Screening effects in nuclear fusion of hydrogen isotopes in dense media

Nuclear-fusion rates of isotopic hydrogen nuclei embedded in dense screening media are calculated. We consider the cases of a uniform degenerate electron gas and the inhomogeneous electron density in solids. We derive an exact wave function for the screened nuclear interaction and an analytical expression for the barrier-penetration factor in the case of homogeneous screening. For qualitative estimates of the screening in solids, we use a Thomas-Fermi description of the electron density. A crossover of the fusion rates of the various isotopic pairs analyzed (p-d, d-d, p-t, and d-t) is predicted for increasing screening length, velocity, or effective temperature of the medium. The effects of variable screening length and local effective temperatures are considered for electron gases in the range of metallic densities and compared with previous experimental and theoretical studies