A new form of continued fraction for the scattering matrix is derived from an equation for the amplitude density. Numerical tests are performed for the case of potential scattering, and it is found that rapidity of convergence of the presented method is even better than in the case of the original method based on the equation for the wave function.

A complex-energy, complex-interaction Nikitinlike model is proposed to describe the vacancy-sharing process when many quasimolecular states are strongly coupled. The vacancy-sharing ratio is obtained in closed analytical form. The general result is used to calculate the L-K vacancy sharing in the ${\mathrm{C}}^{+}$+Ar, ${\mathrm{N}}^{+}$+Ar, and ${\mathrm{O}}^{+}$+Ar collisions.

The free-induction decay (FID) signals emitted by a two-level spin system ($E_1^{\mathcal{’}}$ centers in glassy silica), coherently prepared by a short pulse of resonant radiation, have been experimentally investigated in the frequency domain. Our results show that, under the same conditions in which FID signals are oscillatory in the time domain, the spectra are characterized by a regular series of emission zeros. A vectorial model accounts for the occurrence of the zeros and for their spectral positions.

We investigate the low-density limit of a theory for the structure of a fluid of hard spheres which is made fully consistent on the thermodynamic side [G. Giunta, C. Caccamo, and P. V. Giaquinta, Phys. Rev. A 31, 2477 (1985)]. The space behavior of the tail function is studied analytically up to second order in the packing fraction. The fourth virial coefficient predicted by the theory is also explicitly evaluated and found to slightly underestimate the exact result.

The parametric decay instability of an extraordinary electromagnetic wave into a high-frequency magnetized electron plasma wave and a low-frequency wave (mixed-mode kinetic Alfve’n wave or magnetosonic wave) propagating at an angle with respect to the static magnetic field has been considered. For the typical set of parameters of the tokamak when the kinetic Alfve’n wave is a low-frequency wave, the convective threshold is ∼10 kW/${\mathrm{cm}}^2$. .AE

The complex intrinsic viscosity for a single polymer chain in the presence of self-avoiding interactions is calculated renormalization-group theoretically directly from the Green-Kubo formula. The universal functional form to O(ɛ) (ɛ≡4-d, d being the spatial dimensionality) is presented.

The conductivity exponent governing criticality of randomly stirred superconductor-insulator mixtures is estimated using a novel Monte Carlo simulation approach based on charge-density equilibration rather than random walks of individual charges. This approach is the most direct yet proposed for computing scaling properties in the limit of infinite charge mobility, a limit considered relevant to conductivity scaling for microemulsions. The results are compared to a previous computational estimate, scaling predictions, and microemulsion measurements.

The electrostatic contribution to the viscosity of dilute polyball solutions is calculated using the ‘‘two-fluid’’ model of colloidal liquids. A similar approach is applied to dilute and semidilute ionic solutions of rodlike polyelectrolytes, and the experimentally observed anomalous rise of the reduced viscosity with decreasing polymer concentration, the phenomenological Fuoss law, and the maximum seen at low added-salt concentration are derived.

We introduce three kinds of nontrapping self-avoiding walks which are generated by cluster-growth processes. From Monte Carlo simulation studies, in two dimensions, we get values for the size exponent ν of approximately 0.83, 0.65, and 1 for these walks, which are different from those values for existing nontrapping self-avoiding walks.

Mode-locked lasers provide a train of high-intensity light pulses that can be used to pump nonlinear media in order to produce squeezed light. The squeezed light produced would consist of a train of short-duration pulses. It is shown here that a homodyne detector using a pulsed local oscillator can be used to observe the squeezing even when the response time of the photodetector is much longer than the local oscillator or squeezed light pulse width.

