Correlation Functions of Coulomb Pair

Abstract

The correlation functions of two electrostatically interacting particles have been obtained for the first time, by using the direct algebraic method for finding the cross-correlation functions. The efficiency of this method has been demonstrated by finding almost all unknown elements of the decomposition matrices in the second-order approximation.

Third-Order Correlation Functions for a Coulomb Pair

“…This method is a subject of the presented consideration. The results that have already been obtained in the secondorder approximation [1] make it possible to continue further the development of the exact theory describing the Coulomb pair.…”

“…11 ± , where ̸ = 0 is an unknown constant, which is to be found [1]. The key point of the direct algebraic method is the expansion of operators in the two-operator basis, which is analogous to the expansion of vectors.…”

“…where are unknown constants. These expansions play a substantial role while applying the method of work [1].…”

“…We have already noted [1] that every particle can possess only two different states: states with identical momenta and different spin projections or, vice versa, states with different momenta. Therefore, let us consider four main variants.…”

“…In this paper, the consideration of the exact theory of a Coulomb pair, the fundamentals of which were published in work [1], is continued. Recall that this theory is based on a modification of the direct algebraic method (DAM), which was proposed in work [2] for the determination of correlation functions.…”