Theoretical shapes of L$\alpha_{1}$ X-Ray satellites spectra of 4d transition elements by HFS calculations

The X-ray satellite spectra arising due to 2p$_{3/2}^{-1}$3x$^{-1}$-3x$^{-1}$3d$^{-1}$ (x $\equiv $ s, p, d) transition array, in elements with Z = 40 to 48, have been calculated, using available Hartree-Fock-Slater (HFS) data on 1s$^{-1}$-2p$^{-1}$3x$^{-1}$ and 2p$_{3/2}^{-1}$-3x$^{-1}$,3x'$^{-1}$ Auger transition energies. The relative intensities of all the possible transitions have been estimated by considering cross - sections for the Auger transitions simultaneous to a hole creation and then distributing statistically the total cross sections for initial two hole states 2p$_{3/2}^{-1}$3x$^{-1}$ amongst various allowed transitions from these initial states to 3x$^{-1}$3d$^{-1}$ final states by Coster-Kronig (CK) and shake off processes. In both these processes initial single hole creation is the prime phenomenon and electron bombardment has been the primary source of energy. Each transition has been assumed to give rise to a Gaussian line and the overall spectrum has been computed as the sum of these Gaussian curves. The calculated spectra have been compared with the measured satellite energies in L$\alpha _{1}$ spectra. Their intense peaks have been identified as the observed satellite lines. The peaks in the theoretical satellite spectra were identified as the experimentally reported satellites $\alpha _{3}$, $\alpha _{4}$ and $\alpha _{5}$, which lie on the high-energy side of the L$\alpha _{1}$ dipole line.