Integral equations of scattering in one dimension

A self-contained discussion of integral equations of scattering is presented in the case of centrally symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem, and unitarity relation. We illustrate the present approach with a Dirac delta potential. (C) 2001 American Association of Physics Teachers.

Positronium scattering by a hydrogen molecule including exchange

We perform a three-positronium (Ps) state [Ps(ls,2s,2p)] coupled-channel calculation of Ps-H-2 scattering including the effect of electron exchange. At medium energies, higher excitations and ionization of Ps are treated within the framework of the first Born approximation. In both cases exchange is included using a recently proposed nonlocal model exchange potential which is free of non-orthogonality problems common in the usual antisymmetrization scheme. The present total cross sections at low and medium energies are in encouraging agreement with experiment.

Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is investigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevskii equation.

Effect of electron correlation on positronium formation in positron-helium scattering

A three-parameter correlated wave function for the helium ground state is used to study the scattering reaction e(+) + He --> He+ + Ps, where Ps stands for positronium atom. An exact analytical expression is constructed for the first Born scattering amplitude for Ps formation from helium. Based on this numerical results are presented for both differential and total cross-sections. It is demonstrated that the inner electronic correlation of the target atom plays a crucial role in explaining the discrepency between theory and experiment.

Resonances in positronium-rubidium and positronium-cesium scattering

Scattering of ortho positronium (Ps) by cesium and rubidium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(1s,2s,2p) states using a time-reversal-symmetric regularized electron-exchange model potential. We find a narrow S-wave singlet resonance at 5.057 eV of width 0.003 eV in the Ps-Rb system and at 5.067 eV of width 0.003 eV in the Ps-Cs system. Singlet P-wave resonances in both systems are found at 5.3 eV of width 0.4 eV. Singlet D-wave structures are found at 5.4 eV in both systems. The pronounced P- and D-wave resonances in these systems lead to easily detectable local minima in the low-energy elastic cross sections. We also report results for elastic and Ps-excitation cross sections for Pa scattering by Rb and Cs. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Positronium-positronium interaction: resonance, scattering length, and Bose-Einstein condensation

The low-energy scattering of ortho positronium (Ps) by ortho Ps has been studied in a full quantum mechanical coupled-channel approach. In the singlet channel (total spin s(T) = 0) we find S- and P-wave resonances at 3.35 eV (width 0.02 eV) and 5.05 eV (width 0.04 eV), respectively, and a binding of 0.43 eV of Ps(2). The scattering length for s(T) = 0 is 3.95 Angstrom and for s(T) = 2 is 0.83 Angstrom. The small s(T) = 2 scattering length makes the spin-polarized ortho Ps atoms an almost noninteracting ideal gas which may undergo Bose-Einstein condensation. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Positronium scattering by atoms and molecules at low energies

The recent theoretical and experimental activities in positronium (Ps) scattering by atoms and molecules are reviewed with special emphasis at low energies. We critically compare the results of different groups - theoretical and experimental. The theoretical approaches considered include the R-matrix and close-coupling methods applied to Ps-H, Ps-He and Ps-Li scattering, and a coupled-channel approach with a nonlocal model potential for Ps scattering by H, He, H-2, Ne, Ar, Li, Na, K, Rb, Cs and Ps and for pickoff quenching in Ps-He scattering. Results for scattering lengths, partial. total and differential cross-sections as well as resonance and binding energies in different systems are discussed. (C) 2002 Elsevier B.V. B.V. All rights reserved.

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].

Positronium atom scattering by H-2 in a coupled-channel framework

The scattering of ortho-positronium (Ps) by H-2 has been investigated using a three-Ps-state (Ps(1s,2s, 2p)H-2(X (1)Sigma(g)(+))) coupled-channel model and using the Born approximation for higher excitations and ionization of Ps and B (1)Sigma(u)(+) and b (3)Sigma(u)(+) excitations of H-2. We employ a recently proposed time-reversal-symmetric non-local electron-exchange model potential. We present a calculational scheme for solving the body-frame fixed-nuclei coupled-channel scattering equations for Ps-H-2, which simplifies the numerical solution technique considerably. Ps ionization is found to have the leading contribution to target-elastic and all target-inelastic processes. The total cross sections at low and medium energies are in good agreement with experiment.

Chargino and neutralino production in the 3-3-1 supersymmetric model in e(-)e(-) scattering

The goal of this article is to derive the Feynman rules involving single charginos, neutralinos, double charged gauge bosons, and sleptons in a 3-3-1 supersymmetric model. Using these Feynman rules we calculate the production of double charged charginos with neutralinos and also the production of a pair of single charged charginos, both in an electron-electron linear collider.

The effect of core electrons in e(+)-Na scattering

The scattering of positrons off sodium targets has been investigated using the coupled static model. The sodium atom is represented by the one-active-electron model in which all the electrons of the target have been considered explicitly and the loosely bound valence electron is only involved in transitions. The scattering parameters are presented at low and medium energies. Appreciable differences are noticed between the present results and those obtained by the one-electron model with and without the core potential.

Bose-Einstein condensates in 2D with time-periodic scattering length

We discuss two-dimensional Bose-Einstein Condensates (BEC) under time-periodic variation of the scattering length. In particular we argue that for high-frequency variation there exist stable self-confined condensates without an external trap, when the do component of the scattering length is negative. Our results are based on a variational approximation, on direct averaging of the Gross-Pitaevskii equation and on numerical simulations.

Scattering of photons by an external gravitational field in the framework of higher-derivative gravity

The scattering of photons by a static gravitational field, treated as an external field, is discussed in the context of gravity with higher derivatives. It is shown that the R-2 sector of the theory does not contribute to the photon scattering, whereas the R-mu nu(2) sector produces dispersive (energy-dependent) photon propagation.

Macroscopic quantum tunneling and resonances in coupled Bose-Einstein condensates with oscillating atomic scattering length

We study the macroscopic quantum tunneling, self-trapping phenomena in two weakly coupled Bose-Einstein condensates with periodically time-varying atomic scattering length.The resonances in the oscillations of the atomic populations are investigated. We consider oscillations in the cases of macroscopic quantum tunneling and the self-trapping regimes. The existence of chaotic oscillations in the relative atomic population due to overlaps between nonlinear resonances is showed. We derive the whisker-type map for the problem and obtain the estimate for the critical amplitude of modulations leading to chaos. The diffusion coefficient for motion in the stochastic layer near separatrix is calculated. The analysis of the oscillations in the rapidly varying case shows the possibility of stabilization of the unstable pi-mode regime. (C) 2000 Published by Elsevier B.V. B.V. PACS: 03.75.Fi; 05.30.Jp.

Convergent variational calculation of positronium-hydrogen-atom scattering lengths

We present a convergent variational basis-set calculational scheme for elastic scattering of the positronium atom by the hydrogen atom in S wave. Highly correlated trial functions with appropriate symmetry are needed to achieve convergence. We report convergent results for scattering lengths in atomic units for both singlet (= 3.49 +/-0.20) and triplet (= 2.46 +/-0.10) states.