Dipole transition strengths in Ba<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow /><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>from Rydberg fine-structure measurements in Ba and Ba<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow /><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>

Woods, Shannon L.; Hanni, Mark E.; Lundeen, S. R.; Snow, Erica L.

doi:10.1103/physreva.82.012506

Cited by 16 publications

(11 citation statements)

References 15 publications

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“…Some years later, stimulated by related, but much smaller, anomalies in the structure of high-L Rydberg levels of Si 2+ , these vector splittings were explained as an indirect effect of the spin-orbit splittings in excited 2 P levels of Ba + [25]. These indirect spin-orbit splittings, or K-splittings as they were also called, were later exploited to extract precise measurements of dipole and quadrupole transition strengths in Ba + [26][27][28]. In the meantime, an apparently different type of vector splitting was predicted by Zygelman [15] using a Berry phase argument.…”

Section: Discussionmentioning

confidence: 99%

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Effective-potential model for high-LRydberg atoms

Woods

Lundeen

2012

Phys. Rev. A

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A description of fine-structure patterns in nonpenetrating high-L Rydberg atoms and ions is derived in a perturbative model in which the energy denominators occurring in the second-order perturbation theory are evaluated using the adiabatic expansion. The patterns of Rydberg energies that result are dominated by the expectation value of an effective potential containing a range of tensor orders and increasing negative powers of the Rydberg electron's radial coordinate. The coefficients of each term in the effective potential are expressed in terms of matrix elements and energies of the free ion at the core of the Rydberg system. Smaller corrections to these patterns due to application of the effective potential in second order and due to relativistic and spin contributions are also described. The effective potential provides a framework for extracting ion properties from measurements of high-L fine-structure patterns. )] 2 .The two terms proportional to r −6 agree with the results of Clark, Greene, and Miecznik [12]. The other terms are new. This completes the list of terms which contribute to E [2] proportional to r −s with s 8, as long as J c < 3. This is sufficient to account for all cases studied experimentally to date. The full effective potential to this point consists of the sum of all the second-order terms listed above plus the two first-order terms from Sec. II A. C. Rydberg intermediate statesThe expression for the second-order perturbation energy derived in Sec. II B excluded the contributions to E [2] from intermediate states where the core was in its ground electronic state. The number of such states depends on the ion in question. For an ion with 042505-8 1 2in which α D,2 (J c ) is given by Eq. (77) and

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Section: Discussionmentioning

confidence: 99%

“…The terms proportional to r −4 and r −6 agree with the results of Clark, Greene, and Miecznik [12] except that their expression for the coefficient analogous to β D,0 contains an additional contribution [the second term in their Eq. (28)]. …”

Section: B Second-order Energy (Core Excited Intermediate States)mentioning

confidence: 99%

Effective-potential model for high-LRydberg atoms

Woods

Lundeen

2012

Phys. Rev. A

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“…Experimental values for Ba +2 in the same atomic units are close to the full potential value, in the range of 10.1-10.75. 3,29,110 FIG The variation of moments and polarizabilities with origin and with atomic polarizability values is shown in Table V. The results calculated for the potential of Equation 28are labeled AJR because it matches the ex-core part of the AJR potential and the AJR atomic polarizabilities were used.…”

Section: Baf Potentialmentioning

confidence: 99%

“…[23][24][25] The reference point for very high accuracy analysis to atoms has been the work by Drachman [26][27][28] which has led to impressive results including relativistic and QED effects. 29,30 Limiting behavior in the Rydberg inverse Born-Oppenheimer region has been considered by Zon's group in several publications, including Elfimov et al 31 for the long-range dipole potential of polar molecules, and Dorofeev et al, 32 but these treatments omit the full complexity of interactions with a rotating core. 33 Frequency dependent polarizability is important at frequencies approaching electronic transitions.…”

Section: Introductionmentioning

confidence: 99%

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states

Coy

Grimes

Zhou

et al. 2016

The Journal of Chemical Physics

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The dependence of multipole moments and polarizabilities on external fields appears in many applications including biomolecular molecular mechanics, optical non-linearity, nanomaterial calculations, and the perturbation of spectroscopic signatures in atomic clocks. Over a wide range of distances, distributed multipole and polarizability potentials can be applied to obtain the variation of atom-centered atoms-in-molecules electric properties like bonding-quenched polarizability. For cylindrically symmetric charge distributions, we examine single-center and atom-centered effective polarization potentials in a non-relativistic approximation for Rydberg states. For ions, the multipole expansion is strongly origin-dependent, but we note that origin-independent invariants can be defined. The several families of invariants correspond to optimized representations differing by origin and number of terms. Among them, a representation at the center of dipole polarizability optimizes the accuracy of the potential with terms through 1/r. We formulate the single-center expansion in terms of polarization-modified effective multipole moments, defining a form related to the source-multipole expansion of Brink and Satchler. Atom-centered potentials are an origin independent alternative but are limited both by the properties allowed at each center and by the neglected effects like bond polarizability and charge flow. To enable comparisons between single-center effective potentials in Cartesian or spherical form and two-center effective potentials with differing levels of mutual induction between atomic centers, we give analytical expressions for the bond-length and origin-dependence of multipole and polarizability terms projected in the multipole and polarizability expansion of Buckingham. The atom-centered potentials can then be used with experimental data and ab initio calculations to estimate atoms-in-molecules properties. Some results are given for BaF and HF showing the utility and limitations of the approach. More detailed results on X Σ CaF are published separately.

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“…Being a monovalent atom, it is also amenable to precise theoretical predictions of atomic properties [6,7], making it a testbed for theoretical and experimental techniques. This has lead to high accuracy measurement of a variety of atomic properties including Landè g-factors [8][9][10][11], matrix elements [12,13], branching ratios from the P 1/2 and P 3/2 levels [14][15][16], lifetime measurements of the lower lying metastable D-states [17,18], fine-structure splittings [19] and hyperfine structure of odd isotopes [20,21].…”

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confidence: 99%

Precision measurements on the $^{138}$Ba$^+$ $6s^2S_{1/2}-5d^2D_{5/2}$ clock transition

Arnold,

Kaewuam,

Chanu

et al. 2019

Preprint

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Measurement of the 138 Ba + 6s 2 S 1/2 −5d 2 D 5/2 clock transition frequency and D 5/2 Landè gJ factor are reported. The clock transition frequency ν Ba + = 170 126 432 449 333.93±(0.34)stat±(0.20)sys, is obtained with accuracy limited by the frequency calibration of the maser used as a reference oscillator. The Landé gJ -factor for the 5d 2 D 5/2 level is determined to be gD = 1.200 367 31(24), which is a 100-fold improvement on previous measurements. The g-factor measurements are corrected for an ac magnetic field from trap-drive-induced currents in the electrodes, and data taken over a range of magnetic fields underscores the importance of accounting for this systematic.

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

Cited by 16 publications

References 15 publications

Effective-potential model for high-LRydberg atoms

Effective-potential model for high-LRydberg atoms

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states

Precision measurements on the $^{138}$Ba$^+$ $6s^2S_{1/2}-5d^2D_{5/2}$ clock transition

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