Evaluation of the effective solid angle of a hemispherical deflector analyser with injection lens for metastable Auger projectile states

The accurate determination of the electron yield of a metastable projectile Auger state necessitates the careful evaluation of the corresponding effective solid angle, i.e. the geometrical solid angle convoluted with the decay time of the metastable state. Recently, we presented (Doukas et. al., 2015) SIMION Monte Carlo type simulations of the effective solid angle for long lived projectile Auger states (lifetime τ∼10-9–10-5s) recorded by a hemispherical spectrograph with injection lens and position sensitive detector in the direction of the projectile ion. These results are important for the accurate evaluation of the 1s2s2pP4/2P ratio of K-Auger cross sections whose observed non-statistical production by electron capture into He-like ions, recently a field of interesting interpretations, awaits final resolution. Here we expand and systematize our investigation using the same techniques to expose universal behaviors of the effective solid angle covering life times of 1s2s2pP4 states for all first row ions. Our results are also compared to purely geometrical calculations of the solid angle that omit the lensing effects and serve as a benchmark for a deeper insight into the effect.