The higher-order adiabatic approximation method of solving the Schrödinger equation for slowly transported quantum systems, which contains Berry’s improved adiabatic theorem as its zeroth-order step, is generalized to solve evolution equations for a wide class of slowly transported classical systems. It is shown how the adiabatic condition is broken and transitions between different modes take place. Selection rules for such transitions are shown to be a topological property of the evolution path in parameter space.

Two critical quantities in muon-catalyzed d-t fusion are the d-t fusion rate 〈ψ‖${\delta }^{\mathrm{}\left(3\right)\mathrm{}}$${(\mathrm{r}}_{\mathrm{dt}}$)‖ψ〉 and the α-μ sticking fraction mU〈cphi(r)${\mathrm{e}}^{\mathrm{i}}$q⋅r‖${\mathrm{\delta }}^{\mathrm{}\left(3\right)\mathrm{}}$(r ${}_{\mathit{d}\mathit{t}}{}^{}{}_{}{}^{}$)‖ψ(${\mathrm{r}}_{\mathit{t}}$,r)〉${\mathrm{\Vert }}^2$/ 〈ψ‖${\mathrm{\delta }}^{\mathrm{}\left(3\right)\mathrm{}}$(${\mathrm{r}}_{\mathit{t}}$)‖ψ〉, where ψ is a (dtμ${)}^{+}$ wave function and cphi is a hydrogenic α-μ wave function. It is explained why conventional approaches to calculate these quantities directly are slowly convergent. It is suggested that the use of a basis that explicitly includes terms that appear in the Fock expansion will lead to more rapid convergence. Furthermore, an identity relating 〈ψ‖${\delta }^{\mathrm{}\left(3\right)\mathrm{}}$(r)‖ψ〉 to expectation values of more diffuse operators, which was first derived by Hiller, Sucher, and Feinberg [Phys. Rev. A 18, 2399 (1978)] and then extended by Drake [Nucl. Instrum. Methods Phys. Res. B 31, 7 (1988)] in the context of atomic calculations, is generalized to the calculation of fusion rates and sticking fractions. It is anticipated that these relations will facilitate the accurate calculation of fusion rates and of sticking fractions.

We present measurements of doubly differential cross sections (DDCS) with respect to energy and angle for electron emission produced when 100- and 50-keV/u ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ and ${\mathrm{H}}^{+}$ collide with He. An electron spectrometer designed for this purpose enables us to measure electron distributions which, even at small emission angles, do not present appreciable deformations of the measured distributions by extended gas target effects. Using the ratio of the emissions obtained with ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ and ${\mathrm{H}}^{+}$, we study the dependence of the DDCS on the projectile charge. We confirm a saturation of this emission ratio that increases with increasing angle. Furthermore, we report a sudden enhancement of the emission ratio that is found at and above the electron capture to the continuum peak. These observations are in basic but not quantitative agreement with calculations performed using a model that incorporates the continuum distorted wave and eikonal initial state and that approximately accounts for a two-center interaction of the active electron.

Nuclear-fusion rates of isotopic hydrogen nuclei embedded in dense screening media are calculated. We consider the cases of a uniform degenerate electron gas and the inhomogeneous electron density in solids. We derive an exact wave function for the screened nuclear interaction and an analytical expression for the barrier-penetration factor in the case of homogeneous screening. For qualitative estimates of the screening in solids, we use a Thomas-Fermi description of the electron density. A crossover of the fusion rates of the various isotopic pairs analyzed (p-d, d-d, p-t, and d-t) is predicted for increasing screening length, velocity, or effective temperature of the medium. The effects of variable screening length and local effective temperatures are considered for electron gases in the range of metallic densities and compared with previous experimental and theoretical studies.

