Calculated gadolinium atomic electron energy levels and Auger electron emission probability as a function of atomic number Z

Auger electron interaction with matter is gaining importance in particular in medical application of radiation. The production probability and energy spectrum is therefore of great importance. A good source of Auger electrons is the ¹⁵⁷Gd(n,γ)¹⁵⁸Gd reaction. The present article describes calculations of electron levels in Gd atoms and provides missing data of outer electron energy levels. The energy of these electron levels missing in published tables, was found to be in the 23-24 and 6-7 eV energy ranges respectively. The probability of Auger emission was calculated as an interaction of wave function of the initial and final electron states. The wave functions were calculated using the Hartree-Fock-Slater approximation with relativistic correction. The equations were solved using a spherical symmetry potential. The error for inner shell level is less than 10%, it is increased to the order of 10-15% for the outer shells. The width of the Auger process changes from 0.1 to 1.2 eV for atomic number Z from 5 to 70. The fluorescence yield width changes five orders of magnitude in this range. Auger electron emission width from the K shell changes from 10^-2 to ∼1 eV with Z changing from 10 to 64, depending on the final state. For the L shell it changes from 0 to 0.25 when it Z changes from 20 to 64.