Pair and three-particle correlation functions of spherical dust clusters

Dust particles in a complex plasma usually accumulate a high negative charge inside a plasma which is responsible for their strong repulsive interaction and high coupling. When confined in a parabolic trap, these particles form spherical clusters with a characteristic shell structure. In recent years the phase transition-like crossover from a crystal to a liquid-like state has attracted high interest, e.g.~[1]. While the radial melting is now well understood, here we concentrate on the loss of intra-shell order. The radial pair correlation function $\rho(r_{ij})$ is well suited for homogeneous system but has to be adapted to the spherical symmetry for finite clusters. Here, we present the Center-Two-Particle correlation function that is equally sensitive to intra-shell as well as inter-shell correlation~[2,3]. As a second quantity, we present the Triple Correlation function that is calculated from the ``bonding angles`` of three particles. This quantity is particularly well suited to investigate the orientational order within spherical cluster shells.\\[4pt] [1] J. B\"oning et al., Phys. Rev. Lett. \textbf{100}, 113401 (2008)\\[0pt] [2] P. Ludwig et al., Plasma Phys. Control. Fusion \textbf{52}, 124013 (2010)\\[0pt] [3] A. Schella et al., Phys. Rev. E \textbf{84}, 056402 (2011)