MULTIPOLE MATRIX ELEMENTS 〈nlrβEl'〉v FOR H-LIKE ATOMS AND THEIR APPLICATIONS (AS β = 1, n ≤ 4, Enl < 0 ≤ E ≤ 1).

This article deals with the connection between multipole matrix elements 〈nl|rβ|n&#39;l&#39;〉ν and 〈nl|rβ|El&#39;〉ν for H-like atoms, where ν is the so-called &quot;auxiliary&quot; parameter of Heun&#39;s differential equation and $\tilde{Z}=Z/\nu$ is the &quot;effective&quot; nuclear charge, and new properties of Appell&#39;s function F2(x,y) to the vicinity of the singular point (1, 1) and in addition, here, first V. A. Fock&#39;s idea for the continuous spectrum is taken into consideration. Such an approach allows us to get the explicit expressions for squares of the dipole moments and the certain physical characteristics in atomic physics and also their exact numerical values, e.g., the average oscillator strengths $\bar{f}(nl,El&#39;)$ and the line intensities J(nl, El&#39;), etc., as n ≤ 4, l&#39;= l &#177; 1 and 0 ≤ E ≤ 1 (see Tables 1–3). Besides, diagrams of certain radial functions for the discrete-continuous transitions are given here. [ABSTRACT FROM AUTHOR]