Variational principles for symmetric complex scattering matrices (e.g., the S matrix or the T matrix) based on the Kohn variational principle have been thought to be free from anomalous singularities. We demonstrate that singularities do exist for these variational principles by considering single and multichannel model problems based on exponential interaction potentials. The singularities are found by considering simultaneous variations in two nonlinear parameters in the variational calculation (e.g., the energy and the cutoff function for the irregular continuum functions). The singularities are found when the cutoff function for the irregular continuum functions extends over a range of the radial coordinate where the square-integrable basis set does not have sufficient flexibility. Effects of these singularities generally should not appear in applications of the complex Kohn method where a fixed variational basis set is considered and only the energy is varied.

Cross sections for K-shell ionization by charged particles have been calculated within the framework of the impact-parameter formalism using the distortion approximation. The continuum wave functions are represented by pseudostates. It is confirmed that the pseudostate wave function can well reproduce the shape of the continuum wave function for low-energy electrons. The calculated total K-shell ionization cross sections for a number of ion-atom collision systems are shown to be in good agreement with the experimental results. For protons on copper, the ionization probabilities as a function of impact parameter are also found to agree with the measured values. The present results indicate that the distortion approximation using pseudostates is very useful in the study of K-shell ionization cross sections over a large range of ion-atom collision systems.

The four logarithmic mean excitation energies I(ν) for ν=-1,...,2 have been calculated for hydrogen and helium by the method introduced a few years ago [S. Rosendorff and A. Birman, Phys. Rev. A 31, 612 (1985)]. At that time a parametrization procedure was used for helium that yielded up to ±10% accuracy. It is estimated that for a given wave function the present method of calculation yields an accuracy for I(ν) of 1 part in ${10}^4$. For helium three different Hartree-Fock-type wave functions were used. Correlation effects were thus not included.

The transport of high-energy accelerating charged particles in channeling conditions in a crystalline solid is considered by means of a Fokker-Planck model. Multiple scattering on electrons, appropriate to the channeling of positive particles, and radiation damping due to the emission of channeling radiation are also included. Analytic solutions have been obtained for the case of a harmonic channeling potential. Without acceleration, diffusion due to multiple scattering occurs. With acceleration, the adiabatic damping retards this, although the reduction in critical channeling angle with increasing energy eventually competes. For light particles (positrons), the emission of channeling radiation can lead to a steady state. Implications for crystal accelerator schemes are discussed.

The total ionization rate by a plane-wave field in the long-wavelength approximation from a three-dimensional δ-function potential is reconsidered. Well into the above-threshold ionization regime, the Keldysh approximation turns out to yield virtually the exact ionization rate for circular polarization. For multiphoton orders in excess of n∼10, lowest-order perturbation theory only holds for intensities much lower than those employed in current experiments. For moderate intensities, the total ionization rate is very well approximated by a slope of N+k with integer k≥1. Within the range of most experimental interest where one or several channels are suppressed by the ponderomotive barrier, the slope is again near N and decreasing with increasing intensity.

Dielectronic recombination (DR) cross sections and rate coefficients for the H-like and He-like C and O ions are calculated in the zero-field, zero-density limit. The peak rates are approximately (1.2–1.6)×${10}^{\mathrm{-}12}$ ${\mathrm{cm}}^3$/sec for all four ions. For the H-like ions, the contribution to total rates from high Rydberg states (n≥6) is found large, accounting for nearly one-half of the total rates. Agreements with earlier estimates are at a ±5% level. For the He-like ions, the high-Rydberg-state contribution is strongly suppressed because of the extra Auger channel which opens up at n=5–7. Agreement with previous calculations is again at a 5% level. The DR cross sections for the initial metastable states of the He-like ions are also estimated for a few low-lying resonance states near the DR threshold. The cross section for the 2s ${}_{}{}^1{}_{}{}^{}p$ ${}_{}{}^1{}_{}{}^{}\mathrm{nl}$ excitation capture is found to be very large.

Using a fully quantized dressed-atom approach, we present a theory and interpretation of the pressure-induced resonances in four-wave mixing (PIER4) that may arise when three incident fields interact with an ensemble of two-level atoms. The PIER4 resonances are seen to arise from a collisionally created modulation of a dressed-state population when an operator approach is used to solve the problem and from a level crossing between collisionally populated dressed states when an occupation-number formalism is used.

