Ground state of a confined Yukawa plasma

Abstract

The ground state of an externally confined one-component Yukawa plasma is derived analytically. In particular, the radial density profile is computed. The results agree very well with computer simulations of three-dimensional spherical Coulomb crystals. We conclude in presenting an exact equation for the density distribution for a confinement potential of arbitrary geometry.

Classical and quantum Coulomb crystals

“…In contrast to Coulomb crystals, where the density is approximately constant, with increasing there is an increasingly rapid decay of the density towards the surface. 34,35 As in the 2D case closed shell configurations and a "Mendeleyev table" exist ͑see, e.g., Refs. 23, 24, and 36͒.…”

Ground states of finite spherical Yukawa crystals

“…For larger κ, we also noted the cases where the configurations are different at κ = 5 and 20 (we cannot rule out that, in this range, there occur transitions in addition to those given). The general trend observed earlier [24] was confirmed: with increased screening, more particles tend to populate the inner shell(s) of the cluster giving rise to an average density profile which decreases increasingly fast toward the edge [27,28]. There are, however, three nontrivial deviations ('anomalies') from this shell filling sequence which were analyzed: (i) upon κ increase two particles move to (one of) the inner shell(s) at once, (ii) when the particle number is increased by one, at a fixed κ, one particle moves from the inner to the outer shell, and (iii) at very large κ there exist cases of re-entrent shell fillings: one particle returns from the inner to the outer shell.…”

“…Figure 2 shows a more complicated example with two ground state changes occurring in a small range of screening parameters. For κ < 1.5623 the ground state configuration is (27,4), whereas at κ cr1 = 1.5623 the configuration (26,5) becomes the ground state. Finally, at κ cr2 = 1.6142 this configuration is replaced by (25,6) which remains the ground state for larger κ.…”

“…[31,32]. (26,5) and green for (25,6)] and the end [red for (27,4)] of the occurrence of these configurations in the simulations. The inset shows the energy difference per particle for two stable states: the red The simplest fit for the ground state total energy per particle has the form…”

“…In [24]- [26] it was shown, by comparison with experiments, that the pair interaction is well described by an isotropic Yukawa potential and shell configurations for various values of the screening strength have been presented. It was found that screening leads to a cluster compression, a change of the average density profile [27,28] and to an enhanced population of the inner shells. Yet a detailed understanding of how these shell occupation changes proceed is still missing.…”