Broadening of atomic levels near metal surfaces: first-order model versus coupled-angular-mode method

The reliability of a first-order model that is in use for calculating the widths of resonantly broadened atomic levels near metal surfaces is examined, in particular for large atomic quantum numbers and core charges. The model employs a simplified electronic potential in which image-charge effects are disregarded. Orbital hybridization is simulated by describing the atomic states in terms of hydrogenic wave functions in the parabolic (Stark) representation. For typical cases, first-order resonance widths are compared to widths calculated from the nonperturbative coupled-angular-mode method which uses a fairly realistic electronic potential including the classical image potentials. Good overall agreement is achieved between first-order and nonperturbative results. A plausible explanation for this agreement is given.