Crystallization and melting of a system of charges in a liquid helium cluster
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SORDER, AND PHASE TRANSITION IN CONDENSED SYSTEMS
Crystallization and Melting of a System of Charges in a Liquid Helium Cluster A. M. Livshits and Yu. E. Lozovik Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow oblast, 142092 Russia e-mail: [email protected] Received January 26, 2007
Abstract—A system of like (positive or negative) charges forming “snowballs” or “bubbles” in a three-dimensional liquid helium cluster is investigated. The charges are confined inside the cluster by an “image potential” produced by the polarization of liquid helium. The stability of a multiply charged helium cluster is considered. Computer simulations are used to investigate the crystallization and melting of the system of charges depending on the dimensionless parameter T* = kBTR/e2, where kB is the Boltzmann constant, T is the temperature, is the dielectric constant of liquid helium, R is the cluster radius, and e is a unit charge. Various characteristics, including symmetry groups and moments, have been found for equilibrium configurations of charges in a cluster with N = 1–100 charges. At small N ~ 10, Thomson’s model of successive filling of “belts” of charges can be used to describe the structure of equilibrium configurations of charges. At large N, the description of the structure formed by charges using the idea of a quasi-two-dimensional “closed triangular lattice” with topological defects is more adequate. Formally, this description is valid starting from N = 4. The melting of a “lattice” of charges is described. A number of our conclusions can be generalized to clusters of other noble gases. PACS numbers: 61.46.Bc, 36.40.Wa, 67.40.Jg, 64.70.Nd DOI: 10.1134/S1063776107090142
1. INTRODUCTION The helium cluster is a unique system. At the pressure of its saturated vapor, helium does not solidify as it cools due to its low mass and weak interatomic interaction. Thus, in contrast to all of the other molecular and atomic clusters, the experimentally produced helium clusters are liquid. Moreover, according to theoretical estimates [1, 2], helium clusters of several tens or more atoms at T 1.9 K should have superfluid properties. Although most of the phenomena pertaining to the superfluid state are fundamentally related to the system’s macroscopicity, experiments that allow the superfluid state to be detected in a finite system have been proposed [3, 4]. Thus, the helium cluster can be used as an object for studying changes in the properties of a system in the superfluid state as its sizes decrease. Note in this connection that helium clusters have been produced experimentally in a wide range of sizes, from small clusters of a few atoms [5, 6] to “droplets” of 103– 107 atoms [7]. According to theoretical estimates [8] and experimental measurements [9], the internal temperature of the helium clusters produced by the expansion of a supersonic beam of helium atoms into a vacuum reaches T ≈ 0.3–0.4 K. Most of the experiments on helium clusters include the cluster excitation and ionization [10] by an el
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