Lindhard's polarization parameter and atomic sum rules in the local plasma approximation: a case for excited states

ABSTRACTIn this work, we analyze the effects of Lindhard polarization parameter, χ, on the sum rule, , within the local plasma approximation (LPA) as well as on the logarithmic sum rule , in both cases for the system in an initial excited state. We show results for a hydrogenic atom with nuclear charge Z for the spherically symmetric (l=0) states with n=1, 2 and 3 with p=−1,0,1, and 2. Our calculations are complemented with comparisons to the exact results for this system for the ground state. As a natural extension of our treatment, we report analytical results for helium-like systems in terms of a screened charge for the ground state. Our study shows that by increasing χ, the sum rule for p 0 it increases, and the value p=0 provides the normalization/closure relation which remains fixed to the number of electrons for the same initial state. When p is fixed, the value of increases as the initial excited state increases for p 0. Thus, when using a specific val...