Total stopping and its straggling for protons in heavy targets, fully relativistic calculations for Au, Pb and Bi

C. C MONTANARI; C. D. ARCHUBI; D. M. MITNIK; J. E. MIRAGLIA

Phalaborwa, Sudáfrica

Congreso; 23 International Conference on Atomic Collisions in Solids (ICACS); 2008

Local organizers of the 23 International Conference on Atomic Collisions in Solids

The total stopping power and its straggling is calculated for protons in heavy ions. For the atomic structure calculations we combine the fully-relativistic solutions of the Dirac equation with the Levine-Louie Shellwise Local Plasma Approximation (SLPA).  The valence electron contribution is considered as that of a free electron gas employing the Mermin-Lindhard dielectric function to take into account collective or plasmon excitations.  The fully-relativistic wave functions and their binding energies are introduced within the SLPA for the inner shell contribution to the stopping power. The SLPA employees a shell to shell dielectric response with the Levine-Louie correction to take into account the ionization threshold of each shell.  This description considers linear response and square dependence with the ion charge. It is a perturbative approximation valid in the intermediate to high energy range. Previous calculations (for atoms with atomic number Z<54) were based on the widely known non-relativistic Hartree-Fock wave functions set. The relativistic approach allows us to extend the range of calculations to atoms with higher atomic number. We present calculations performed for three different targets: Au, Pb and Bi, and we compare our results with the available experimental data. For stopping cross sections, in the case of Au, the results are surprisingly good, even in the low energy rage (i.e. energies below 25 keV).  In the case of Bi, the description is good but it underestimates the experimental results for energies below 25 keV.  The same tendency seems to follow the calculation for Pb.  For energy loss straggling, the three cases studied show very good agreement with the few experimental data available. We obtain the correct asymptotic behavior to Bohr high energy limit. In the shell to shell description, the tendency of each shell to saturate at a value proportional to the number of electrons in this shell is obtained. Our theoretical description tends to Bohr limit from below without overshooting (or Bethe shoulder) usually found experimentally around the energies corresponding to the stopping maximum. This emphasizes the possibility that the overshooting could be related to the rougosity or inhomogenity of the samples and not to the statistical energy loss straggling.