A new variational method is presented which permits a direct and rapidly convergent calculation of almost divergent sums over complete sets of intermediate states, using a finite-basis-set representation. The formalism for first-order perturbation calculations of infinite sums for two-electron systems is presented and the technique is used to calculate the first-order perturbation correction to the Bethe logarithm in two-electron systems. Estimates of higher-order coefficients in the $\frac{1}{Z}$ expansion are given.

In this paper we consider screened Coulomb potentials of the Yukawa type and treat them using a scaling variational method based on the SO(2, 1) subgroup of the full SO(4,2) dynamical group of the point Coulomb problem. In this formulation the tilting angle is treated as a variational parameter and the relevant matrix elements of the Yukawa potential can be expressed as matrix elements of an analytically continued finite SO(2, 1) transformation of the parabolic type. We calculate the energy eigenvalues, wave functions (essentially scaled Coulomb wave functions), and normalization factors. Our energy eigenvalues are more accurate than those found by the analytic perturbation theory of McEnnan et al., while the normalization factors are less accurate. Thus our method may be considered as complementary to the analytic perturbation theory.

We have obtained equivalent local potentials (ELP's) to matrix effective potentials for $e$-He scattering at 200 and 400 eV by means of semiclassical WKB inversion of the phase shifts. The absorptive parts of these ELP's are compared with current models for absorption potentials.

Scattering of electrons from neon atoms is investigated by the polarized-orbital method. The perturbed orbitals calculated with use of the Sternheimer approximation lead to the polarizability $2.803a_0^3$, in fairly good agreement with the experimental value $2.66a_0^3$. Phase shifts for various partial waves are calculated in the exchange, exchange-adiabatic, and polarized-orbital approximations. They are compared with the previous results. The calculated elastic differential, total, and momentum-transfer cross sections are compared with the experimental results. The polarizedorbital approximation yields results which show general improvement over the exchange-adiabatic approximation.

Absolute $e^{-}$-He elastic differential scattering cross sections have been determined from relative scattered electron angular distribution measurements in the energy range from 2 to 19 eV. The absolute cross sections have been determined to within errors which vary from ±9% to ±2% within this energy range. The $s$, $p$, and $d$ phase shifts determined in this work are roughly in agreement with previous determinations, while the total and momentum-transfer cross sections determined in this work in some cases do not agree with previous determinations. The total and momentum-transfer cross sections found in this work at 2 and 5 eV are in excellent agreement with the previous direct measurements of Golden and Bandel and of Crompton et al., respectively.

We have investigated elastic and inelastic scattering of electrons by sodium atoms at intermediate energies (6-25 eV) by the atomic-recoil technique, using a new atomic-beams apparatus. The effects of the apparatus geometry, atomic velocity, and electron energy distributions on the analysis of the experimental results have been examined in detail, and their effects on small-angle scattering have been incorporated into the present work. We present absolute measurements of the elastic ($e^{-}$, Na) differential cross section at 10 eV for electron polar angles ranging between 12° and 22°. These measurements are in good agreement with the normalized results of S. K. Srivastava and L. Vuskovic [J. Phys. B 13, 2633 (1980)] and in reasonable agreement with the two-state close-coupling calculation of M. R. Issa (Ph.D. theis, University of Durham, 1977). We also present absolute measurements of an integral over small angles of the $3{}_{}{}^2{}_{}{}^{}P$ impact-excitation differential cross section, together with a precise prescription for comparison with theory. We found that the distortedwave-polarized-orbital calculation of J. V. Kennedy, V. P. Myerscough, and M. R. C. McDowell [J. Phys. B 10 3759 (1977)] gives results which are too high in the forward direction, while those of Issa are somewhat low.

We have measured effective cross sections for the scattering of electrons by CsBr, RbBr, CsCl, RbCl, and KI, using the molecular-recoil technique, in the 1-22.5-eV energy range. We show that these can be expressed as an integral of the differential cross section folded with an apparatus form factor, which has the effect of suppressing the very large small-angle contribution to scattering. The apparatus form factor is calculated explicitly, and a precise prescription for comparison with theory is given. The data are compared with calculations using the rotating-dipole first Born approximation and semiclassical perturbation theory [A. S. Dickinson, J. Phys. B 10, 967 (1977)] differential cross sections.

