From the condition for invariance of the energy under rotations of the Jacobi coordinates, a relationship is obtained that relates the expected values of combinations of degrees of interparticle separations in quantum-mechanical 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 permutational symmetry. The application of this criterion is illustrated for the example of the asymmetric ~4Heμ~-e~- mesoatom.
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