Spectroscopic tests of the symmetrization postulate and of the statistics for nuclei in molecules

We discuss the implications of the spin-statistics connection and of the symmetrization postulate on the quantum states of three identical nuclei arranged in rigid symmetrical molecules. We show that in the case of three identical nuclei a whole class of rotational states are forbidden also by the symmetrization postulate, and not only by the spin-statistics connection. We then present the experiments we are performing on NH3 to search for the possible existence of these states forbidden by the symmetrization postulate, and on CO2 to improve the sensitivity for detection of exchange-antisymmetric states of spin-0 nuclei. Preliminary results of the latter experiment indicate that violations of the statistics for oxygen nuclei, if present, are smaller than 10^-11 with an improvement of more than two orders of magnitude with respect to previous experiments.