authors reported previously is consistent and explicable. The questions of plasma confinement and turbulent fluctuations were touched upon then and are discussed here more completely.

The author has identified his result for resonant ionization by the simultaneous absorption of two photons by a ground-state electron [Phys. Rev. A 17, 659 (1978)] with the high-laser-power large-intermediate-state ionization rate result derived by Eberly and co-workers using a steady-state rate theory. This result gives $R{\sigma }_{22}$ for all power levels considered, where $R$ is the one-photon ionization rate for the intermediate state and ${\sigma }_{22}$ is its steady-state population factor. The result can be cast in this form, but it is found that ${\sigma }_{22}$ must be much less than ${\sigma }_{11}$, the ground-state population factor. Thus the resonant process can be described by a rate limit for conserving energy by simultaneous absorption only when the ground-state population factor remains unity to order $\frac{{\Omega }^2}{R^2}$, where $\Omega$ is the Rabi rate for the bound-bound transition. In other words, the simultaneous and sequential processes are physically equivalent in this limit.

The authors present a survey of the photoionization cross sections and photoelectron angular distributions for the outer $p$ subshell of the chalcogen atoms O, S, Se, and Te and the halogen atoms F, Cl, Br, and I. Results are presented in the Hartree-Fock approximation as well as in the central-potential-model approximation. An extensive analysis and comparison of the results obtained is presented which finds that exchange-interaction effects are strongest for the $n=3\mathrm{}$ row elements.

A detailed theoretical analysis of ac Stark splitting in double optical resonance and resonance fluorescence by a nonmonochromatic complex chaotic field is presented. It is shown that a one-photon transition undergoes Stark splitting, which is strongly affected by the intensity fluctuations of the chaotic light. On resonance, the lines in the doublet structure of double optical resonance and the sidebands of the triplet structure in resonance fluorescence are broadened by the intensity fluctuations and tend to copy the Rayleigh distribution of the field amplitude. Off resonance, the asymmetry of the doublet in double optical resonance is reversed and a sideband asymmetry appears in resonance fluorescence for finite bandwidth of the incident light. While on resonance the splitting is always reduced, off resonance the intensity fluctuations may lead to an enhancement of the splitting in comparison to phase-diffusing light.

The two-state model of laser-induced collisions introduced by Gudzenko and Yakovlenko is shown to lead to cross sections with a universal behavior in terms of the variables $z=\left|C_3\right|E_0{v}^{-\frac{3}{5}}{\left|C_6\right|}^{-\frac{2}{5}}$ and $d=\delta {\left|C_6\right|}^{\frac{1}{5}}{v}^{-\frac{6}{5}}\mathrm{sgn}\left(C_6\right)$. In terms of a physical description the dimensionless frequency-detuning variable is $d\propto$ (detuning of the laser from the large-$R$ resonance) (time of collision at the Weisskopf radius). The dimensionless variable $z$ is independent of laser frequency and measures the power dependence of the cross section. It is in fact proportional to $\int {-\infty }^t\frac{C_3{E}_0\mathrm{dt}}{R{\mathrm{}\left(t\right)\mathrm{}}^3}$ evaluated at an impact parameter given by the $b_{\nu }={\left(\frac{C_6}{v}\right)}^{\frac{1}{5}}\propto$ Weisskopf radius = impact parameter where the phase shift due to the Van der Waals potential becomes $\pi$. Above, $\frac{C_3{E}_0}{R^3}$ is the coupling parameter at intranuclear separation $R$ and $E_0$ is the laser field amplitude. The cross section is of the form $\sigma ={\left(\frac{\left|C_6\right|}{v}\right)}^{\frac{2}{5}}H(d,z)\mathrm{}$, where $H(d,z)\mathrm{}$ is tabulated in detail. For large laser fields (i.e., $z>\mathrm{}2\mathrm{}$), the line shape for collisions at a particular relative velocity $v$, laser field amplitude $E_0$, and detuning (from the large-$R$ resonance frequency), $\sigma$ becomes symmetric about $\delta =0\mathrm{}$ with the width decreasing with increasing laser power. The physical reason for the symmetric $H(d,z)\mathrm{}$ at large $z$ is shown to be the decreased importance of curve-crossing effects for large positive $d$ corresponding to the onset of adiabatic behavior and the increased importance of contributions to $\sigma$ from such large impact parameters that the Van der Waals shifts can be neglected. Correspondingly, at large $z$ the linewidth is due entirely to time-of-collision effects. When $z\ge 2$, both the long-range version of the atom-atom interaction and the assumption of straight-line orbits are excellent because of the dominant contribution to $\delta$ from impact parameters > 15 Å.

The total photoabsorption coefficient has been measured from 500 to 600 eV around the $K$ edge of oxygen in gases ${\mathrm{O}}_2$, C${\mathrm{O}}_2$, CO, and ${\mathrm{N}}_2$O by means of a gold continuum source and crystal spectrometer with better than 1-eV resolution. The cross sections are dominated by discrete molecular-orbital transitions below the $K$-edge energy. A few Rydberg transitions were barely detectable. Broad shape resonances appear at or above the $K$ edge. Additional broad, weak features above the $K$ edge possibly arise from shake up. The authors give quantitative results that have about 10% accuracy ($3\sigma$), except on the very strong peaks. All the measured features are discussed in relation to other related measurements and theory.

