  We present analytical solutions to a quantum-mechanical three-body problem in
three dimensions, which describes a helium-like two-electron atom. Similarly to
Hooke's atom, the Coulombic electron-nucleus interaction potentials are
replaced by harmonic potentials. The electron-electron interaction potential is
taken to be both screened (decaying faster than the inverse of the
interparticle separation) and regularized (in the limit of zero separation). We
reveal the exactly solvable few-electron ground state, which explicitly
includes electron correlation, for certain values of the harmonic containment.
