Strong-coupling constant in coordinate space

The coordinate-space behavior of (vector) strong-coupling constant in the background field alpha (B)(r) is compared with that in standard perturbation theory alpha (V)(r). The numerically calculated two-loop coupling constant alpha (B)(r) is shown to exceed alpha (V)(r) by 1-5% at very small distances, r less than or similar to 0.02 fm, and to be in agreement with lattice measurements of the static potential. At large distances, alpha (B)(r) approaches the freezing value at r greater than or similar to 0.5 fm. An analytic form of alpha (B)(r) is proposed that approximates alpha (B)(r) with a precision less than or similar to2% in the region r greater than or similar to 0.5 fm. (C) 2000 MAIK "Nauka/Interperiodica".