Dipole and quadrupole transition strengths inBa+from measurements ofKsplittings in high-Lbarium Rydberg levels

Dipole transition strengths in Ba+from Rydberg fine-structure measurements in Ba and Ba+

“…The energy levels can then be expressed in terms of V eff by [1] (nL) + E [2] (nL), (6) where E 0 (n) is the zeroth-order energy of a Rydberg level with principle quantum number n. The second term, E rel , is a relativistic correction due to the p 4 contributions to kinetic energy and is given by…”

“…The fourth term, E [2] (nL), comes from application of V eff in second order and has been calculated analytically by Drake and Swainson [10] in the approximation that only the term proportional to α 2 D is significant. The relatively small contributions to the measured frequency offsets from E rel and E [2] can be calculated and subtracted from the measured offsets to form a quantity that should scale simply with the radial expectation values in the relevant states. Specifically, we expect…”

“…Note that the intercept from this alternate fit is consistent with the result obtained. 000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 (∆E obs -∆E rel -∆E [2] )/∆<r …”

“…Some years later, the physical origin of these anomalously large level splittings was traced to the influence of nonadiabatic corrections to the Rydberg fine structure, which introduces K splittings in the Rydberg levels proportional to the fine-structure splittings in the excited levels of the Ba + ion [13]. The Rydberg fine-structure energies and the related K splittings are dominated by the second-order perturbation energies with contributions from all multipole orders, but the K splittings vanish identically if the core excitation energies are large enough so that the adiabatic approximation is valid [2]. More generally, the perturbation energies can be expanded in a sequence of nonadiabatic corrections that give nonzero values of the K splittings.…”

“…In some cases, however, the transitions to the lowest excited states are dominant, allowing the Rydberg measurements to determine specific transition strengths. A good example is the recent study of transition strengths in the Ba + ion [2]. A measurement of that ion's dipole polarizability, obtained from study of fine-structure patterns in high-L barium Rydberg levels [3], was combined with measurements of K splittings in the same Rydberg levels [3] to infer transition strengths between the 6 2 S 1/2 ground state of Ba + and the two 6 2 P excited levels.…”