  Experimental measurements in terrestrial laboratory, space and astrophysical
observations of variation and fluctuation of nuclear decay constants,
measurements of large enhancements in fusion reaction rate of deuterons
implanted in metals and electron capture by nuclei in solar core indicate that
these processes depend on the environment where take place and possibly also on
the fluctuation of some extensive parameters and eventually on stellar energy
production. Electron screening is the first important environment effect. We
need to develop a treatment beyond the Debye-Huckel screening approach,
commonly adopted within global thermodynamic equilibrium. Advances in the
description of these processes can be obtained by means of q-thermostatistics
and/or superstatistics for metastable states. This implies to handle without
ambiguities the case q<1.
