Applications of Pade approximation to range calculations

Using the technique of the direct operational method, the approximate solutions for the moment equations of the spatial distribution of bombarded ions has been obtained. Numerical evaluations of the range parameters have revealed that the present formula gives as accurate solutions as the Brice's second order solutions without the iteration technique. In order to investigate the effect of the different treatments of the electronic stopping on the x range parameters, the Firsov and LSS electronic stopping formulas are employed. From numerical calculations it is known that the difference between two theories is negligible for calculations of projected range and straggling, but that the difference is detectable in calculating the higher moments for the ion-atom combination with large mass ratio. (author)