Erratum: Determination of dipole and quadrupole polarizabilities of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Ba</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>by measurement of the fine structure of high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>L</mml:mi></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>9</m

Snow, Erica L.; Gearba, M. A.; Komara, R. A.; Lundeen, S. R.; Sturrus, William G.

doi:10.1103/physreva.74.049905

Cited by 11 publications

(22 citation statements)

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“…As in Ref. ͓4͔,the Gallagher et al data are treated for the relativistic and effective second-order energy contributions. The error bars on the Gallagher et al TABLE IV.…”

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confidence: 99%

Fine-structure measurements in high-Ln=17and 20 Rydberg states of barium

Snow

Lundeen

2007

Phys. Rev. A

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Fine-structure intervals in n = 17 and 20 barium Rydberg levels with 6 Յ L Յ 11 have been measured precisely with the resonant excitation Stark ionization spectroscopy microwave technique. The measured intervals were analyzed using the long-range polarization model, including allowance for the large nonadiabatic effects of the Ba + 5d level and the contributions of higher-order terms. The analysis determined improved values in atomic units of both dipole and quadrupole polarizabilities of Ba + , ␣ 1 = 123.88͑5͒ and ␣ 2 = 4420͑250͒.

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“…As in Ref. ͓4͔,the Gallagher et al data are treated for the relativistic and effective second-order energy contributions. The error bars on the Gallagher et al TABLE IV.…”

Section: ͑4͒mentioning

confidence: 99%

Fine-structure measurements in high-Ln=17and 20 Rydberg states of barium

Snow

Lundeen

2007

Phys. Rev. A

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“…We also give contributions from correlation effects and discuss them in terms of lower order many-body perturbation theory. PACS numbers: 31.15.Ar,31.15.Dv,31.25.Jf,32.10.Dk For a long time, studies of dipole and quadrupole polarizabilities have been highly interesting in many important aspects for both neutral atoms and ions [1,2,3,4,5,6,7,8,9,10,11]. These quantities are used in the case of ions to remove the quadratic Stark shifts in the recent proposed optical frequency standards where suitable instruments are not available for very precise measurements [12,13].…”

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confidence: 99%

An ab initio relativistic coupled-cluster theory of dipole and quadrupole polarizabilities: Applications to a few alkali atoms and alkaline earth ions

Sahoo

2007

Chemical Physics Letters

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We present a general approach within the relativistic coupled-cluster theory framework to calculate exactly the first order wave functions due to any rank perturbation operators. Using this method, we calculate the static dipole and quadrupole polarizabilities in some alkali atoms and alkaline earthmetal ions. This may be a good test of the present theory for different rank and parity interaction operators. This shows a wide range of applications including precise calculations of both parity and CP violating amplitudes due to rank zero and rank one weak interaction Hamiltonians. We also give contributions from correlation effects and discuss them in terms of lower order many-body perturbation theory. PACS numbers: 31.15.Ar,31.15.Dv,31.25.Jf,32.10.Dk For a long time, studies of dipole and quadrupole polarizabilities have been highly interesting in many important aspects for both neutral atoms and ions [1,2,3,4,5,6,7,8,9,10,11]. These quantities are used in the case of ions to remove the quadratic Stark shifts in the recent proposed optical frequency standards where suitable instruments are not available for very precise measurements [12,13]. Relativistic effects are also investigated for these properties [14,15]. Often theoretical studies are limited by many approximations to only approximate accuracy of the results [17,21]. In many cases, semiempirical methods, which combine the calculated E1 and E2 matrix elements of important states and the experimental excitation energies, are used to calculate these quantities [18,19]. Core electron contributions are always only estimated in this approach [1,18]. Therefore, an ab initio method is necessary to be able to, in principle, explain the importance of the electron correlation effects in the above properties and also test the manybody theories employed. These results are largely used to determine the van der Waals coefficients or dispersion factors [19,20,21,22]. In some cases, the Dirac-Fock (DF) method and relativistic random-phase approximations (RPA) for the Dalgarno-Lewis [21,22,23] or scalar relativistic Douglas-Kroll [15,16] effective Hamiltonians are used to determine these quantities. A number of calculations on these quantities using molecular codes and pseudopotentials have also been reported [9,15,16,17].Using the relativistic coupled-cluster (RCC) theory, we report here a novel approach for the first time to calculate wave functions up to all orders in the residual Coulomb interaction and first order due to any kind of perturbed operator in one valence systems. This takes care of the sum-over-states approach of the many-body perturbation † theory (MBPT) as an exact solution. This method can be applied to calculate the first order wave function due to dipole and quadrupole transition operators. Hence, polarizabilities can be obtained by calculating the expectation values of the corresponding operators. As an ab initio test of the theory, it is also possible to calculate the light shift ratio in ions like Ba + using the present method as proposed in [24]...

