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A: Fachverband Atomphysik

A 20: Precision Spectroscopy of Atoms and Ions III

A 20.4: Talk

Wednesday, March 4, 2009, 17:45–18:00, VMP 6 HS-B

An efficient accurate representation of the three-body Coulomb problem: new perspectives for highly doubly excited states of helium — •Johannes Eiglsperger¹, Javier Madroñero^1,2, and Bernard Piraux² — ¹Physik Department, TU München, Germany — ²Unité de physique atomique, moléculaire et d’optique, UC Louvain, Belgium

A comprehensive understanding of the general structure of the energy spectrum and eigenstates of two-electron atoms at and near the double ionization threshold requires sophisticated theoretical approaches.

We present a spectral method of configuration interaction type for 3D helium [1] which combines the complex rotation method with an appropriate expansion of the atom wave function in a basis of products of Coulomb-Sturmian functions of the electron radial coordinates with independent dilation parameters for the two electrons and bipolar harmonics of the angular coordinates. The freedom on the choice of the dilation parameters permits us to access highly excited states with rather small sizes of the basis. The associated eigenvalue problem is represented by full matrices. The computation of the matrix elements of 1/r₁₂ is by far the most time-consuming part in our calculations. A combination of Gauss-Laguerre integration techniques with the generalized Wigner-Eckart theorem and recurrence relations [2] allows an efficient and stable calculation of these matrix elements [3].

[1] E. Foumouo et al., Phys. Rev. A 74, 063409 (2006).

[2] J. Zamastil et al., Phys. Rev. A 75, 022506 (2007).

[3] J. Eiglsperger et al., in preparation.