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Binding energy of the positronium negative ion via dimensional scaling

We determine the binding energy of the negative positronium ion in the limits of one spatial dimension and of infinitely many dimensions. The numerical result for the one-dimensional ground state energy seems to be a rational number, suggesting the existence of an analytical solution for the wave function. We construct a perturbation expansion around the infinitely-dimensional limit to compute an accurate estimate for the physical three-dimensional case. That result for the energy agrees to five significant figures with variational studies.