Using scattering theory to calculate the ground state energy of lithium atom

Abstract

The problem of bound states of atoms with many electrons does not have an analytic solution; therefore, standard methods of approximation are utilized to solve it, and among them, we can find the variational method, the perturbation method and the Hartree Fock method. Said methods may be very difficult to implement and may take a great amount of computational time, even when they are applied to the lithium atom. An alternative method that is considerably easier to implement is proposed in this paper. This involves considering the Hamiltonian for the lithium atom as a collision between an electron and an ionized lithium atom; in this way, the energy of the lithium atom is the sum of energies of a helium atom (with nuclear charge Z = 3) and the energy that an electron needs to be bound to an ionized lithium atom in a collision process. The Quantum Collision Theory under the focus of Jost function was used to calculate the bound state energies of one electron with an ionized lithium atom. Using this approach, we calculated the ground state energy of lithium atom with an error with respect to the experimental value of 0.3%. This error is very low; therefore, the proposed method produces very good results and it can be taken as basis to study atoms with more electrons. Hopefully, In the future, this method could be part of quantum physics books because it is a novel method to observe the formation of atoms.