The time-dependent close-coupling method for atomic and molecular collision processes

We review the development of the time-dependent close-coupling method to study atomic and molecular few body dynamics. Applications include electron and photon collisions with atoms, molecules, and their ions.

Quantum-mechanical calculations of vibrationally resolved cross sections for non-dissociative charge transfer of O3+ with H-2

Charge transfer due to collisions of ground state O3+ (2s(2)2p P-2) ions with molecular hydrogen is investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method, and electronic and vibrational state-selective cross sections along with the corresponding differential cross sections are calculated for projectile energies of 100, 500, 1000 and 5000 eV/u at the orientation angles of 25 degrees,45 degrees and 89 degrees. The adiabatic potentials and radial coupling matrix elements utilized in the QMOCC calculations were obtained with the spin-coupled valence-bond approach. The infinite order sudden approximation (IOSA) and the vibrational sudden approximation (VSA) are utilized to deal with the rotation of H-2 and the coupling between the electron and the vibration of H-2. It is found that the distribution of vibrationally resolved cross sections with the vibrational quantum number upsilon' of H-2(+) (upsilon') varies with the increment of the projectile energy; and the electronic and vibrational stateselective differential cross sections show similar behaviors: there is a highest platform within a very small scattering angle, beyond which the differential cross sections decrease as the scattering angle increases and lots of oscillating structures appear, where the scattering angle of the first structure decreases as E-P(-1/2) with the increment of the projectile energy E-P; and the structure and amplitude of the differential cross sections are sensitive to the orientation of molecule H-2, which provides a possibility to identify the orientations of molecule H-2 by the vibrational state-selective differential scattering processes.

Ab initio calculations of differential cross sections for single charge transfer in He-3(2+)+He-4 collisions

The single charge transfer process in He-3(2+)+He-4 collisions is investigated using the quantum-mechanical molecular-orbital close-coupling method, in which the adiabatic potentials and radial couplings are calculated by using the ab initio multireference single- and double-excitation configuration interaction methods. The differential cross sections for the single charge transfer are presented at the laboratorial energies E = 6 keV and 10 keV for the projectile He-3(2+). Comparison with the existing data shows that the present results are better in agreement with the experimental measurements than other calculations in the dominant small angle scattering, which is attributed to the accurate calculations of the adiabatic potentials and the radial couplings.

Low-energy direct muon transfer from H to Ne10+, S16+ and Ar18+ using the two-state close-coupling approximation to the Faddeev-Hahn-type equation

We perform a three-body calculation of direct muon-transfer rates from thermalized muonic hydrogen isotopes to bare nuclei Ne10+, S16+ and Ar18+ employing integro-differential Faddeev-Hahn-type equations in configuration space with a two-state close-coupling approximation scheme. All Coulomb potentials including the strong final-state Coulomb repulsion are treated exactly. A long-range polarization potential is included in the elastic channel to take into account the high polarizability of the muonic hydrogen. The transfer rates so-calculated are in good agreement with recent experiments. We find that the muon is captured predominantly in the n = 6, 9 and 10 states of muonic Ne10+, S16+ and Ar18+, respectively.

Low-density three-dimensional foam using self-reinforced hybrid two-dimensional atomic layers

Low-density nanostructured foams are often limited in applications due to their low mechanical and thermal stabilities. Here we report an approach of building the structural units of three-dimensional (3D) foams using hybrid two-dimensional (2D) atomic layers made of stacked graphene oxide layers reinforced with conformal hexagonal boron nitride (h-BN) platelets. The ultra-low density (1/400 times density of graphite) 3D porous structures are scalably synthesized using solution processing method. A layered 3D foam structure forms due to presence of h-BN and significant improvements in the mechanical properties are observed for the hybrid foam structures, over a range of temperatures, compared with pristine graphene oxide or reduced graphene oxide foams. It is found that domains of h-BN layers on the graphene oxide framework help to reinforce the 2D structural units, providing the observed improvement in mechanical integrity of the 3D foam structure.

