2p$_{3/2}^{-1}$3x$^{-1}$-3x$^{-1}$3d$^{-1}$ X-Ray satellites in the L$\alpha_{1}$ spectra of 4d transition elements

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. 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.