Abstract
A regular method for deriving the consecutive terms of a series in powers of field strength F for the intensities of hydrogen radiation lines is presented both analytically and numerically. Specific modification of the perturbation theory for degenerate states and the Sturm-series expansion for the completely reduced CoulombGreen function in parabolic coordinates are used to derive simple analytical formulas for matrix elements and the intensities of the radiation transitions between circular states. Particular cases of transitions between the closest Rydberg levels are presented and discussed in detail. Analytical expressions are also derived for the quadrupole matrix elements, which may contribute to the probability of σ-transitions with the selection rule for the magnetic quantum number Δm = ±1 and determine the probability of the dipole-forbidden radiation transitions between Stark levels with Δm = ±2. PACS Nos.: 32.60.+i, 32.70.n, 32.70.Fw
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