6s and 8d state self-energy for hydrogen-like ions and new results on the self-energy screening

We use a recently published method for the renormalization of the self-ener gy to calculate the self-energy of 6s and 8d levels to all orders in Z alph a. We demonstrate the accuracy of the method and its potential for high-n, low-Z applications. We also show that this method is perfectly suited for t he evaluation of the two-electron self-energy (self-energy screening). For the first time, evaluation of the screening of the 1s electron by a second one in either the 1s, 2s, 2p(1/2) Or 2p(3/2) shells has been performed, for 30 less than or equal to Z less than or equal to 92.