Dipole polarizability for confined two-electron atomic systems: simple approximations

The electric dipole polarizability is analyzed for a two-electron system embedded in an impenetrable spherically symmetric cavity. Methods to find simple estimates of polarizability and corrections to them are considered. The expressions for matrix elements in Hylleraas coordinates required for energy and polarizability variational calculations are presented for the two-electron atomic system. The results of simple polarizability estimates are presented for the ground state of the helium atom and are compared with polarizabilities calculated using Hylleraas variational perturbation theory and with recently calculated polarizabilities reported in the literature for confined systems.