Lower Bound to the Ground-State Energy and Mass Polarization in Helium-Like Atoms

Using a method which involves finding the expectation value of the square of the Hamiltonian, lower bounds to the ground state energies of He, Li^+, and O^6+ have been obtained from existing Hylleraas-type wave functions. The limit of error in the Chandrasekhar-Herzberg 18-parameter helium upper bound, -2. 9037063 atomic units (a. u. ), is found to be in absolute value less than 0. 00179 a. u. and "probably" less than 0. 00009 a. u. (20 cm^-1). These results would seem to indicate that the Hylleraas series is not as rapidly convergent as previously thought. Again using existing Hylleraas-type wave functions, values have been obtained for the mass polarization (specific mass effect) in the same helium-like atoms. The value obtained for helium is somewhat different from that given by Bethe.