For the computation of the induced-dipole moment, the collisional complex consisting of two ${\mathrm{H}}_2$ molecules is treated like one molecule in the self-consistent-field and size-consistent, coupled electron pair approximations that separates correctly at distant range. The basis set accounts for 95% of the correlation energies. The radial transition matrix elements of the induced-dipole components are obtained for the two cases $v_1$=$v_2$=0 and $v_1$=0,$v_2$=1, where the $v_i$ are the vibrational quantum numbers of the interacting ${\mathrm{H}}_2$ molecules (i=1 or 2). The dependence of these elements on the most important rotational states (${\mathit{j}}_1$, ${\mathit{j}}_1$’,${\mathit{j}}_2$,${\mathit{j}}_2$ ’=0,...,3) involved is obtained and seen to be significant in the fundamental band. The results are recast in a simple, but accurate analytical form that is used in a quantum formalism for computations of the spectral moments (sum rules) and line shapes of the collision-induced absorption spectra of molecular hydrogen pairs in the infrared 2.4-μm band. The calculations are based on a proven isotropic potential model that we have extended to account for effects of vibrational excitations. Numerical consistency of the line-shape calculations with the sum rules is observed at the 1% level. The comparison of the computational results with the available measurements at temperatures from 20 to 300 K shows agreement within the estimated uncertainties of the best measurements (≊10%). This fact suggests that theory is capable of predicting these spectra reliably at temperatures for which no measurements exist, with an accuracy that compares favorably with that of good laboratory measurements.

Nineteen γ-ray lines in the energy range 0.4–3.0 MeV, produced by the Ni(n,γ) and Fe(n,γ) reactions, were scattered from a natural U target at angles of θ=1.02° for the Ni source, and θ=1.80° for the Fe source. Differential cross sections were measured relative to carbon and were found to be dominated completely by Rayleigh scattering. The smallness of the scattering angles and the large values of the Rayleigh cross sections present a unique opportunity to make an accurate comparison with the popular theoretical calculations based on the modified form factors. The results were found to agree fairly well with the form-factor calculations, but discrepancies averaging 8% were observed in the momentum transfer range 0.6–1.3 A${̊}^{\mathrm{-}1}$.

Methods are presented for determining singlet-triplet mixing angles from measured energy-level data in two-valence electron systems, and for utilizing these mixing angles to specify E1 and M1 oscillator strengths and magnetic g factors from LS coupling and hydrogenic formulas and from data obtained in single-valence electron systems. These methods are tested through studies of line strengths in the He, Mg, Ne, Si, and S isoelectronic sequences and of g factors in the Kr and Pb atoms.

Forward- and backward-directed, stimulated emissions have been observed following two-photon pumping of the 5p states of krypton and the 6p’, 7p, 8p, and 4f states of xenon. Multiphoton ionization spectra are also obtained and compared with the photon-detected excitation spectra. In krypton coherent emissions from the 5p states to the 5s are observed, and for xenon many p→s, d→p, and f→d cascade emissions are observed. By analogy to the well-studied alkali-metal and alkaline-earth examples, the emissions are assigned as amplified spontaneous emission. Several intensity anomalies in the xenon p→s emissions are not understood at present. Interference effects due to coherent cancellation between competing excitation pathways may be occurring.

The signal generation in four-wave-mixing Raman spectroscopy and stimulated Raman spectroscopy is theoretically investigated for focused Gaussian beams. Signal strength as a function of interaction length and total signal generation are calculated for both types of coherent Raman spectroscopies. We further discuss the application of our theory to spatially inhomogeneous broadening, especially optical Stark broadening, induced by one of the laser beams. Intensity and phase contours of a Gaussian beam are also presented to enhance the understanding of intensity-dependent interactions.

