Many-body Hamiltonian with screening parameter and ionization energy

We prove the existence of a Hamiltonian with ionization energy as part of the eigenvalue, which can be used to study strongly correlated matter. This eigenvalue consists of total energy at zero temperature (E ₀) and the ionization energy (ξ). We show that the existence of this total energy eigenvalue, E ₀±ξ, does not violate the Coulombian atomic system. Since there is no equivalent known Hamilton operator that corresponds quantitatively to ξ, we employ the screened Coulomb potential operator (Yukawa-type), which is a function of this ionization energy to analytically calculate the screening parameter (σ) 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 ξ eigenvalue, which is also important in the field of spintronics.