Experimental test of the Pauli Exclusion Principle

A short review is given of three experimental works on tests of the Pauli Exclusion Principle (PEP) in which the author has been involved during the last 10 years. In the first work a search for anomalous carbon atoms was done and a limit on the existence of such atoms was determined, $^{12}\tilde{\mathrm C}$ / $^{12}$C $< 2.5\times10^{-12}$. In the second work PEP was tested with the NEMO-2 detector and the limits on the violation of PEP for p-shell nucleons in $^{12}$C were obtained. Specifically, transitions to the fully occupied $1s_{1/2}$-shell yielded a limit of $4.2\times10^{24}$ y for the process with the emission of a $\gamma$-quantum. Similarly limits of $3.1\times10^{24}$ y for $\beta^-$ and $2.6\times10^{24}$ y for $\beta^+$ Pauli-forbidded transition of $^{12}$C $\to$ $^{12}\tilde{\mathrm N}$($^{12}\tilde{\mathrm B}$) are reported. In the third work it was assumed that PEP is violated for neutrinos, and thus, neutrinos obey at least partly the Bose-Einstein statistics. Consequences of the violation of the exclusion principle for double beta decays were considered. This violation strongly changes the rates of the decays and modifies the energy and angular distributions of the emitted electrons. It was shown that pure bosonic neutrinos are excluded by the present experimental data. In the case of partly bosonic neutrinos the analysis of the existing data allows one to put an upper bound for $sin^2\chi < 0.6$. The sensitivity of future measurements is also evaluated.