Coulomb Interactions in the Model of an Isolated Atom with a Screened Ion

Abstract

This paper continues the study of the properties of the graphene lattice based on the model of a hydrogen-like atom. The relevance of this topic is not fading away due to the not fully understood mechanism of the conductivity of such fine carbon structures and the processes of emission from their surface. To describe the properties of the lattice, we use a modification of the Brandt–Kitagawa approach with screened ions, which we proposed earlier. In the cold lattice approximation, this model assumes that three valence atoms oriented along bond lines belong to the screening shell of the ion. And only one valence electron determines the ground state of the lattice atom and the inhomogeneous angular distribution of its field. In this study, it is proposed to take into account the Coulomb interactions of electrons in the outer shell of an atom with its own ion and its nearest environment. For this, a modification of the electron density distribution of the shielding shell is developed, taking into account its Coulomb interaction with an electron of a hydrogen-like atom. The problem of the parameters of the ground state of a lattice atom is solved numerically using a variational approach. In the numerical experiments, the parameters of the interaction of a weakly bound electron with an ion are obtained. It is also shown that, for an isolated carbon atom, taking into account the Coulomb interaction of an electron with the shielding shell of an ion makes it possible to accurately calculate the ionization potential of the ground state. The proposed numerical technique leads to adequate results for the calculation of the ionization potential for all light atoms from Li to Ne.