Two-Dimensional Noise-Predictive Maximum Likelihood Method for Magnetic Recording Channels

Noise-predictive maximum likelihood (NPML) is a well known signal detection technique used in partial response maximum likelihood (PRML) scheme in 1D magnetic recording channels. The noise samples colored by the partial response (PR) equalizer are predicted/ whitened during the signal detection using a Viterbi detector. In this paper, we propose an extension of the NPML technique for signal detection in 2D ISI channels. The impact of noise prediction during signal detection is studied in PRML scheme for a particular choice of 2D ISI channel and PR targets.

A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

Electron-impact ionization of atomic hydrogen close to threshold

A systematic study of the ionization of atomic hydrogen by electron impact from 0.3 eV to a few eV above the ionization threshold has been carried out using a semiclassical-quantal calculation. Differential and integrated cross sections are presented at 0.3 eV above the energy threshold. Triple- differential cross sections (TDCS) are presented at constant theta(12) geometry where theta(12)=180degrees and 150degrees. Good agreement is achieved with the measurement [Roder, Phys. Rev. Lett. 79, 1666 (1997)] and calculations based on exterior complex scaling at 2 eV and 4 eV above threshold. Results of triple-differential cross sections are also presented at 0.3, 0.5, and 1.0 eV above threshold at both theta(12)=180degrees and 150degrees. At theta(12)=180degrees the small local maximum in the TDCS around theta(1)=90degrees reported by Pan and Starace [Phys. Rev. A 45, 4588 (1992)] at 0.5 eV above threshold is not observed in our calculation at energies down to 0.3 eV above threshold. The shape of our double differential cross sections seems to disagree qualitatively with the available calculations as we found two local maxima around 15degrees and 165degrees in our calculation. Single differential cross sections in our formulation appear naturally as a function of total excess energy E and, therefore, constant for all combinations of individual electron energies E-1 and E- 2 with E=E-1+E-2. Total ionization cross sections are also compared with measurement and available theoretical calculations and found to be in reasonably good agreement up to 10 eV above ionization threshold.

Low-energy three-body charge transfer reactions with Coulomb interaction in the final state

Three-body charge transfer reactions with Coulomb interaction in the final state are considered within the framework of coordinate-space integro-differential Faddeev-Hahn-type equations within two- and six-state close-coupling approximations. The method is employed to study direct muon transfer in low-energy collisions of the muonic hydrogen H-mu by helium (He2+) and lithium (Li3+) nuclei. The experimentally observed isotopic dependence is reproduced.

Close-coupling calculations of positronium formation in positron-helium scattering

Positronium (Ps) formation in positron-helium scattering has been investigated in different partial waves at medium energies including the Ore gap region using the close-coupling approximation with realistic wavefunctions for the following states: He(1s1s), He(1s2s), He(1s2p), He(1s3s), He(1s3p), Ps(ls), Ps(2s), Ps(2p). Calculations are reported of rearrangement cross sections to Ps(ls), Ps(2s) and Ps(2p) states for incident positron energies up to 200 eV. The present partial cross sections are in good agreement with experimental results and a variational calculation in the Ore gap region.

Ps-He scattering using the three-state positronium close-coupling approximation

A three-state target elastic positronium close-coupling approximation (CCA) is employed to investigate Ps-He scattering in the energy range 0-200 eV with and without electron exchange. Low-lying phase shifts below the first excitation threshold and the total integrated cross sections using both the models are reported. Estimation of integrated excitation cross sections for Ps(1s --> 2s) and Ps(1s --> 2p) using CCA are presented for the first time. The present total cross sections are in good agreement with the measured data in the incident Ps energy range 20-30 eV.

Close-coupling calculations of elastic and inelastic positron-helium scattering

Elastic and inelastic positron-helium scattering have been investigated in different partial waves at medium energies using the close-coupling approximation with realistic wavefunctions employing the following states: He(1s1s), He(1s2s), He(1s2p), He(1s3s), He(1s3p), Ps(1s), Ps(2s) and Ps(2p). All excitations of the helium atom are in the spin-singlet electronic state. Calculations are reported of cross sections to He(1s1s), He(1s2s), and He(1s2p) transitions for incident positron energies up to 200 eV. These cross sections are in good agreement with experimental results.