Dispersion relations of lattice waves in three-dimensional strongly coupled complex plasma crystals

Dispersion relation matrices, with the screened Coulomb interaction between a charged dust particle and all other particles taken into account, are derived for waves in body centred cubic (bcc) and face centred cubic (fcc) lattices in three-dimensional strongly coupled complex plasma crystals separately. The matrices are then calculated in characteristic directions to obtain the longitudinal and transverse eigenmodes. The longitudinal and transverse waves for these cases are discussed separately.