N. Billy, D. Delande, L. Hilico, B. Grémaud

Presentation

• The bidimensional three-body problem has several interests. For example it is present in the physics of trions, entities made of two electrons and one hole (eeh) or two holes and one electron (ehh) which appear in quantum well structures. It is also useful for the spectroscopy of helium, where some double ionization processes mainly occur in a fixed plane.
  
• In two dimensions, it is no longer possible to use the perimetric coordinates to represent the positions of the three particles. Indeed, for a given value of the perimetric coordinates, there are several possible configurations of the three bodies.
• Therefore we have introduced a new system of coordinates, based upon the parabolic coordinates. The hamiltonian of the three-body problem  in two dimensions can then be represented by four harmonic oscillators coupled by various terms of degree up to  12.

• This approach allows to represent states of arbitrary angular momentum of the three-body problem in 2D. Numerically, it allows to work with sparse band matrices which allow to converge the eigenenergies with a very good accuracy of 10^-14 atomic unit and to obtain excellent wave functions.

Results

• Rydberg series of 2D helium.
• Wave functions of the resonances (energies and widths).
  

References (publications)

Collaborations

 Andreas Buchleitner, Javier Madronero, université de Dresde.