Confined Ground State of Beryllium Atom and Its Isoelectronic Ions

In the framework of the variational Monte Carlo and the Hartree-Fock methods, the four-electron system is investigated to calculate several properties of the beryllium atom. For the beryllium atom and its isoelectronic ions, we calculated the ground-state energy eigenvalues and the energy of the compressed ground state beryllium atom in an impenetrable spherical box at different radii of the spherical box. Furthermore, the correlation energies are calculated as well. Moreover, the pressure and the kinetic energy of the confined beryllium atom are also calculated at certain radii of the spherical box. A good agreement between the calculated values and the corresponding available previous results is shown. The results obtained using the variational Monte Carlo method are slightly better than those obtained using the Hartree-Fock method.