International Conference on Computational Science , ICCS 2012 Coulomb Few-Body Systems in the Framework of a Set of Coupled Integral

Abstract Three-charge-particle quantum systems with arbitrary masses are treated by a general formalism based on coordinate space integral-differential Faddeev-Hahn-type equations. To solve these equations we expand the wave function components in terms of bound states in initial and final channels and project these equations on these bound states as in the close coupling method used in the Schrodinger equation. After a proper angular momentum projection, a set of coupled integral-differential equations for the unknown expansion coeffcients results, which is solved numerically by discretization for the calculation of both bound state and rearrangement scattering. In this work, the formalism is employed to study atomic 3-body systems like negative ion of positronium Ps − =(e + e - e - ). Details of the applied numerical schemes are presented.

[1]  Yuko Fujiwara,et al.  Innovative Computational Methods in Nuclear Many-Body Problems. , 1998 .

[2]  R. E. Moss.  LETTER TO THE EDITOR: Energies of low-lying vibration-rotation levels of H2+ and its isotopomers , 1999 .

[3]  J. Ye,et al.  Dipolar collisions of polar molecules in the quantum regime , 2010, Nature.

[4]  J. Cohen.  Capture of negative exotic particles by atoms, ions and molecules , 2004 .

[5]  J. Ye,et al.  A High Phase-Space-Density Gas of Polar Molecules , 2008, Science.

[6]  R. Sultanov,et al.  A comparative study of the low energy HD+o-/p-H2 rotational excitation/de-excitation collisions and elastic scattering , 2011, 1111.2599.

[7]  C. Ticknor,et al.  Quasi-universal dipolar scattering in cold and ultracold gases , 2009, 0901.1281.

[8]  D. Manolopoulos,et al.  ABC: a quantum reactive scattering program , 2000 .

[9]  A. Avdeenkov.  Collisions of bosonic ultracold polar molecules in microwave traps , 2009, 0903.3202.

[10]  S. Merkuriev.  On the three-body Coulomb scattering problem , 1980 .

[11]  E. Braaten.  Universal Relations for Fermions with Large Scattering Length , 2010, 1008.2922.

[12]  Sadhan K. Adhikari,et al.  Coordinate-space Faddeev-Hahn-type approach to three-body charge-transfer reactions involving exotic particles , 2000 .

[13]  Eduardo Garrido,et al.  The three-body problem with short-range interactions , 2001 .

[14]  A. Frolov.  TWO-STAGE STRATEGY FOR HIGH-PRECISION VARIATIONAL CALCULATIONS , 1998 .

[15]  T. Shirai,et al.  Hyperspherical coupled-channel calculation for antihydrogen formation in antiproton-positronium collisions , 1994 .

[16]  M. S. Kaschiev,et al.  A New Method for Solving an Eigenvalue Problem for a System of Three Coulomb Particles within the Hyperspherical Adiabatic Representation , 2000 .

[17]  S. T. Rittenhouse,et al.  Three body recombination of ultracold dipoles to weakly bound dimers. , 2010, Physical review letters.

[18]  K. Nagamine.  Muonic Anti‐Hydrogen—Formation and Test of CPT Theorem , 2005 .