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The gamma-rays which are emitted in the decays of Nb^96 to Mo^96 and Zn^71 to Ga^71 together with the gamma-rays following thermal neutron capture by Fe^54, have been investigated with the use of lithium drifted germanium semiconductor detectors. The much higher resolution of these counters allowed to reveal, with great accuracy, several details in the structure of Mo^96, Ga^71 and Fe^55 nuclei, which have never been previously detected with NaI (Tl) counters. These investigations show the high capabilities of the lithium drifted germanium detectors in nuclear research.