We show that the resonance wave function can be generally thought of as being unit normalized under an appropriate analytic continuation procedure and that, so normalized, the resonance eigenfunctions obtained from a finite-basis-set calculation can be used to evaluate partial widths. Numerical results are given for two model problems.

We report the derivation of an analytical expression of the one-photon transition amplitude for free-free transitions occurring in the course of the collision of fast electrons with a hydrogen atom, in the presence of a laser. The calculation is performed within the framework of the conventional time-dependent perturbation theory to lowest nonvanishing order. The projectile electron wave function is approximated as a plane wave and the infinite sums running over the H-atom spectrum are accounted for exactly by using a compact representation of the Coulomb Green’s function. As an illustration of the usefulness of our formalism, we discuss the occurrence of dips of two distinct origins in the cross sections and compare the respective importances of absorption and stimulated emission.

An expression, originally due to Wigner, for the R matrix for potential scattering, in the form of an infinite product, is rederived using the properties of Green’s functions. The new derivation yields the formula R($k^2$)=R(0)${\prod }_{m=1\mathrm{}}^{\infty }$ (1-$k^2$/$q_m^2$) /${\prod }_{n=1\mathrm{}}^{\infty }$(1-$k^2$/$k_n^2$), in which the parameters R(0), $q_m^2$, and $k_n^2$ (the zero-energy R matrix and the eigenvalues of the Hamiltonian corresponding to eigenfunctions with vanishing value and derivative at the boundary r=a) are clearly identified. It is shown, both via general arguments and in the context of a model problem, that a truncated version of the infinite product exhibits superior convergence to an analogous truncation of the standard direct summation, and that a closure-corrected product is superior to a summation with the Buttle correction. Moreover, the closure correction to the product does not require a new solution of a zeroth-order Schrödinger equation at each energy of interest. The method is readily generalized to the multichannel case, and since, in the analysis of real systems, the parameters in the product appear to be calculable to greater accuracy than those that enter the sum, we suggest that the method offers the possibility of performing improved numerical calculations.

Rayleigh scattering amplitudes and elastic photon-atom scattering cross sections have been calculated for ${\mathrm{C}}^0$, ${\mathrm{C}}^{1+}$, ${\mathrm{C}}^{2+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{Ne}}^0$, ${\mathrm{Ne}}^{1+}$, ${\mathrm{Ne}}^{2+}$, ${\mathrm{Ne}}^{4+}$, ${\mathrm{Ne}}^{6+}$, ${\mathrm{Ne}}^{8+}$, and ${\mathrm{Ne}}^{9+}$ atoms and ions in their ground state. Some data were also obtained for oxygen. X-ray energies considered are in the regions above and below the threshold energy for K-shell photoionization. Except in the immediate neighborhood of this threshold energy, the primary effect of ionization on the atomic cross section is to reduce the number of electrons from which scattering occurs. The resonance region near threshold widens with increasing ionization, as with vacancies in deeper-lying states transitions to intermediate states further below threshold are allowed. Above the threshold energy, K-shell amplitudes in an isonuclear sequence, except for hydrogenlike-ion cases, share a common curve differing only in the position of the threshold. Further, when the photon energy is expressed in units of the K-shell threshold energy, both carbon and neon imaginary amplitudes share a common curve. Well above the threshold, the real part of amplitudes approach form-factor predictions.

We report measurements of the 2$s^2$2$p^n$-2s2$p^{n+1\mathrm{}}$ transitions in the ions Kr xxviii and Kr xxix, fluorinelike and oxygenlike krypton. The measured line positions are used to determine fine-structure intervals in the ground-state configurations of these ions. The results are compared with semiempirical and Dirac-Fock calculations.

