Nucleus Decay Anomalies and Nonlinear Quantum Dynamics

Nucleus radioactivity law is one of fundamental laws of modern physics; in accordance with it, decay parameters for any particular nuclei are constant and independent of environment. Recently, several experiments reported temporary decay rate variations for alpha and beta-decay of some heavy nuclei of the order $.05 \%$ [1,2]. Beside well-established exponential time dependence of nuclei decay rate, authors found additional periodic terms corresponding to annual and daily decay rate oscillations. Obtained data suppose that decay rate variation can be related to variation of Sun gravitation potential $U$ in the lab., due to elliptic form of Earth orbit and its daily rotation [1]. We argue that such effects can be explained by the presence of additional nonlinear terms in the interaction of quantum systems with external fields, proposed first by Kibble [3]. In our approach, modified Doebner-Goldin nonlinear quantum formalism [4] is used for description of gravitation field influence on decay rate. As the result, such nonlinear Hamiltonian induces sizable annual and daily decay rate variations for Gamow $\alpha$-decay theory. Its shown that the best fit to experimental data for nucleus $\alpha$-decay gives nonlinear Hamiltonian term proportional to $\mathbf{U}$ time derivative.