  We prove the existence of a new Hamiltonian that can be used to study
strongly correlated matter, which consists of the total energy at temperature
equals zero (E_0) and the ionization energy (\xi) as eigenvalues. We show that
the existence of this total energy eigenvalue, E_0 \pm \xi, does not violate
the Coulombian atomic system. Since there is no equivalent known Hamilton
operator that corresponds quantitatively to \xi, we employ the screened Coulomb
potential operator, which is a function of this ionization energy to
analytically calculate the screening parameter (\sigma) of a neutral Helium
atom in the ground state. In addition, we also show that the energy level
splitting due to spin-orbit coupling is inversely proportional to \xi
eigenvalue.
