Electrostatic energy and phonon properties of Yukawa crystals

We study electrostatic and phonon properties of Yukawa crystals. It is shown that in the harmonic approximation these systems which is in use in the theory dusty plasma can be described analytically by the model from the theory of neutron stars and white dwarfs. Using this approximation we consider properties of body-centred cubic (bcc), face-centred cubic (fcc), hexagonal close-packed (hcp), and MgB$_2$ lattices. MgB$_2$ and hcp lattices have never been studied earlier in the context of Yukawa systems. It is shown that they never possess the smallest potential energy and the phase diagram of stable Yukawa crystals contains bcc and fcc lattices only. However, corrections to the charge density $\propto (\kappa a)^4$ can noticeably change the structural diagram of Yukawa systems. The developed analytical model also allows to describe low-temperature effects where numerical simulations are difficult.