We show that in order to satisfy the condition of relativistic invariance for the one-photon radiative transition amplitudes of a composite system to relative order
c21 in an approximately relativistic canonical theory, the position operator in the theory should satisfy a condition which encompasses the world-line condition of Currie, Jordan, and Sudarshan. We also obtain the expression for the
E1 and the
M1 single-photon transition amplitudes of the composite system in the center of momentum frame, including the relativistic corrections of leading order. These expressions show that the relativistic corrections are qualitatively different for the electrically charged and neutral composite systems. They also depend, especially in the case of the
M1 amplitudes, rather sensitively on the binding interaction among the constituent particles. There are also relativistic corrections which depend simultaneously on the recoil momentum of the composite system and on the use of the relativistic center-of-mass variables in the problem and which so far have not been considered in the literature.
We report here the first observation and measurement of the transition magnetic moment for a strongly forbidden S-S transition of an alkali atom. By using single-photon excitation of the 6S1/2-7S1/2 caesium transition in a quasi-static electric field, we have detected an electronic polarization of the excited state, specific to an interference effect occurring in mixed electric magnetic dipole transitions. Our measurements, independent of the vapour density, indicate that the magnetic dipole amplitude M 1 has the same size as the electric dipole amplitude E1 , induced by an electric field, parallel to the light wave polarization, and equal to 2.62 ± 0.21 V/cm. We also obtain the relative sign of M 1 and E1. Using a theoretical value of E 1 and a well-defined phase convention, we deduce for the magnetic moment of the transition < 7S, 1/ 2 | μ z | 6S, 1/ 2 > = - (4.24 ± 0.34) 10-5 |μB|, in good agreement with a theoretical estimate. This result can also be expressed in terms of the oscillator strength in zero electric field f6S-7S = 4.05 × 10-15, or of the single-photon M1 decay rate Γ 7S-6S = 0.93 x 10-6 s-1.
A relativistic and non-Markovian study is carried out on the magnetic-dipole emission of a hydrogen-like atom of large atomic number Z without perturbation approximation. The correlation spectra are derived analytically and the corresponding correlation functions are calculated numerically. The Markovian approximation is seen to be satisfied with more accuracy as compared with the case of electric-dipole emission while the relativistic corrections are quite larger. In transition 2S1/2 to 1S1/2, the relativistic values even become several times of the non-relativistic values. As a comparison with the magnetic-dipole emission, the electric-quadrupole emission in the case of the 2D3/2 to 1S1/2 transition is also studied.