shellcorrection

Shell correction refers to a method used to incorporate quantum shell effects into a smooth macroscopic description of a finite Fermi system, most notably atomic nuclei and metal clusters. In a macroscopic model such as the liquid-drop model, the binding energy is smooth and featureless with respect to particle number. Real systems, however, exhibit pronounced fluctuations in energy due to the discrete arrangement of single-particle levels. The shell correction is the difference between the actual sum of occupied single-particle energies and a smoothed, averaged reference energy.

The standard approach, known as the Strutinsky shell-correction method, starts from a mean-field potential and a set of single-particle levels. The sum of the occupied levels gives the microscopic energy. A smoothed energy is then constructed by applying a convolution (smoothing function, typically a Gaussians) to the level density and integrating up to the Fermi level, with curvature corrections of order p. The shell correction energy is the difference between the microscopic and the smoothed energies: E_shell = E_micro − E_smooth. The total energy is often written as E_total = E_LDM + E_shell in macroscopic-microscopic models. A plateau condition, involving the smoothing width and the order of the correction, is sought to ensure physical independence from these arbitrary parameters.

Shell corrections are widely used to predict binding energies, deformation effects, and fission barriers in nuclei, as well as stability and magic numbers in metal clusters. Limitations include dependence on the chosen mean field and smoothing parameters, and the method’s semi-empirical character. Extensions address finite temperature and pairing correlations.