Configuration Interaction

The CI method is one of the standard approaches for computing atomic structures [36], so only a brief description needs to be given here. The atomic wave function is taken to be a linear combination of states created by coupling atomic states with single particle positron states using the usual Clebsch-Gordan coupling coefficients;

In this expression $i(Atom\ LiSi) is an antisymmetric atomic wave function with good L and S quantum numbers. The function <f>j{ro) is a single positron orbital. The positron orbitals and the electron orbitals that make up the wave function are written as a product of a radial function and a spherical harmonic, viz.

The main problem in applying the CI method to a positron binding system is a consequence of the attractive electron-positron interaction. The electron-positron correlations are so strong that for some systems (e.g. e+Na) it is best to regard the electron and positron as coalescing into something approximating a positronium cluster. The accurate representation of a Ps cluster with single particle orbitals centered on the nucleus requires the inclusion of orbitals with quite high angular momenta.

The first CI calculation able to confirm positron binding to a neutral atom was carried out upon positronic copper [37], In the fixed core model, e+Cuonly had two active particles, the positron and the valence electron. This calculation had 120 electron and 120 positron orbitals and a maximum orbital angular momentum of Lmax — 10- Despite the large basis, the calculation was only able to achieve about 60% of the expected binding energy.

Two criteria should be satisfied for the CI method to provide accurate quantitative information. First, it must be possible to vary the number of orbitals for a fixed L systematically. This will establish convergence in the radial basis for a particular L. It is also necessary to do calculations for a maximum value of L close to 10. Although an extrapolation procedure is needed to establish the Lmax -»• oo limit, choosing Lmax sufficiently large means the errors introduced by the extrapolation can be minimized.

So far two approaches satisfying these criteria have been developed. One approach is to generate a B-spline basis in a finite range cavity, use this to solve the Schrodinger equation, and then analytically extrapolate

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