Criterion for the accuracy of wave functions of asymmetric atomic and molecular systems

From the condition for invariance of the energy under rotations of the Jaco bi coordinates, a relationship is obtained that relates the expected values of combinations of degrees of interparticle separations in quantum-mechani cal systems. This relationship, which is satisfied for atoms and molecules with like particles identically, because of the permutational symmetry, is an extremely sensitive criterion for the accuracy of the wave functions of asymmetric systems, consisting of unlike particles and having no permutatio nal symmetry. The application of this criterion is illustrated for the exam ple of the asymmetric He-4 mu(-)e(-) mesoatom. (C) 2000 MAIK "Nauka/Interpe riodica".