Shell model and the nature of the collective oscillations of shells

The specific form of the change in overlap interaction between ions due to the presence of dipole polarizability implied by the shell model lacks any microscopic justification, while all other terms of the model have a sound quantum-mechanical basis. Recently we have shown that within the framework of the Heitler-London approach this modified overlap term of the shell model is microscopically justifiable. This calculation provides a method of evaluating the parameters of the model directly from the wave functions of the ions. Since the shell model has been successful in describing the different lattice-mechanical properties, it seems instructive to investigate how far it can reproduce the collective dynamics of the electrons in insulators. Starting from the Hartree-Fock wave function of the ions the calculation is presented for the dispersion relations of the collective oscillation of the shells in the shell model by relaxing the usual adiabatic condition for the two crystals: namely, KCl and NaCl. It is interesting to note that the →q→0 frequencies of these collective oscillations of shells of these two crystals together with those of the other fourteen crystals obtained phenomenologically are found to compare satisfactorily with the measured plasma frequencies.