Bad Qubits — Learn Quantum by Doing

Multiple choice

In the one-parameter variational treatment of the helium ground state (Z = 2) using a product of hydrogen-like 1s orbitals with effective charge Z_eff, minimizing the energy gives Z_eff = 27/16 is approx 1.69. Why is the optimal Z_eff less than the bare nuclear charge of 2?

Because each electron partially screens the nucleus from the other, so each electron feels a reduced effective charge
Because the electrons increase the nuclear charge through their negative charge
Because relativistic corrections add 0.31 to the bare charge
Because the Pauli principle forces Z_eff to be exactly half of Z