Abstract. Finite systems of charge carriers confined by a harmonic trap are considered. The onion shell model for Coulomb clusters is analyzed and an improved model is proposed which is able to more accurately reproduce the results of numerical experiments. The ground state energy is determined, and the transition to an infinite system is discussed.
IntroductionThe investigation of particles in a trap is of high current interest in many fields. Examples are bose condensates of alkali metals, electrons in quantum confined semiconductor structures, e.g. [1,2], ions in Penning and Paul traps, e.g. [3] and dusty plasmas, for an overview see e.g. [4,5,6,7,8]. Intense studies of trapped strongly correlated ions were performed in the last two decades of the previous century demonstrating, in particular the possibility of three-dimensional Coulomb crystals [9,10,11]. In parallel, a large number of theoretical and numerical investigations of Coulomb crystals was performed over the last 15 years, see e.g. [12,13,14,15,16,17,18] and references therein.Meanwhile the experimental methods in many fields have improved essentially allowing to investigate in detail the structure of three-dimensional plasma crystals. Three-dimensional spherical dust crystals were recently observed at room temperature [19], and it was shown by computer simulations that their structure is very well explained by a statically screened Coulomb repulsion together with a constant parabolic confinement [20], in contrast to alternative theoretical models [21,22]. These strongly correlated charged particle systems are a new and intesting kind of plasmas far outside the "normal" parameter range. Here many questions are still open. For completeness, we mention our recent theoretical investigations of the Coulomb crystallization conditions in a two-component plasma [23] and our analysis of macroscopic charged particle systems in traps, see Ref. [24] in this volume.In this paper we will consider finite (mesoscopic) charged particle systems in a trap. In particular we will analyze the total energy. The trap is assumed to be realized by a parabolic potential and confines the particles thereby taking over the role of a neutralizing background which otherwise is needed to compensate the repulsive forces of the charged particles. We consider, thus, a true one component plasma (OCP) in a trap in contrast to the OCP (or jellium) model. Further, we discuss the transition to a macroscopic system.