Gauge-invariant amplitudes of relativistic multipole transitions 周祥順 ^{1*}^{1}光電科學研究所, 國立台灣海洋大學, 基隆, Taiwan* presenting author:周祥順, email:hschou@mail.ntou.edu.tw In the conventional formulation [1], the amplitudes of relativistic multipole transitions are gauge-dependent for the nonresonant transitions. This is due to the fact that the transition matrix for longitudinal potentials vanish only for the resonant transitions. In this paper, we obtain the amplitudes of relativistic multipole transitions from the gauge-invariant formulation [2]. We show that the transition matrix for the longitudinal potential vanish for all transitions. Therefore, the transition amplitudes are gauge-invariant order by order for all transitions. The two formulations agree for the resonant transitions. For the nonresonant transitions, the gauge-invariant formulation gives the correct result, whereas the conventional formulation gives an incorrect result. For the electric dipole transitions, the Coulomb gauge leads to the corrected dipole velocity form of the matrix element in the nonrelativistic limit and the Babushkin gauge gives the dipole length form. With the corrected dipole velocity form, the conventional formulation is gauge-invariant for all transitions.
[1] I. P. Grant, J. Phys. B : Atom. Molec. Phys. 7, 1458-1475 (1974). [2] K. H. Yang, Ann. Phys. (N. Y.) 101, 62-96 (1976). Keywords: transition amplitude, gauge-invariant |