Relativistic and correlation effects, gauge dependence

30 Role of gauge dependence in electronic transitions 30.2 Relativistic and correlation effects, gauge dependence 

As was shown in Chapter 4 (formula (4.22)), relativistic corrections of the order a2 to the intercombination 1-transitions in length form for accurate wave functions compensate each other. It follows from formulas (4.18)-(4.20) that for the velocity form of the 1-transition operator the relativistic corrections are of the order a2 and may be presented in length, velocity and acceleration forms. Calculations of the 1-radiation for the Be isoelectronic sequence (Z = 4 92) indicate that these relativistic cor- 

To demonstrate how the /-values change when a certain amount of correlation is taken into account, let us consider the 2s2p lP-2p2 1S transition in Be-like OV. The dependence of oscillator strengths, obtained 

by employing general formulas for oscillator strengths, results can be obtained which are useful both in practical calculations and in studying the role of correlation effects on transition probabilities. 

Let us also notice that slow variations of K with Z imply that the gauge condition K may be treated as a semi-empirical parameter in practical calculations to reproduce, with a chosen K, the accurate oscillator strength values for the whole isoelectronic sequence. Thus, dependence of transition quantities on K may serve as the criterion of the accuracy of wave functions used instead of the comparison of two forms of 1-transition operators. In particular, the relative quantities of the coefficients of the equation fEi = aK2 + bK +c (the smaller the a value, the more exact the result), the position of the minimum of the parabola Kf = 0 (the larger the K value for which / = 0, the more exact is the approximation used, in the ideal case / = 0 for K = +oo) may also help to estimate the accuracy of the method utilized. 

---