The influence of the optical Stark effect on spectral line shapes in four-wave-mixing Raman spectroscopy (FWMRS) and stimulated Raman spectroscopy (SRS) is investigated experimentally and theoretically. While both high-resolution spectroscopic techniques commonly use focused Gaussian beams with rather high laser intensities, the contribution of the optical Stark effect to the line shapes has not been well explored. Using an experimental setup, capable of rapid alternation between the simultaneous measurement of coherent Stokes Raman spectroscopy and inverse Raman spectroscopy spectra at low (mild-focusing) and high (tight-focusing) intensities, together with a sophisticated frequency reference scheme, we are able to perform a rather direct comparison between Stark-broadened and non-Stark-broadened spectra of both classes of Raman spectroscopies. Experimental spectra of lines in the vibrational Q branch of molecular nitrogen (${\mathrm{N}}_2$) are obtained for low and high pump-laser peak intensities in copropagating focused Gaussian beams. At high pump intensities, the optical Stark effect leads to strong asymmetric broadening for both types of coherent Raman spectroscopy. Our experimental results demonstrate that SRS spectra show more Stark shift and broadening than their FWMRS counterparts. Using the theory of signal generation in focused Gaussian beams, we have generated theoretical Stark-broadened spectra for both spectroscopies. While the experimental SRS spectra show excellent agreement with theoretical calculations, simultaneously measured FWMRS spectra do not perfectly agree with our theory. We demonstrate that this discrepancy can be partly reconciled by the inclusion of a resonant fifth-order process in the commonly employed third-order theory of FWMRS.

We present measurements and calculations of the time-dependent behavior of an electron bound in a Coulomb potential placed in an additional static electrical field. The time-dependent behavior is studied by means of the evolution of a wave packet. The wave packet is created by coherent superposition of several k states of one Stark manifold. It is pointed out that the oscillation of this ‘‘parabolic’’ wave packet corresponds to an oscillation of the angular momentum l. In the case of a hydrogen atom the spacing between the k states is constant, leading to a dispersion-free wave packet. For this situation the parabolic wave packet ‖Ψ(x,z)${\Vert }^2$ is plotted as a function of time. The oscillations of the parabolic wave packet can be measured by photoionization, because the photoionization probability is l dependent. The time-dependent photoionization probability is calculated in two steps. First the l-population coefficients are calculated as a function of time. Then we calculated the transition probability of each l state to the continuum. Combining these two allows us to calculate the time-dependent ionization probability. Experimentally, a wave packet is created by coherent superposition of k states of rubidium atoms with a 7-ps laser pulse. The ionization probability is probed by a second laser pulse, which is delayed with respect to the first one. In this way as many as ten oscillations of the parabolic wave packet are observed. The calculations (for hydrogen) agree well with the experimental result of the pump-probe experiment. The ac Stark shift of a k manifold due to the laser field was measured in a separate experiment; the determined value of 0.01 meV/(GW/${\mathrm{cm}}^2$) is low enough to ensure that intensity effects can be neglected.

Excitation and decay of the 4$d^{\mathrm{-}1}$(4,ε)f giant resonances of atomic Sm, Eu, and Gd have been investigated by photoabsorption and photoelectron spectroscopy. The experimental total and partial cross sections are compared to those predicted by many-electron theories. Autoionization into the 4$f^{\mathrm{-}1}$εl continuum dominates. The character of the giant resonances is closer to that of a 4$d^{\mathrm{-}1}$4f resonance than to that of a 4$d^{\mathrm{-}1}$εf shape resonance encountered for Ba and La.

The numerical multiconfiguration Hartree-Fock method is used to study in detail the photoionization of atomic beryllium near the 1s threshold. Electron correlation effects, which are found to be very important in the K-shell partial photoionization cross section, have been taken into account very accurately through the configuration-interaction procedure. The present results are compared with experimental measurements of the relative contributions of the three major ionization channels and are found to be in excellent agreement. The existence of the principal resonances reported by the experiment has been confirmed and assignments made to these contributions based on accurate energy calculations.