A semiclassical formula for the term energy of a many - electron atom

A semiclassical formulation for the term energy of a many-electron atom is presented which includes gross structure, fine structure, core polarisation and core penetration effects. A very simple model combining perturbed Keplerian orbits with the BohrSommerfeld-Wilson quantisation hypothesis yields an explicit formula which, in appropriate limits, reduces to the familiar core polarisability and quantum defect parametrisations. The formula also provides a new parametrisation in terms of an effective core charge within an effective core radius, which has been applied to predict higher term values in the 3sng states of Si III.