Since the β decay of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ is first-forbidden unique, the ratio ρ of bound-state to continuum β decay of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ reduces to a problem in atomic physics. A knowledge of ρ is required if one is to connect the experimentally determined value of the rate of continuum decay to a value of the half-life $T_{1/2}$ for the β decay of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$. The value of $T_{1/2}$ plays a significant role in the use of the geochemically determined ratio of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ to ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ in the estimation of the age of our galaxy. Our results for ρ, based on the Hartree-Fock-Dirac single-configuration and the multiconfiguration Dirac-Fock approximations strengthen the conclusion of Williams, Fowler, and Koonin [Astrophys. J. 281, 363 (1984)] based on a modified Thomas-Fermi model, that ρ is only of the order of 1%. We also include a few values of the rate for a process first considered by Perrone [Ph.D. thesis, Rice University (1971)], the bound-state β decay of a bare ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ nucleus. (Since the mass of the ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ nucleus is less than the sum of the masses of its daughter nucleus ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ and of an electron, continuum decay of a bare ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ nucleus is forbidden; neutral ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ can β decay only because of the greater binding energy of the electrons of ${}_{}{}^{187}{}_{}{}^{}\mathrm{Os}$ than of ${}_{}{}^{187}{}_{}{}^{}$Re.)

The first Born approximation of Belkić, Gayet, and Salin [Phys. Rep. 56, 279 (1979)] with correct boundary conditions for charge exchange is thoroughly investigated. Functional analysis is used to derive general result $T_{\mathrm{nlm};n\mathcal{’}l\mathcal{’}m\mathcal{’}}^{\mathrm{}\left(1\right)\mathrm{}}$ of the transition amplitude for electron capture from hydrogenlike and multielectron atoms by bare nuclei. The basic matrix element is a two-center Dalitz integral with the logarithmic Coulomb phase factors, which has a broad spectrum of applications in both atomic and molecular physics. Multielectron target atoms are treated within an independent-particle model which goes beyond the customary procedure for scaled hydrogenlike wave functions. An accurate and efficient algorithm is encoded for both hydrogenic and Roothaan-Hartree-Fock orbitals into a single program for charge exchange between completely stripped ions and arbitrary atoms. An exemplary computation of the total cross sections is presently carried out for electron capture from all shells of Li by α particles in the energy range from 250 to 2500 keV. Good agreement is found with recent experimental data of McCullough et al. [J. Phys. B 15, 111 (1982)] and Sasao et al. [J. Phys. Soc. Jpn. 55, 102 (1986)].

A detailed investigation of multiple ionization of He (ionization charge states q=1,2), Ne (q=1–3), and Ar and Kr (q=1–4) is presented for proton impact energies ranging from 10 keV to a few MeV. Absolute cross sections for various ionization pathways have been obtained by combining some new measurements with previously published experimental results and, in certain cases, with existing theoretical information. It is shown how each of these pathways contribute to the various stages of target ionization that are observed after the collision and how these experimentally measured quantities are related to the cross sections for initial inner- and outer-shell vacancy production. Areas where additional data are required or where the existing data are not internally consistent are pointed out. In general, it is shown that the existing data are sufficient to describe the ionization of helium as well as the lower levels of ionization of neon, argon, and krypton. However, for the higher degrees of ionization, particularly for Kr, our understanding is hampered by substantial gaps in the available inner-shell ionization data—both in cross-section and branching-ratio information. Nevertheless, the data are sufficient to indicate the relative importance of the various pathways. For all targets, direct multiple outer-shell cross sections were extracted. Analyzing the energy dependences of these cross sections provided some hints as to how to calculate multiple-ionization cross sections, e.g., information as to where the multiple ionization is dominated by the first-order or by a higher-order term in the perturbation expansion of the proton-target interaction is obtained.

The total cross sections for electron and positron scatterings by lithium, sodium, and potassium in the intermediate energy range from 40 to 1000 eV are calculated using the modified Glauber and second Born approximations. A model potential approach is developed to enable an exact inclusion of the core-interaction effects. Within this approach, the positron cross sections are predicted to be somewhat smaller than those of electron scattering. Calculations have also been performed with the consideration of the inert-core and frozen-core assumption and the use of the Clementi wave function to represent the target electrons. Comparison to existing experimental data is made.

