INHOMOGENEOUS ELECTRON LIQUID - H ATOM DIRAC DENSITY-MATRIX IN LIMIT OF INFINITE NUMBER OF CLOSED SHELLS

The Dirac density matrix rho(N)((r) over right arrow (r) over right ar row(l)) for the H atom with N closed shells is here treated in the lim it N tends to infinity. Then rho(infinity)((r) over right arrow, (r) o ver right arrow(l)) is shown to be derivable exactly from the zero ene rgy limit of the bound state only Green function Gb((Z))((r) over righ t arrow, (r) over right arrow(l); E). It is further demonstrated for n uclear charge Ze that the Laplace transform of G(b)((Z)) with respect to Z satisfies a useful equation of motion. Finally the s-wave only co mponents of rho(N) and G(b)((Z)) are considered.