Photoelectron spectra have been taken between 2460 and 2600 eV photon energy across the discrete and continuum resonances in the vicinity of the sulfur K edge in gaseous ${\mathrm{SF}}_6$. Results at the below-threshold S 1s→6$t_{1u}$ resonance indicate that ‘‘highly excited’’ S 2p and S 2s satellites (with two core holes) are the primary autoionization final states of ${\mathrm{SF}}_6$${\mathrm{}}^{+}$. An observed asymmetric profile in the S(LVV) Auger angular distribution suggests interference effects in the alignment of these resonantly produced ${\mathrm{SF}}_6$${\mathrm{}}^{+}$ ions. Decay of the low-energy S 1s continuum resonances near 2507 eV photon energy into S 2p, S 2s, and/or valence photoemission channels indicates autoionizing character. These features are assigned as doubly excited states, leading to S 1s satellite thresholds observed here for the first time. At higher photon energies, between 2520 and 2570 eV, large oscillations in the S 1s cross section are reproduced well by multiple-scattering Xα calculations, but are not explained adequately by single-scattering plane-wave extended x-ray absorption fine structure effects. We speculate that improvements in the description of both the electron scattering process and the molecular potential are necessary to model the diffractive and nondiffractive (barrier interaction) effects in this energy region.

Dielectronic recombination has been found to be the dominant recombination process in the determination of the ionization balance of selenium near the Ne-like sequence under conditions relevant to the exploding-foil EUV laser plasmas. The dielectronic recombination process tends to populate excited levels, and these levels in turn are more susceptible to subsequent excitation and ionization than are the ground-state ions. If one defines an effective recombination rate which includes, in addition to the primary recombination, the subsequent excitation and ionization of the additional excited-state population due to the primary recombination, then this effective recombination rate can be density-sensitive at relatively low electron density. We present results for this effective dielectronic recombination rate at an electron density of 3×${10}^{20}$ electrons/${\mathrm{cm}}^3$ for recombination from Ne-like to Na-like selenium and from F-like to Ne-like selenium. In the former case, the effective recombination rate coefficient is found to be 1.8×${10}^{\mathrm{-}11}$ ${\mathrm{cm}}^3$/sec at 1.0 keV, which is to be compared with the zero-density value of 2.8×${10}^{\mathrm{-}11}$ ${\mathrm{cm}}^3$/sec. In the latter case (F-like to Ne-like), the effective recombination rate coefficient is found to be 1.3×${10}^{\mathrm{-}11}$ ${\mathrm{cm}}^3$/sec, which is substantially reduced from the zero-density result of 3.3×${10}^{\mathrm{-}11}$ ${\mathrm{cm}}^3$/sec. We have examined the effects of dielectronic recombination on the laser gain of the dominant Ne-like 3p-3s transitions and have compared our results with those presented by Whitten et al. [Phys. Rev. A 33, 2171 (1986)]. The results obtained for the gain of the J=2 transitions at 206.9 and 209.8 Å disagree by a factor of 2, and the calculated F-like to Ne-like isoelectronic sequence ratio differs by a factor of 4. These discrepancies are investigated and are found to be due to three factors: inclusion of post-recombination collision effects, inclusion of Rydberg levels, and choice of line shape.

Optical pumping of cesium vapor in a heat-pipe oven in which the energy of two near-infrared photons is close to the 6D states results in high conversion efficiency (up to 1.7%) of the near-infrared pump light to intense blue, forward-propagating radiation. The blue light corresponds to the 7P-6S transition. The dependence of conversion efficiency upon focusing conditions, cell length, and pump intensity is presented. Absorption and gain coefficients are measured in a second heat pipe. The results are discussed in terms of optically pumped stimulated emission (OPSE), stimulated electronic Raman scattering (SERS), and subsequent nonlinear four-wave mixing of two pump-laser photons and one SERS or OPSE infrared photon, leading to parametric generation at ω=2${\omega }_L$-${\omega }_{\mathrm{ir}}$. Two-photon resonant, three-photon ionization cross sections are also studied experimentally and theoretically for the case of resonant enhancement at the 6D levels of cesium. For comparison, similar results for rubidium are also presented for the 5D levels.

The temperature and density dependence of the rotational Raman linewidths and line shifts for the diatomic molecules ${\mathrm{N}}_2$ and ${\mathrm{H}}_2$ has been measured using stimulated Raman gain spectroscopy. Room-temperature results for the density-broadening coefficients, B, in ${\mathrm{N}}_2$ are compared with ab initio calculations, while the low-temperature (80 and 195 K) results are the first to be reported, to our knowledge. Values of γ in the relation, B∝$T^{\gamma }$, were determined from fits to the data for self-broadening in ${\mathrm{N}}_2$ yielding 0.25<γ<0.39. Foreign-gas (${\mathrm{O}}_2$) broadening coefficients for the ${\mathrm{N}}_2$ transitions were also measured and found to be 10–15 % smaller than the self-broadening coefficients. Our linewidth and line-shift results for ${\mathrm{H}}_2$ are in general agreement with previous measurements.

