RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .1. THEORETICAL DEVELOPMENT

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three-dimensional scattering integral equations satisfying constraints of relativistic unitarity and convariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three-dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and convariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The three-particle equations we derive are very practical and suitable for performing relativistic scattering calculations. (C) 1994 Academic Press, Inc.

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.

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.

Positronium-hydrogen-atom scattering in a five-state model

The scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for Ps(1s)H(2s,2p) and Ps(2s,2p)H(1s) excitations using a recently proposed electron-exchange model potential. The higher (n greater than or equal to 3) excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts. elastic, Ps and H excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range, and resonance energy obtained in various model calculations. These correlations suggest that if a Ps-H dynamical model yields the correct result for one of these four observables, it is expected to lead to the correct result for the other three. The present model, which is constructed so as to reproduce the Ps-H resonance at 4.01 eV, automatically yields a Ps-H bound state at - 1.05 eV that compares well with the accurate value of - 1.067 eV. The model leads to a singlet scattering length of 3.72a(0) and effective range of 1.67a(0), whereas the correlations suggest the precise values of 3.50a(0) and 1.65a(0) for these observables, respectively. [S1050-2947(99)07703-3].

Effect of electron exchange in positronium-hydrogen scattering

The elastic and inelastic scattering of ortho-positronium (Ps) by the hydrogen atom have been investigated using a three-Ps-state close-coupling approximation. The higher (n greater than or equal to 3) excitations and ionization of the Ps atom are treated within the framework of the Born approximation. In both cases the effect of electron exchange has been included by a parameter-free nonlocal model potential derived from an antisymmetrization of the wavefunction followed by the removal of nonorthogonality. Calculations are reported of scattering lengths,phase shifts, and of elastic, Ps excitation, and total cross sections. The trend of present target elastic total cross section agrees qualitatively with available experimental results on Ps-impact scattering.

Electron exchange model potential: Application to positronium helium scattering

The formulation of a suitable nonlocal model potential for electron exchange is presented, checked with electron-hydrogen and electron-helium scattering, and applied to the study of elastic and inelastic scattering and ionization of orthopositronium (Ps) by helium. The elastic scattering and the n=2 excitations of Ps are investigated using a three-Ps-state close-coupling approximation. The higher (n greater than or equal to 3) excitations and ionization of Ps atoms are treated in the framework of the Born approximation with present exchange. Calculations are reported of phase shifts and elastic, Ps excitation, and total cross sections. The present target elastic total cross section agrees well with experimental results at thermal to medium energies. [S1050-2947(99)04201-8].

Differential and partial cross sections of elastic and inelastic positronium-helium-atom scattering

Scattering of positronium (Ps) by a helium atom has been investigated in a three-Ps-state coupled-channel model including Ps(1s,2s,2p) states using a recently proposed time-reversal-symmetric regularized electron-exchange model potential. Specifically, we report results of differential cross sections for elastic scattering and target-elastic Ps excitations. We also present results for total and different partial cross sections and compare them with experiment and other calculations.

Neutron-C-19 scattering near an Efimov state

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A comparative study of the low energy HD plus o-/p-H-2 rotational excitation/de-excitation collisions and elastic scattering

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

COMPLEX KOHN VARIATIONAL PRINCIPLE FOR 2-NUCLEON BOUND-STATE AND SCATTERING WITH THE TENSOR POTENTIAL

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled S-3(1), D-3(1), channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves S-1(0), P-1(1), D-1(2), and S-3(1)-D-3(1) of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the S-3(1)-D-3(1) channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters. (c) 1995 Academic Press, Inc.

NEAR-RESONANT SCATTERING FROM NONSYMMETRIC DIMERS - APPLICATIONS TO SUBSTITUTED POLYANILINES

In this work we show that, beyond the prediction of the random dimer model [Wu and Phillips, Phys. Rev. Lett. 66, 1366 (1991)], it is possible to have near resonant scattering from nonsymmetric dimers. It is shown by direct density of states calculations as well as by a procedure similar to the random dimer model that protonated chains of alkyl-substituted polyanilines support extended electronic states at the Fermi energy when a disordered distribution of symmetric or asymmetric bipolarons is present. An extension of the random dimer model to include resonant scattering by nonsymmetric dimers is proposed.

Positronium scattering from ions, atoms and molecules

Elastic and inelastic scattering of positronium (Ps) by H, He, He(+) and H(2) have been studied using coupled-channel calculations with a regularised nonlocal model exchange potential. Suitability and reliability of the theoretical scheme have been demonstrated by studying scattering cross-sections in various systems and also by addressing critical dynamic features like binding and resonances of Ps to open-shell-atoms. Results are found to be in good agreement with Variational predictions and experimental observations. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Differential cross sections for target excitation and positronium formation in positron-helium scattering

Positronium formation and target excitation in positron-helium scattering have been investigated using the close-coupling approximation with realistic wave functions for the positronium and helium atoms. The following eight states have been used in the close-coupling scheme: He(1s1s), He(1s2(1)s), He(1s2(1)p), He(1s3(1)s), He(1s3(1)p), Ps(1s), Ps(2s), and Ps(2p), where Ps stands for the positronium atom. Calculations are reported of differential cross sections for elastic scatering,, inelastic target excitation to He(1s2(1)s) and He(1s2(1)p) slates, and rearrangement transition to Ps(1s), Ps(2s), and Ps(2p) states for incident positron energies between 40 and 200 eV. The coincidence parameters for the transition to the He(1s2(1)p) state of helium are also reported and briefly discussed. [S1050-2947(98)05101-4].

S-, P-, and D-wave resonances in positronium-lithium-atom scattering

We investigate ortho-positronium-lithium-atom (Ps-Li) scattering using static-exchange and three-Ps-state coupled-channel calculations. The present three-PS-state scheme, while closely agreeing with the resonance and binding energies in the Ps-H system, predicts S-, P-, and D-wave resonances at 4.25 eV, 4.9 eV, and, 5.25 eV. respectively, in the electronic spin-singlet channel of Ps-Li scattering. The present calculation also yields a Ps-Li binding in this attractive singlet channel with an approximate binding energy of 0.218 eV, which is in adherence with the recent findings of a chemically stable PsLi system using stocastic variational and quantum Monte Carlo calculations. We further report elastic, Ps(2s)-, and Ps(2p)-excitation cross sections at low to medium energies (0.068-30 eV).