Oscillator strengths and the accuracy of atomic wavefunctions

General expressions (both relativistic and non-relativistic) for the electric multipole transition operators, having not specified values of the gauge condition of the electromagnetic field potential, are presented. The dependence of oscillator strengths for electric dipole transition on the gauge is studied. In the general case it has the form of a parabola. The coefficients of the equation, describing this curve, as well as the values of the gauge for which the oscillator strength equals zero are expressed in terms of the length and velocity forms of the electric dipole transition operators. Transitions in Be-like ions are considered and the results of the calculations are compared with experimentally determined oscillator strengths. (Auth.)