It is shown that the scattering length can be obtained by solving a Riccati
equation derived from variable phase theory. Two methods of solving it are
presented. The equation is used to predict how long-range interactions
influence the scattering length, and upper and lower bounds on the scattering
length are determined. The predictions are compared with others and it is shown
how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure
