  The properties of nuclei embedded in an electron gas are studied within the
relativistic mean-field approach. These studies are relevant for nuclear
properties in astrophysical environments such as neutron-star crusts and
supernova explosions. The electron gas is treated as a constant background in
the Wigner-Seitz cell approximation. We investigate the stability of nuclei
with respect to alpha and beta decay. Furthermore, the influence of the
electronic background on spontaneous fission of heavy and superheavy nuclei is
analyzed. We find that the presence of the electrons leads to stabilizing
effects for both $\alpha$ decay and spontaneous fission for high electron
densities. Furthermore, the screening effect shifts the proton dripline to more
proton-rich nuclei, and the stability line with respect to beta decay is
shifted to more neutron-rich nuclei. Implications for the creation and survival
of very heavy nuclear systems are discussed.