Calculations of the electron-impact ionization cross sections and photoionization cross sections for ten ions in the palladium isoelectronic sequence from Ag ii to W xxix were performed using a nonrelativistic single-configuration distorted-wave approximation. The 4$d^9$kf ${\mathrm{}}^1$P partial wave was found to be sensitive to the exchange potential involving 4d core electrons, resulting in large qualitative differences between cross sections computed in the term-dependent Hartree-Fock potential and the configuration-averaged potential.

Multiconfiguration variational calculations are carried out of the electronic wave functions of the a ${\mathrm{}}^3$${\Sigma }_g^{+}$ and b ${\mathrm{}}^3$${\Sigma }_u^{+}$ states of molecular hydrogen, and the electric dipole transition moment between them is obtained. The dipole moment is used in a calculation of the probabilities of radiative transitions from the discrete vibrational levels of the a ${\mathrm{}}^3$${\Sigma }_g^{+}$ state to the vibrational continuum of the repulsive b${\mathrm{}}^3$${\Sigma }_u^{+}$ state as functions of the wavelength of the emitted photons, and a comparison is made with measurements of the emission spectra of the v’=0 levels of ${\mathrm{H}}_2$ and of ${\mathrm{D}}_2$. The total transition probabilities and radiative lifetimes of levels v’=0–20 are presented.

The time evolution of alignment and orientation of excited atoms in an electric field is described using a density-matrix treatment. Orientation is produced by applying a tilted static electric field on levels aligned by beam-foil interaction. The modulation of polarization of the light is observed either inside the zone of constant field, by moving along the atomic beam, or downstream, in the field-free zone, by sweeping the field strength. Two different geometries are used for relative directions of ion beam, electric field vector, and foil normal. Tensor polarizabilities and cross sections for excitation of Zeeman sublevels are deduced from frequencies and amplitudes of quantum beat signals. Results are given for n ${\mathrm{}}^1$$D_2$ levels of ${}_{}{}^4{}_{}{}^{}\mathrm{i}(\mathit{n}=3\mathrm{}$, 4, and 5).

We report new results on the effect of collisions on radio-frequency (rf) -laser double resonances in an atomic vapor under conditions of velocity-selective optical pumping. Our experiments are performed on Zeeman resonances in the 4$f^6$6$s^2$ ${\mathrm{}}^7$$F_1$–4$f^6$6s6p ${\mathrm{}}^7$$F_0$ transition in samarium vapor in the presence of rare-gas perturbers (He, Ne, Ar, Xe). The collisional relaxation of the rf-generated sublevel coherence is studied using Raman heterodyne detection; this recently introduced spectroscopic technique is capable of separately yielding signal contributions originating from optically resonant and off-resonant atoms. The corresponding measurements clearly reveal that velocity-changing collisions (VCC) can completely determine the characteristics of the rf-laser double-resonance signals. Our experimental findings on the linewidths and line shapes of the rf resonances are in satisfactory quantitative agreement with theoretical predictions that are based on a novel four-level density-matrix calculation; here a Keilson-Storer collision kernel is used to describe the velocity diffusion processes. The comparison of calculated and measured results also permits us to derive cross sections for VCC and depolarizing collisions; moreover, information on the spectrum of the velocity changes connected with alignment-preserving collisions can be obtained.

Transition probabilities involving the continuous spectrum of many-electron atoms exhibit a variety of resonance phenomena and deviations from independent-particle model predictions. We present a general theory of photoionization which (i) utilizes function spaces for initial and final states which are state specific and are based on numerical as well as on analytic basis sets. The valence, Rydberg, scattering, and virtual orbitals are optimized by different methods. (ii) In addition, our theory is formulated within a configuration-interaction, reaction-matrix, and multichannel quantum-defect approach suitable for the treatment of the continuous and of the discrete Rydberg spectrum via the use of numerical frozen-core Hartree-Fock channel orbitals. In this work we have calculated the cross sections for the simultaneous photoionization and photoexcitation to the n=2 shell of ${\mathrm{He}}^{+}$. Our results for the ratio of the cross section at the degenerate ${\mathrm{He}}^{+}$ thresholds 2s and 2p agree with those of published close-coupling calculations and disagree with those of a many-body perturbation theory. We also compute values for energies very close to and at the threshold, previously not available. The autoionization widths and quantum defects of the Rydberg series 2snp, 2pnd, and 2pns are also in agreement with previous close-coupling calculations.

