Experimental determination of the effective solid angle of long-lived projectile states in zero-degree Auger projectile spectroscopy

Highlights: • First experimental determination of the solid angle of electron spectrometers for long-lived Auger projectile states. • The determination of the solid angle is free of possible cascade effects. • Electron-optics simulations of the solid angle for hemispherical and two-stage parallel plate analyzers in agreement with measurements. • Important application to capture processes in He-like ion–atom collisions with emphasis on cascade feeding of metastable states. - Abstract: In zero-degree Auger projectile spectroscopy (ZAPS), electrons are measured with high energy resolution at 0° with respect to the beam direction and state-selective cross sections can be determined. However, for Auger electrons from long-lived projectile states such as the 1s2s2_p⁴p_j (with lifetimes ranging from ns to ms depending on atomic number Z_p and total angular momentum J) these zero-degree electrons are emitted all along the projectile path towards the spectrometer making their detection solid angle $\overline{\Delta \Omega }$ and therefore their cross section difficult to determine. To date, $\overline{\Delta \Omega }$ has been modeled theoretically leading to significant corrections of the determined cross sections. Here, using ZAPS, we experimentally determine $\overline{\Delta \Omega }$ using the $1s^{2}2s2p{}_{3}P$ metastable component of 17.5 MeV O⁴⁺ and 6.6 MeV C²⁺ Be-like ion beams. Both the long-lived $1s2s2p{}_{4}P$ state and the similarly configured prompt $1s\left(2s2p{}_{3}P\right){}_{2}P$ (also known as the ${}_2{P}_{-}$) state are readily produced by 1s ionization in a cascade-free environment in the ratio of 2:1, according to spin statistics. This allows for the determination of $\overline{\Delta \Omega }$ for the ${}_{4}P$ state in relation to the known point solid angle ΔΩ₀ of the prompt ${}_2{P}_{-}$ state. Using this technique new results are obtained with our hemispherical deflector analyzer (HDA), as well as from the re-analysis of the older ZAPS measurements of Lee et al. (1992) [26] which used a two-stage parallel plate analyzer (2PPA). SIMION electro-optical simulations for both spectrometers and geometrical calculations for the 2PPA are compared to our experimental results and found in acceptable agreement. The ramifications of these results on recent 2p capture measurements using $\left(1s2s{}_{3}S\right)$ C⁴⁺ and F⁷⁺ ions involving the production of $1s2s2p{}_{4}P$ states are discussed.