In formulations of scattering theory which use an expansion in adiabatic eigenfunctions, such as the perturbed-stationary-state approximation, the coupled-channel equations include derivative couplings. The $R$ matrix is not Hermitian in regions where the derivative couplings are nonzero. It is shown that a superposition of the logarithmic derivative matrix and the derivative coupling matrix is Hermitian.

A rigorous theory for low-energy scattering in arbitrary dimension $n\ge 2$ with general, possibly long-range interactions is presented. Several applications are discussed. For $n=2\mathrm{}$, the question about the existence of scattering parameters is resolved and the important role of a parametrization of scattering observables in the study of adsorbed systems is illustrated. For $n=3\mathrm{}$, an analytic expansion of the phase shift and scattering length for charged-particle scattering around their neutral counterparts is derived, taking into account explicitly the finite extent of the charge.

Relative emission yields of Balmer lines as functions of the dwell time ($t_D=0.97-54.1\mathrm{}$ fs) in thin carbon foils (2-68 μ g/${\mathrm{cm}}^2$) have been measured with (0.2-0.8)-MeV/amu ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{H}}_3^{+}$ incident on thin carbon foils. Large molecular effects for emission yields of Balmer lines have been observed for ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{+}$, where the molecular effect for ${\mathrm{H}}_3^{+}$ is larger than that for ${\mathrm{H}}_2^{+}$. The molecular effects for ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{+}$ depend on the principal quantum number ($n=3-6\mathrm{}$), but this $n$ dependence disappears at the largest $t_D (=54.1\mathrm{}$ fs). The molecular effects rapidly decrease with increasing $t_D$ in the small-$t_D (\lesssim 2$ fs) region and more slowly decrease in the large-$t_D (\gtrsim 2$ fs) region. The magnitudes of the molecular effects at the largest $t_D (=54.1\mathrm{}$ fs) are in good agreement with those by Andresen et al. [Phys. Scr. 19, 335 (1979)]. Relative populations of $n$-state hydrogens in the large-$t_D (\gtrsim 2$ fs) region have been derived from the relative yields of Balmer lines as functions of $n$ and $t_D$. The molecular enhancement for relative populations of $n$-state hydrogens for ${\mathrm{H}}_2^{+}$ depends on $n$ and $t_D$, and decreases with increasing $t_D$ and increases with increasing $n$. Some discussions are presented on the mechanism of production of excited $\mathrm{H}\mathrm{}\left(n\right)\mathrm{}$ atoms from incident ${\mathrm{H}}^{+}$ and of $\mathrm{H}\mathrm{}\left(n\right)+{\mathrm{H}}^{+}$ or ${2\mathrm{H}}^{+}$ breakup fragments from incident ${\mathrm{H}}_2^{+}$ (${\mathrm{H}}_3^{+}$).

We present a method for the calculation of cross sections for electron capture from an arbitrary $n$,$l$,$m$ shell of a hydrogenic target atom into an arbitrary $n^{\prime }$,$l^{\prime }$,$m^{\prime }$ shell of a fast hydrogenic projectile in the continuum-intermediate-state approximation. We reduce the scattering amplitude to a one-dimensional integral in real space. The numerical results are presented for the reaction ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(2l\right)\mathrm{}\to \mathrm{H}\left({3l}^{\prime }\right)+{\mathrm{H}}^{+}$. Comparison is made with a recent eikonal calculation.

A method for measuring the Rayleigh scattering cross sections of $\gamma$ rays at forward angles is described. The measured integral Rayleigh scattering cross sections below 7° for 661.6-keV $\gamma$ rays in copper, zinc, tin, and lead are presented and compared with form-factor calculations. The present results show a good agreement with the nonrelativistic form-factor values of Hubbell et al. (1975) as pointed out by Kissel et al. (1980) and Roy et al. (1983). In the case of high-$Z$ elements, the relativistic form-factor values appear to be slightly too large.

The important dynamic parameters, partial photoionization cross section σ and angular distribution parameter $\beta$, have been determined for atomic Mn between 12 and 110 eV by electron spectroscopy with synchrotron radiation (ESSR). The single-electron photolines from the $3d$ and $4s$ subshells and the associated two-electron satellite lines were measured, and the resonance region of $3p\to 3d$ excitation around 50 eV was studied in detail. Absolute partial cross sections were derived. For the $3d$-subshell properties, we find good agreement with the many-body perturbation-theory calculation (MBPT) by Garvin et al. over the entire energy range and with the random-phase-approximation results by Amusia et al. over the $3p$ resonance region. Available calculation (MBPT) underestimates the enhancement of $\sigma \mathrm{}\left(4s\right)\mathrm{}$ through the $3p$ resonance. Where overlap exists, the experimental data by Bruhn et al. and by Kobrin et al. agree well with our results. The work on Mn, taken in toto, provides a good overall understanding of the photoionization dynamics of the $3d$ transition series element Mn, which has a half-filled subshell, although a number of problems, e.g., two-and three-electron transitions and the low-energy region, remain to be further studied. A need for an accurate determination (5-10%) of the total photoabsorption cross section is indicated.

