Boundary Conditions Effects on the Ground State of a Two-Electron Atom in a Vacuum Cavity

Abstract

Abstract:The ground state properties of the two-electron atom with atomic number 2 Z ≥ in the spherical vacuum cavity with general boundary conditions of "not going out" are studied. It is shown that for certain parameters of the cavity such atom could either decay into the one-electron atom with the same atomic number and an electron or be in stable state with the binding and ionization energies several times bigger than the same energies of the free atom. By analogy with the Wigner-Seitz model of metallic bonding, the possibility of the existence of such effects on the lattice formed by the vacuum cavities filled with the two-electron atoms of the same type is discussed.

H 2 + in a lattice of cavities: Ammonia-like splitting of the lowest level

“…In accordance with [30], the limiting value (a) is obtained from the equation (25) Now, let us study the behavior of the lowest elec tronic energy term of the molecular hydrogen ion as a function of R, depending on the specific values of a, V 0 , and d. The shell parameters are chosen so that they correspond to the scale of the real sizes of microvoids, in which the confinement of the atomic system can occur (see the discussion in [29][30][31]). For V 0 , the opti mal characteristic of the general case is Ӎ10 eV and the lowest energy level has an exponential dependence on distance.…”

“…a C < < a 2 , we introduce the following sampling functions (31) The f L, R φ functions are the eigen functions of H L, R with an exponential accuracy [35], where φ is the nor malized wave function of a double well Schrodinger operator that corresponds to E 0 . The probability, P L , of finding the particle in the left well is given by (32) since the integral in the range a 1 < a < a 2 is exponen tially small.…”

“…For the term confinement stresses, unlike for the case of the prob lems of atoms and molecules in cavities with an imper meable potential barrier at the border, the retention of particles does not necessarily imply a vanishing wave function at the border [13-17, 19-21, 23]. This situa tion occurs in a number of topical problems of quan tum chemistry and condensed matter physics [13,14,23,[28][29][30][31] and in chiral models of quark confinement in hadrons [32,33]. In particular, the Neumann con ditions of the wave function on the borders of the cav ity describe not only the state of localization inside the cavity, but the periodic extension of the electron wave function similar to the Wigner-Seitz model of alkaline metals as well [28].…”

“…The dependence of the properties of the ground state one electron and two electron atoms in the cav ity on boundary conditions of the general form was investigated in [29][30][31]. In this work, the properties of the electronic level of the ground state molecular hydrogen ion inside a spherical cavity are investigated, in their dependence on the cavity parameters.…”