The solution of the positron diffusion trapping model tested for profiling of defects induced by proton implanted in stainless steel

The exact analytical solution of the diffusion trapping model for defect profiling using the variable energy positron beam is reported. The solution is based on the Green’s function valid for the case of a discreet step-like vacancy distribution. The solution is applied to the description of experimental data from slow positron beam measurements for samples of stainless steel exposed to high-energy proton multi-implantation. This implantation ensured to obtain an approximate step-like vacancy distribution. The measured annihilation line shape parameter versus positron incident energy is well described by this solution. The determined positron trapping rate, which is proportional to the concentration of vacancies induced during proton implantation, increases linearly with the total dose. The comparison with the commonly used VEPFIT numerical code is also performed. The presented solution can be an alternative to other numerical codes commonly used for evaluation of data from positron beam experiments.