Testing unitarity of the 3 × 3 neutrino mixing matrix in an atomic system

Unitarity of the 3 × 3 lepton flavor mixing matrix V is unavoidably violated in a seesaw mechanism if its new heavy degrees of freedom are slightly mixed with the active neutrino flavors. We propose to use the atomic transition process |e)→|g) + γ + νi + ν j (for i, j = 1, 2, 3), where |e) and |g) stand, respectively for the excited and ground levels of an atomic system, to probe or constrain the unitarity-violating effects of V. We find that the photon spectrum of this transition will be distorted by the effects of V V†1 and V†V1 as compared with the V V† = V†V = 1 case. We locate certain frequencies in the photon spectrum to minimize the degeneracy of effects of the unitarity violation and uncertainties of the flavor mixing parameters themselves. The requirements of a nominal experimental setup to test the unitarity of V are briefly discussed.