The semiempirical mass formula for spheroidal and rotating Coulomb crystals

The recently proposed semiempirical mass formula for spherical Coulomb crystals is generalized to include spheroidal deformations and Maclaurin-type rotations. The external focusing frequencies are adjusted in such a way that in the interior the forces due to focusing and Coulomb repulsion are cancelled out exactly. With the help of molecular dynamics calculations isometric configurations of non-spherical Coulomb crystals formed due to a non-spherical trapping potential or due to rotation are found to have less energy than the spherical ground state with the same number of particles. Possible collective multipole excitations of the neutral background are discussed.