The two-electron self-energy contribution to the ground-state energy o
f helium-like ions is calculated both for a point nucleus and an exten
ded nucleus in a wide interval of Z. All the two-electron contribution
s are compiled to obtain mast accurate Values for the two-electron par
t of the ground-state energy of helium-like ions in the range Z = 20-1
00. The theoretical value of the ground-state energy of U-238(90+), ba
sed on currently available theory, is evaluated to be -261382.9(8) eV,
without higher-order one-electron QED corrections. (C) 1997 Published
by Elsevier Science B.V.