Interaction energy in the Poisson-Boltzmann plus hole approximation in asymmetric complex plasmas

We analyse two-component electroneutral systems of classical finite-sized macroions with the charge Z >> 1 and point oppositely charged microions with a unit charge. The article deals with a modification of the Debye-Huckel plus hole approximation when nonlinear screening effect is taken into account in asymmetric complex plasmas. We calculate the interaction energy in the Poisson-Boltzmann plus hole approximation considering the interaction of all particles (both inside and outside the hole). This energy has a greater value than some previous results. In addition, we subdivide all hole microions into two types, free microions and bound ones, and show a significant reduction of an effective macroion charge Z* in comparison with its initial charge Z due to the nonlinear screening by a thin high-concentration bound microions envelope. We demonstrate that this procedure increases the Debye radius that takes the screening by microions and macroions outside the hole into account.