<i>L</i> and <i>M</i> edges of copper: Theory and experiment

Characteristic electronic transitions and the associated fine structure in the near-edge region are investigated with electron-energy-loss spectroscopy for the copper <i>L</i> and <i>M</i> edges. In a single-particle scattering picture this fine structure represents the unoccupied density of states selected by the matrix elements. However, electronic processes can often complicate this simple approach. In order to test the applicability of this model, full multiple-scattering calculations within a real-space formalism are presented and compared with measurements. An expression is derived and implemented in order to include excitations described by the first Born approximation for the initial and final states of the primary electron. Calculating the generalized oscillator strengths shows that different core edges of Cu behave differently with regard to the dipole selection rules. Some edges favor dipole-allowed transitions at large momentum transfer, while others show dipole-forbidden transitions even at small momentum transfer.