Testing the Symmetrization Postulate on Molecules with Three Identical Nuclei

We propose an experiment to look for possible small violations of the symmetrization postulate of Quantum Mechanics, in systems composed by three identical particles. Such violations could be detected by investigating the population of particular roto-vibrational states of symmetrical molecules containing three identical nuclei. We discuss the symmetry properties of such states, and the implications of the symmetrization postulate and of the spin-statistics. A high sensitivity spectroscopic investigation on simple molecules such as SO3, BH3 and NH3 could lead to the first test of the symmetrization postulate for spin-0 and spin-1/2 nuclei.