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

Journal article, 2017

In this work, we analyze the effects of Lindhard polarization parameter, chi, on the sum rule, S-p, within the local plasma approximation (LPA) as well as on the logarithmic sum rule L-p = dS(p)/dp, 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 Z* for the ground state. Our study shows that by increasing., the sum rule for p<0 decreases while 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 Sp increases as the initial excited state increases for p<0 and decreases for p>0. Thus, when using a specific value of. to adjust to a particular Sp sum rule value, the sum rule becomes unbalanced for other values of p. Our results show that the dipole oscillator strength distribution, within the LPA, provides good results for the sum rules for excited states.