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“…By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values. DOI Experimental tests of atomic theory often involve the measurement of atomic state lifetimes, oscillator strengths, polarizabilities [1], and other properties which depend directly on atomic dipole matrix elements. Absolute measurements of these quantities can be difficult.…”

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Precision Measurement of Light Shifts in a Single TrappedBa+Ion

et al. 2005

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Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the 6S 1=2 and 5D 5=2 states to 0.1% precision. We find R S = D ÿ11:49413 at 514.531 nm where S;D are the light shifts of the m 1=2 splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.Experimental tests of atomic theory often involve the measurement of atomic state lifetimes, oscillator strengths, polarizabilities [1], and other properties which depend directly on atomic dipole matrix elements. Absolute measurements of these quantities can be difficult. Another approach [2] is to make high precision measurements of properties which can be directly calculated using modern atomic theory techniques and depend on ratios of atomic matrix elements. Here we report a 0.1% measurement of the ratio R of the ac Stark effect [or light shift (LS)] in the 6S 1=2 and 5D 3=2 states of a singly ionized barium ion, isoelectronic to the well-studied alkali atom Cs. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory.Since R is expressible as ratios of matrix elements (shown below), this measurement also establishes a sum rule relating the barium matrix elements known to 1% or better (i.e., h6S 1=2 jjrjj6P 1=2;3=2 i) to matrix elements with about 10 times worse experimental precision [3-6]. One of the latter, h5D 3=2 jjrjj6P 1=2 i, is crucial for a proposed atomic parity violation experiment [7][8][9]. In our scheme, a particular matrix element can be studied by choosing a light shift wavelength close to the corresponding dipole transition so that other contributions remain small. The technique is generalizable to other trapped ion species with metastable states.To second order in perturbation theory an off-resonant light beam of intensity I, frequency !, and polarization causes a frequency shift k;m in atomic level jk; mi ofwhere is the fine-structure constant, k stands for atomic quantum numbers nlj, and W k is the unperturbed energy of level k. The sums extend over continuum states. Though it is difficult to measure the light intensity at the site of a trapped ion, I cancels in a measured ratio of light shifts. The light shift due to circularly polarized off-resonant light acts effectively as a magnetic field pointing along the direction of light propagation [10,11]. In our case, a laboratory magnetic field (B 0 2:5 G) is aligned with the light shift beam (see Fig. 1). Therefore, if the same magnetic sublevels in two atomic states are used, there is only second order dependence of the ratio on polarization errors and misalignment of the li...

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Erratum: Determination of dipole and quadrupole polarizabilities ofBa+by measurement of the fine structure of high-Ln=9

Cited by 11 publications

References 0 publications

Fine-structure measurements in high-Ln=17and 20 Rydberg states of barium

Fine-structure measurements in high-Ln=17and 20 Rydberg states of barium

An ab initio relativistic coupled-cluster theory of dipole and quadrupole polarizabilities: Applications to a few alkali atoms and alkaline earth ions

Precision Measurement of Light Shifts in a Single TrappedBa+Ion

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