Measurement and uncertainties of energy loss in silicon over a wide Z₁ range using time of flight detector telescopes

The energy loss of projectiles with Z₁ in the range 3-26 has been experimentally measured in the 0.1-0.7 MeV per nucleon energy range in the same Si stopping foil of 105.5 μg cm^-2 thickness using a time of flight-energy (ToF-E) elastic recoil detection analysis (ERDA) setup. A detailed study of the experimental uncertainties for ToF-E and ToF-ToF-E configuration has been made. For ERDA configurations where the energy calibration is taken against the edge positions small uncertainties in the angle at which recoils are detected can introduce significant absolute uncertainty. The relative uncertainty contribution is dominated by the energy calibration of the Si E detector for the ToF-E configuration and the position of the second ToF detector in ToF-ToF-E measurements. The much smaller calibration uncertainty for ToF-ToF-E configuration implies this technique is superior to ToF-E measurements with Si E detectors. At low energies the effect of charge changing in the time detector foils can become important. It was found that empirical stopping numbers which include the effect of effective-charge were more closely clustered about a trend line when plotted against the Bohr ξ parameter than the corresponding Bethe parameter. Study of the deviations from the trend line showed evidence of a shell dependant effect that exceeded the anticipated maximum relative uncertainties. Crown