An experiment to search for 2β processes in 116Cd with the help of enriched (to 82%) cadmium tungstate crystal scintillators is in progress at the Gran Sasso National Laboratory of the INFN (LNGS, Italy). After 11074 h of data taking in the last configuration, the preliminary estimate for the half-life of 116Cd relatively to 2ν2β decay is T1/2 = [2.52 ± 0.02(stat.) ± 0.14(syst.)] × 1019 yr. By using the data of previous stages of the experiment with a similar level of background (≈ 0.1 counts/(keV kg yr) in the energy interval 2.7 – 2.9 MeV; the total time of measurements is 19770 h) we have obtained a new limit on the 0ν2β decay of 116Cd to the ground state of 116Sn: T1/2 ≥ 1.9 × 1023 yr at 90% C.L. New limits on different 2β processes in 116Cd (decays with majorons, transitions to the excited levels) are obtained on the level of T1/2 ≥ 1020 – 1022 yr.

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