Some doubly excited autoionizing states of heliumlike nitrogen ions converging on the N=3, N=4, and N=5 hydrogenic thresholds are calculated by a method of complex-coordinate rotation. Hylleraas-type wave functions are used for L=0 and L=1 resonances, and products of Slater-orbital-type wave functions with expansion lengths up to 323 terms for L≥2. Results can be used for experimental references in the recently identified doubly excited autoionization states of ${\mathrm{N}}^{5+}$ ions in double-electron charge-transfer collision experiments between ${\mathrm{N}}^{7+}$ ions and helium atoms.

Atomic Coulomb capture ratios A(B,M) for pions have been measured in chromium, iron, and nickel borides. Those for mixtures of respective metals and boron were also obtained. The ratios for the compounds are less than half of those of the mixtures and depend on the species of the borides. These results for the borides are not predicted by any model. The mesomolecular model revised to take account of the Auger process reproduces the present results. The electron charge densities deduced by applying the model are compared with theoretical predictions.

Differential and integrated cross sections for the elastic scattering of low- and intermediate-energy (3–300 eV) positrons and electrons by argon atoms are calculated. Higher transport cross sections, representing moments of 1-(costheta${)}^n$, for these systems are also obtained for n=1–4. Model potentials are used to represent the interactions between positrons or electrons and argon atoms. For each impact energy, the phase shifts of the lower partial waves are obtained exactly by numerical integration of the radial equation. The Born approximation is used to obtain the contribution of the higher partial waves to the scattering amplitude. The phase shifts of the seven lowest partial waves are tabulated for various impact energies of positrons and electrons.

The calculation of infrared radiative corrections to scattering cross sections, to which a great deal of attention has been devoted in the past, is reconsidered here and carried to a higher order of accuracy within the context of a specific relativistic model. Earlier work, initiated by Low [Phys. Rev. 110, 974 (1958)] and developed further by others, which led to soft-photon approximations for bremsstrahlung amplitudes, is extended to apply to virtual- as well as real-photon emission and absorption processes. As in the earlier work the requirement of gauge invariance plays a central role in the analysis. Evaluation of the new correction term obtained here requires, as input, the physical (on-mass-shell) amplitude for scattering in the absence of radiative interactions. The new term is expected to lead, in most cases, to only small modifications of the results obtained by standard methods; verification of this expectation would provide a useful check on the range of validity of these standard procedures. It is pointed out that for scattering in the neighborhood of a very narrow resonance the new correction term, which properly accounts for rapid variations of the scattering amplitude with energy, could become numerically significant. In an attempt to examine this possibility in a very preliminary yet quantitative manner the radiative correction terms derived here have been evaluated with the aid of a simple Breit-Wigner representation of the radiation-free scattering amplitude, and some typical results are reported.

The collision strengths for the electron-impact excitation of inelastic transitions in Mg xi have been calculated by use of the R-matrix method. Eleven lowest LS target states 1$s^2$ ${}^1$S, 1s2s ${}^1$,3S, 1s2p ${}^1$,3P°, 1s3s ${\mathrm{}}^1$,3S, 1s3p ${\mathrm{}}^1$,3P°, and 1s3d ${\mathrm{}}^1$,3D are included in the expansion of the total wave function. These target states are represented by accurate configuration-interaction wave functions. The lower partial-wave (L≤8) results obtained in the R-matrix method are supplemented by higher partial waves obtained in the close coupling with exchange terms omitted (L=9–15), Coulomb-Born (L=16–36), and Coulomb-Bethe (L>36) approximations. Rydberg series of resonances converging to n=2 and 3 thresholds are considered in the calculations. Results are obtained over a wide electron energy range (97.66–350.0 Ry) and are compared, where possible, with the previously available five-state Coulomb-exchange distorted-wave approximation results of Bednell. These collision strengths are then integrated with the assumption of a Maxwellian distribution of electron energies to obtain effective collision strengths for temperatures between ${10}^5$ and 4×${10}^7$ K.

The probe-absorption spectrum of an atom, immersed in a finite-bandwidth laser field and a perturber gas, is calculated. Both single-mode and multimode excitation is treated, and the solutions of the occurring stochastic multiplicative processes are obtained in closed form. Different features of the profile are discussed, and it is seen that the spectrum is not determined by the laser line shape only, but that knowledge of the higher-order stochastic properties of the driving field is required.