Bounds on Mean Excitation Energies-Lamb Shift, Stopping Power, Straggling, and Grazing Collision of High-Energy Charged Particle

Abstract

The complementary variational-bound theory for dynamic polarizability, developed by Robinson, is extended to various mean excitation energies. The theory in the present paper provides both upper and lower bounds on the mean excitation energy for the grazing collision of a fast charged particle with an atom or a molecule ( I -1 ), for its stopping power ( I 0 ), for its mean fluctuation ( I 1 ), and for the Lamb shift of an atomic energy level ( I 2 ). Application to the 1s and 2s states of a hydrogen atom by use of 15-term trial functions yields bounds on ln I -1 , ln I 0 , ln I 1 , and ln I 2 with a relative error of the order of 10 -7 , 10 -5 , 10 -3 , and 10 -10 , respectively, if the I k 's are given in Rydberg units. An extrapolation procedure increases accuracy by about two orders of magnitude.