Gauge effects in bound-bound Rydberg transition matrix elements

Accurate data on electric-dipole transition matrix elements (EDTMs) for bound-bound Rydberg-atom tran-sitions have become increasingly important in science and technology. Here we compute radial EDTMs of rubidium in length, velocity, and acceleration forms for electric-dipole-allowed transitions between states with principal and angular-momentum quantum numbers n and t ranging from 15 to 100. Wave functions are computed based upon model potentials from [Phys. Rev. A 49, 982 (1994)]. Length-gauge EDTMs of strong low-t Rydberg transitions, often employed in research and technology, are found to deviate from the funda-mentally more accurate velocity-gauge form by approximately-n-independent and series-dependent shifts. The shift amount peaks at about 0.34 ea0 for the Rb nD <-> (n + 1)P series, a particularly strong Rydberg-transition series in Rb. The shift corresponds to relative EDTM corrections of up to approximate to 10(-3), which can be of concern in high-precision applications. We discuss the physical reasons for the observed gauge differences, explain the conditions for applicability of the velocity-and length-gauge forms for different transition series, and present a decision tree of how to choose EDTMs.

Automated summary

This study computes the electric-dipole transition matrix elements (EDTMs) of rubidium using different gauges. It is found that the commonly used length-gauge EDTMs for strong low-Rydberg transitions deviate from the more accurate velocity-gauge form, with a shift amount that is independent of the principal quantum number n and dependent on the transition series. This shift can have significant impact in high-precision applications.