A semiempirical mass formula for spherical Coulomb crystals

In analogy to the Bethe-Weizsaecker formula for nuclei we establish a semiempirical mass formula for the energies of Coulomb crystals including Madelung, surface, compression and curvature energy terms. The surface tension and the incompressibility are extracted as well. The coefficients are fitted at data obtained from molecular dynamics calculations for spherically confined systems of charged particles with particle numbers up to about 100 000 under their mutual Coulomb repulsion and under constant radial focusing. The systems are cooled down until the excess energy stays constant up to 10-8. For particle numbers below about 10 000, they settle in icosahedral structures whose faces are rounded off. At about 10 000 particles there is a transition to body centred cubic (bcc) crystals where particles are arranged in parallel layers. The icosahedra have lower surface energy but slightly higher Madelung energy of -0.8949, in contrast to the bcc crystals which have the lower Madelung energy of -0.8959 but essentially larger surface energy. The icosahedra are more compressible than the bcc crystals