On the method of interpolation of transition energies in doubly ionized atoms

Abstract

In X-ray emission spectrum, while the diagram lines are emitted by transitions in the singly ionized atom, the X-ray satellite lines are emitted due to transitions in the multiply ionized atom. The X-ray satellite energy is the difference between the energies of initial and final states which are both doubly or multiply ionized. To calculate the energy of a satellite theoretically, the difference in energies of the double vacancy initial and final states has to be calculated with the help of several tabulations in which necessary data are available. One of such tabulations is by Parente et al. [1], which gives values of energies of all the transitions which possibly can give rise to origin of L satellites only for 11 elements. For finding the values of the energy for a particular transition for intermediate elements, two methods are possible: linear interpolation method and polynomial fitting method. In the present work, we have examined whether the linear interpolation method or the polynomial method is suitable for finding values of energies for intermediate elements. The linear interpolation method has been found to be the best method for finding the value of the energy for a particular transition for intermediate elements.