It is shown that in the zero-energy scattering of a particle by a center of force, where no bound state exists, the Kohn variational principle provides an upper bound on the scattering length. A bound may also be obtained from Hulthén's method, although with the same form of trial function the Kohn result will be lower (and therefore better) than the one obtained from the Hulthén principle. The Rubinow formulation need not provide a bound; for those calculations which have been performed in this form, the results may be converted without any further calculations so that they correspond to the Kohn form, and therefore, under the circumstances considered, do give a bound. Analogous results hold for states of nonzero orbital angular momentum. Direct generalizations of the above results are valid for scattering by a compound system.

• Received 22 June 1959

DOI:https://doi.org/10.1103/PhysRev.116.1034