Lower bound to the reciprocal of the scattering length: II

It is shown that, for the scattering of zero-energy particles by a compound system, Kohn's variational method used in conjunction with `inappropriately normalized' trial functions provides an absolute lower bound to the reciprocal of the scattering length in the following cases: (i) there exists no composite bound state and the Born approximation to the scattering length a B < 0; (ii) there exists one composite bound state, a B < 0 and the exact scattering length a >or= 0; (iii) there exists no composite bound state and a >or= 0. The theorems are illustrated by the calculations of the scattering lengths for collisions of electrons and positrons with hydrogen atoms and helium atoms. An error in the previous paper by Moiseiwitsch is corrected.