The normal mode spectra of two-dimensional finite clusters of charged particles $\left(-e\right)$ confined by a Coulomb potential resulting from a displaced positive charge $\mathrm{Ze}$ are obtained. This is a classical two-dimensional model system for atoms. We obtain the frequencies of the normal modes as a function of the confinement charge Z and the number of particles N. The analysis of the lowest normal mode frequency reveals a good agreement with the experimental results obtained in a system with screened interaction between charged particles. The dependence of the normal mode spectra as a function of a perpendicular magnetic field is also discussed and we found that the shearlike character of the modes is enhanced in the presence of the magnetic field. For large values of the magnetic fields the normal modes fall into two bands, a low frequency band with frequency $\sim 1/{\omega }_c$ and a high frequency band with frequency $\sim {\omega }_c.$

• Received 9 July 2003

DOI:https://doi.org/10.1103/PhysRevE.68.066405