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We determine the binding energy of the negative positronium ion in the limitsof one spatial dimension and of infinitely many dimensions. The numericalresult for the one-dimensional ground state energy seems to be a rationalnumber, suggesting the existence of an analytical solution for the wavefunction. We construct a perturbation expansion around theinfinitely-dimensional limit to compute an accurate estimate for the physicalthree-dimensional case. That result for the energy agrees to five significantfigures with variational studies.

Binding energy of the positronium negative ion via dimensional scaling