The technique of electric field ionization has been used to study molecular Rydberg states of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ formed by electron capture of ${\mathrm{H}}_2^{+}$ or ${\mathrm{D}}_2^{+}$ beams in ${\mathrm{H}}_2$. The neutral molecules were passed through two intense electric field ionization regions in tandem, separated by an ∼ ${10}^{-7\mathrm{}}$-sec drift region. Up to 15% of the Rydberg population removed by the first ionization region was repopulated during transit through the drift region. This result has been interpreted in terms of nonadiabatic state mixing of nearly degenerate adiabatic molecular states. A difference in the state repopulation between Rydberg states of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ was observed, indicating the importance of the rovibrational spectrum on the repopulation mechanism. By comparison, similar studies on atomic Rydberg states showed no difference between H and D. Moreover, the atoms exhibited only a small repopulation effect, consistent with the contribution due to $\overrightarrow{1}·\overrightarrow{\mathrm{s}}$ coupling.

The dynamic properties of the ruby NMR laser are discussed from the point of view of synergetics. The authors present a theoretical approach together with the experimental verification. The cooperative features of the instabilities and the disorder-order transitions far from thermal equilibrium of the ruby NMR laser are described by means of order parameters and their dynamic equations, which are generalized Bloch equations. The heat-reservoir description of the conventional spin dynamics in ruby is thereby taken into account. The theory is applied to the free-running NMR laser with its threshold, the critical narrowing of cw NMR lines below threshold, and the steady-state output above threshold. The theory is then extended to the driven NMR laser where an external resonant rf field is applied to form, together with the self-induced radiation field, a competitive- or cooperative-field configuration. The authors present data concerning bistability and hysteresis of the driven NMR laser; in particular, its first-order-type phase transitions from a competitive- to a cooperative-field configuration are discussed. Finally, a novel pulsation mode of the ruby NMR laser is described.

Induced Compton scattering of high-intensity radiation, $N(\nu ,t)=\frac{c^{2}I(\nu ,t)}{2h{\nu }^3}\gg 1$, by a plasma is governed by a nonlinear integro-differential kinetic equation of the Boltzmann type. For a Maxwellian electron distribution, the transition probability kernel takes the form $K(\nu ,{\nu }^{\prime })\propto (\nu -{\nu }^{\prime })$ $\exp [-\frac{{(\nu -{\nu }^{\prime })}^2}{2{\left(\Delta {\overline{\nu }}_D\right)}^2}]$, where $\nu$ and ${\nu }^{\prime }$ are the photon frequencies before and after scattering and $\Delta {\overline{\nu }}_D={\left[\right(\frac{2k{T}_e}{m_e{c}^2}\left)\right(1-cos\alpha \left)\right]}^{\frac{1}{2}}\nu$ is the Doppler width associated with the scattering angle $\alpha$. Only limiting cases with local approximative forms of the kernel have been treated up to now: for a broad photon spectrum ($\delta \nu \gg \Delta {\overline{\nu }}_D$) the kinetic equation was approximated by the Kompaneets differential equation corresponding to $K(\nu ,{\nu }^{\prime })\propto {\delta }^{\prime }(\nu -{\nu }^{\prime })$; for a narrow photon spectrum ($\delta \nu \ll \Delta {\overline{\nu }}_D$), the kernel was approximated by $K(\nu ,{\nu }^{\prime })\propto (\nu -{\nu }^{\prime })$. Qualitative red-shift evolutions of particular initial spectrum profiles were found. Here, the general integro-differential kinetic equation which governs the nonlinear and nonlocal interaction between photons and electrons is studied by a numerical treatment and asymptotic analytical approaches are exhibited. Starting from several initial conditions—narrow or broad spectrum profiles, in the presence or in the absence of a noise spectrum—general spectral evolutions for one-dimensional conservative photon systems are obtained. In the presence of a constant noise spectrum $N_0$ a universal asymptotic solution of the soliton type is obtained: Whatever the initial conditions, a narrow photon spectrum $N(\nu ,t)$ evolves towards a photon soliton moving downwards in the frequency axis with the form $\ln \left[\frac{N(\nu ,t)}{N_0}\right]=\left[\ln \right(\frac{N_m}{N_0}\left)\right]\exp \{-[\frac{{({\nu }_S-\sigma t-\nu )}^2}{2{\left(\Delta {\overline{\nu }}_D\right)}^2}\}$, where $N_m$ is the maximum amplitude and $\sigma =\mathrm{const}(N_m-N_0){\left[\ln \right(\frac{N_m}{N_0}\left)\right]}^{-\frac{3}{2}}$ is the speed. A broad spectrum, however, is decomposed into a set of such solitons which are ordered by amplitude (proportional to their speeds) in their downward motion. In the absence of a constant noise spectrum, an initial narrow Gaussian profile moves downwards (on the $\nu$ axis) with decreasing speed, growing in amplitude and narrowing in width.

The quantum theory is developed for an arbitrarily stratified one-dimensional optical cavity which transmits light at one of its end The field is expanded in terms of the modes of the universe and each universal mode is quantized separately by means of the usual method. A class of coherent states which yields oscillation wave shapes of the cavity quasimodes as the field eigenvalue is studied. A state of this class gives an eigenvalue for the annihilation operator of a universal mode which is an analytic function of the mode frequency except for a mode-dependent phase factor. The mathematical meaning of the phase factor is studied. A new scheme of field quantization is developed which absorbs the above phase factor and yields simpler forms of the eigenvalue equations for the above class of states. For a state of the class, the local intensity, its fluctuation, and the various correlations of the field decay with time. For the local field inside or outside of an optical structure which is coupled to the free space, the almost definite phase relationship among the universal modes plays a decisive role.