Mass formula for He 3 clusters

We have obtained an analytic expression for the total energy of $^{3}\mathrm{He}$ clusters composed of N atoms. It is a variational solution of an energy density functional, where the extended Thomas-Fermi method has been used for the kinetic-energy density. The energy is calculated as an expansion in decreasing powers of the cluster radius, R\ensuremath{\propto}${\mathit{N}}^{1/3}$. Contributions of volume (${\mathit{R}}^{3}$), surface (${\mathit{R}}^{2}$), curvature (R), constant (${\mathit{R}}^{0}$), (1/R), and (1/${\mathit{R}}^{2}$) are identified in the formula. Simple analytical formulas are also derived for relevant quantities such as chemical potentials, fusion and fission potentials, surface thickness, unit radii, and relative compression. Our results are compared with other available theoretical calculations.