Many-body Hamiltonian with screening parameter and ionization energy

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.