Motivated on the very recent experiments to determine the acceleration of the alpha decay of meta-stable radionuclides in metallic environment some work has been done to strengthten the importance in the process of electrons screening in metals. Thus, by combining the Gamow decay theory with electrostatic screening in Debye--Hückel approximation (jellium model) a formula for ``the shift'' in screening energy which enters in the decay enhancement factor expression that copes well with these experiments has been derived. It was established that to simulate the poly-atoms system containing decaying isotopes in QM\&MD codes calculations, and to include ``the screening energy shift'' of protons, decay alpha, beta⁺ particles due to all surrounding interacting effects, it is sufficiently only to substitute the code ruly pseudo-potential input for hydrogen-like atoms (including alpha) by a screened Coulomb potential as from the well-known Gamow alpha decay theory. For demonstration is used the QM\&MD code package which usually performs density-functional theory (DFT) total-energy calculations for materials ranging from insulators to transition metals. This package employs first-principles pseudo-potentials and a plane-wave basis-set, and it was used to do a special calculus for some metal environments (Pd) where protons--deuterons are implanted or when it is alloyed with a radionuclide-like isotopes (¹⁷⁴Hf₇₂), the results compare well with the existing experiments on the decay enhancement. These works give further arguments for a cheap solution to remove the transuranic waste (involving all alpha-decay) of used-up rods of fission reactors in a time period of a few years.

PACS numbers: 52.25.--b, 31.15.--p, 32.70.--n