Relativistic calculation of Lβ\₂ satellite spectra of W and Au

L$\beta\_2$ X-ray satellite spectra of tungsten and gold are calculated using the Multi-Configuration Dirac-Fock energies and compared with recent experimental data. New calculations of L$\_1$-L$\_3$M$\_5$ Coster-Kronig transition energies for tungsten are presented, confirming the origin of the L$\beta\_2$ visible satellites reported by two experimental groups. We found the value 5.09 eV for the average energy of the L$\_1$-L$\_3$M$\_5$ Coster-Kronig transition in tungsten. A detailed calculation of the L$\beta\_2$ and L$\beta\_{15}$ satellite spectra was performed for gold.