Theoretical shapes of L$\alpha _{1 }$X-Ray Satellites spectra of $_{40}$Zr, $_{42}$Mo, $_{44}$Ru, $_{46}$Pd and $_{48}$Cd for lead as predicted 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 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 CK and shake off processes. 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. On the basis of agreement between the computed spectra and measured satellites, it is observed that the satellite $\alpha _{3}$ is observed due to intense transition, $^{3}$F$_{4}-^{3}$F$_{4}$, in order of decreasing contribution of intensity. It has been found that the transition $^{1}$F$_{3}-^{1}$G$_{4}$ is the main source of the emission of the satellite $\alpha _{4 }$in the elements $_{42}$Mo to $_{48}$Cd. The line $\alpha _{5}$, observed in the spectra of elements with Z = 40-48, has been assigned to the $^{3}$D$_{3}-^{3}$F$_{4}$, $^{3}$D$_{2}-^{3}$F$_{3}$, $^{1}$P$_{1}-^{1}$D$_{2}$ and $^{1}$F$_{3}-^{1}$D$_{2}$ transitions.