The Stark splitting due to an applied electric field in molecular iodine was measured in individual hyperfine lines belonging to the $B-X$ electronic transition by using the technique of intermodulated fluorescence saturation spectroscopy. The anisotropic polarizability of the $B$ state was determined to be (16.8±10%) ${\mathrm{\AA }}^3$. The difference between the isotropic polarizability of the $B$ state and that of the $X$ state was found to be (+2.15±15%) ${\mathrm{\AA }}^3$.

We report a new, more precise determination of the ground-state hyperfine-structure interval $\Delta \nu$ in positronium, which is based on extensive new data at low ${\mathrm{N}}_2$-gas densities combined with previous data from our group at Yale University. Our experimental value $\Delta \nu =203.389\mathrm{}10\left(74\right)\mathrm{}$ GHz (3.6 ppm) agrees with the current theoretical value $\Delta \nu =203.400\mathrm{}$ GHz, for which the estimated uncertainty is about 50 ppm.

Nonradiative transitions in nonclosed-shell atoms K ($Z=19\mathrm{}$), Ag ($Z=47\mathrm{}$), and Au ($Z=79\mathrm{}$) with $\mathrm{ns} \mathrm{}(n=4,5,6\mathrm{})\mathrm{}$ outer electron are studied by comparing the calculated transition rates with the experimental ones. Auger transitions involving the next inner shell show clear fine structure due to the coupling of the outer $\mathrm{ns}$ electron with the holes producted in the Auger decay. The observed intensity distribution is found to be reproduced reasonably well with the calculations which explicitly take into account the open-shell structure.

Formulas are derived for the differential and integral cross sections associated with laser-induced excitation transfer. The theory is patterned closely after our recent treatment of laser-induced chemi-ionization. It is found that cross sections specific to single-photon absorption are proportional to the square of the cosine of the angle between the laser polarization and the initial relative velocity of the two colliding atoms. The distortion by a laser of the cross section for an elastic scattering event also is treated. Finally, a cross-section formula is derived for a collision-induced two-photon absorption, mediated by a single intermediate electronic state.

The statistical properties of radiation emitted in a scattering process between a relativistic electron beam and two interfering crossed laser fields are discussed, when the radiation system is coupled to a reservoir (electron-beam system). The conditions to obtain anticorrelation effect are presented, and the presence of super-Poissonian statistics, when the short-time approximation is adopted, is shown.

Boundary-value solutions are constructed for Helmholtz equations, which describe parametric oscillation, stimulated Raman scattering, four-wave mixing, amplified reflection, and phase conjugation in the nondepleted-pump-field approximation, in nonlinear media with high indices of refraction where matching at both right and left boundary interfaces is important, and in thin films of less than a wavelength thickness. The present method is compared with the slowly-varying-envelope approximation, and can be used to check the regime of validity of the approximation.

In this paper we analyze the steady-state and stability properties of bistable optical systems, lasers with an injected signal, and ordinary free-running lasers. The starting point of our study is a unified model of a ring cavity containing a finite-size cylindrical sample of homogeneously broadened two-level atoms, and capable of supporting a single field mode with a Gaussian transverse profile. After solving the equations of motion in the steady state, we carry out a linear stability analysis of the stationary solutions, identify the domains of unstable operation of each of the three systems, and compare in detail the results of this work with those of earlier plane-wave uniform-field calculations. In the case of the laser with an injected signal, we find a significant enhancement of the instability domain relative to the plane-wave limit. A similar conclusion holds for mixed absorptive and dispersive optical bistability, although the enhancement of the domain of instability is less pronounced. Unstable behavior is predicted to occur for experimentally accessible values of the bistability parameter, and to be favored by the absence of bistability and by the selection of atomic and cavity detunings having opposite signs. This configuration ensures that the instability will be responsible for the emergence of undamped output pulsations of the type that will make the bistable system behave as an optical clock.