In practically all known methods of nuclear chronometry until now, research has usually taken into account the life-times of only the fundamental states of α-radioactive nuclei. But in the processes of nuclear synthesis in stars and under the influence of constant cosmic radiation on the surfaces of planets the excitations of the α-radioactive nuclei are still ongoing. Between these processes there are states with excited α-particles inside the parent nuclei leading to much smaller life-times. And inside the large masses of stellar, terrestrial and meteoric substances there are transitions between different internal conditions of radioactive nuclei that are accompanied by infinite chains of γ-radiations with subsequent γ-absorptions, further γ-radiations, etc. For a description of the α-decay evolution that accounts for such excited states and multiple γ-radiations and γ-absorptions inside stars, and under the influence of cosmic radiation on the Earth’s surface we present a quantum-mechanical approach, which is based on the generalized Krylov-Fock theorem. A few simple estimations are also presented. These approaches lead to the conclusion that the usual (non-corrected) “nuclear clocks” do really point not to realistic values but to the upper limits of the durations of α-decay in stellar and planet processes.
 J. Audouze, S. Vauclair, An Introduction to Nuclear Astrophysics, The Formation and the Evolution of Matter in the Universe (Reidel Publish. Comp. 1980) Ch. VIII
 V. S. Olkhovsky, Atti dell’Accademia Peloritana dei Pericolanti, Vol. LXXVI (UniversitaŠ di Messina, Messina, Italy, 1998) 59
 V. S. Olkhovsky, Influence of excited radioactive nuclei for results in large-scale nuclear chronometry, In: Proceedings of the International Conference of Nuclear Physics at Border Lines, 21–24 May 2001, Messina, Italy (2001) 241
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.