Thermodynamic perturbation theory is used to evaluate the free energy of an atom interacting via dipole coupling with the blackbody radiation field. An expression, exact through order $e^2$, for the interaction free energy is obtained. In the high-temperature limit the result is π$e^2$($k_B$T${)}^2$/3ħ${\mathrm{mc}}^2$, consistent with experiment and in agreement with an earlier exact calculation for the oscillator.

The small-signal gain for an electromagnetically pumped free-electron laser is calculated for an amplifier configuration which includes an axial-guide magnetic field. The large-amplitude electromagnetic wave acts like the magnetostatic wiggler in a conventional free-electron laser, and the expression for the gain is shown to reduce to the well-known result in the limit of a magnetostatic wiggler. Substantial enhancements in the gain are found when ${\Omega }_0$≃${\gamma }_0$(${\omega }_w$+$k_w$$v_{?}$), where ${\Omega }_0$ is the axial gyrofrequency, ${\gamma }_0$ is the relativistic factor for the electron beam, $v_{?}$ is the axial velocity of the electron beam, and (${\omega }_w$,$k_w$) are the frequency and wave vector of the electromagnetic wiggler.

Theoretical calculations regarding the collinear intracavity nearly degenerate four-wave mixing are presented when a Fabry-Perot cavity is externally driven by a strong pump and probed by a weak signal. The calculations are performed for two different limits: the mean-field and the small-signal gain approximations. The results suggest the bistable behavior for all the three signals (pump, probe, and conjugate) with several different shapes of the hysteresis loops. Furthermore, for certain values of the parameters in the mean-field approximation, calculations show a resonance behavior of probe and conjugate signals with respect to the incident pump intensity, with probe and conjugate transmittance as high as ${10}^3$–${10}^4$ in the case when the pump transmission does not exhibit bistability. In the small-signal gain approximation, theory also demonstrates strong dependence of probe amplification on the normalized detuning when it is smaller than the probe-cavity mistuning.

Fluorescein-doped boric acid glass is a material characterized by an extremely low saturation intensity of ∼15 mW${\mathrm{?}}^{\mathrm{-}2}$ and a nonlinear susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ as large as ∼1 esu. The saturated absorption of this material is shown both theoretically and experimentally to depend on the state of polarization of the saturating beam, even though the unsaturated absorption is polarization insensitive. Phase-conjugate reflectivities as large as 0.6% have been obtained through use of degenerate four-wave mixing in this material. These measured reflectivities are in good agreement with the predictions of a theory that includes the effects of excited-state absorption and grating washout. In addition, two-beam coupling due to the nonlinearity of saturable absorption has been demonstrated in this material. The magnitude of the coupling is maximized by inducing a frequency shift between the two beams of ∼0.1 Hz.

We propose and analyze an experiment in which atoms in a coherent superposition of atomic states are injected into a high-Q maser cavity. We show that the symmetry of the field in the cavity is ‘‘broken’’ in the same way as results from a classical signal injected into a laser cavity. This broken symmetry can be detected by monitoring the atomic excitation of a probe atom.

We present a general formalism for obtaining a coupled set of first-order rate equations for the optical field at a finite number of points in an optical resonator. We compare these local-field equations to an expansion in modes of the individual resonators and point out a shortcoming of the latter technique that has not been recognized before. We consider the special case of a set of two coupled resonators and derive the coupled rate equations for the fields in each of the two cavities with coupling coefficients. The resulting formulas are both simpler than those derived from coupled-mode theory and more accurate in the sense that they give a steady-state response which agrees with that calculated from the composite cavity modes. We show how the use of a single local-field rate equation can carry the same information as a full set of multimode rate equations in some cases, in particular, that of partial reflection back into a laser from a distant source.