Scaling law for the fluid-solid phase transition in Yukawa systems (dusty plasmas)

Yukawa systems serve as models for plasmas and colloidal suspensions of charged particles. The state of these systems is determined by two dimensionless parameters: k = a/λ D , which is the ratio of the mean interparticle distance to the Debye length λ D , and Γ = Z d 2 e 2/aT d , which is the ratio of the Coulomb potential energy to the particle temperature T d (Z d is the charge of each particle). We propose an empirical scaling law for the critical coupling parameter Γ c needed for crystallization in Yukawa systems. The dependence of Γ c on k is in good agreement with recent molecular dynamics simulations.