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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 7131–7132
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Spectroscopy on a single trapped 137Ba+ ion for nuclear magnetic octupole moment determination: erratum

Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 7131-7132 (2013)
http://dx.doi.org/10.1364/OE.21.007131


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Abstract

A sign error in the equations for the mixing correction factors η and ζ from [Phys. Rev. A 77, 012512 (2008)] was identified. These equations were used in our article [Opt. Express 20, 21379 (2012)], resulting in a miscalculation of the corrected hyperfine constants and nuclear octupole moment. The revised values are presented.

© 2013 OSA

We recently became aware that Eq. (4) from [1

1. K. Beloy and A. Derevianko, “Second-order effects on the hyperfine structure of P states of alkali-metal atoms,” Phys. Rev. A 78, 032519 (2008) [CrossRef] .

] has an additional (−1)JJ factor in front compared to the corresponding equation from [2

2. K. Beloy, A. Derevianko, and W. R. Johnson, “Hyperfine structure of the metastable 3P2 state of alkaline-earth-metal atoms as an accurate probe of nuclear magnetic octupole moments,” Phys. Rev. A 77, 012512 (2008) [CrossRef] .

]. This equation is used for the calculation of the second-order energy corrections to a J level due to the mixing with a J′ level. For a typical JJ′ = 1 difference (mixing with the nearest J level), this leads to an additional (−1) factor which follows through to the values of the mixing correction factors η and ζ. As a result, η and ζ (Eqs. (5) and (6)) from [1

1. K. Beloy and A. Derevianko, “Second-order effects on the hyperfine structure of P states of alkali-metal atoms,” Phys. Rev. A 78, 032519 (2008) [CrossRef] .

] have the wrong sign. Similarly, we believe that the equations for η and ζ (Eqs. (6) and (7) from [2

2. K. Beloy, A. Derevianko, and W. R. Johnson, “Hyperfine structure of the metastable 3P2 state of alkaline-earth-metal atoms as an accurate probe of nuclear magnetic octupole moments,” Phys. Rev. A 77, 012512 (2008) [CrossRef] .

]) have the wrong sign. These were used in this form in our article [3

3. Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ ion for nuclear magnetic octupole moment determination,” Opt. Express 20, 21379–21384 (2012) [CrossRef] [PubMed] .

] and yielded wrong results for the corrected values of the hyperfine constants A, B and C, as well as the calculated nuclear octupole moment.

In order to avoid further confusion, we use Eq. (4) from [1

1. K. Beloy and A. Derevianko, “Second-order effects on the hyperfine structure of P states of alkali-metal atoms,” Phys. Rev. A 78, 032519 (2008) [CrossRef] .

] for writing the two correction factors in terms of any (γJ,γJ′) electronic states
η=(1)JJEγJEγJ(I+1)(2I+1)Iμ2[γJT1eγJ]2
(1)
ζ=(1)JJEγJEγJ(I+1)(2I+1)I2I+32I1μQγJT1eγJγJT2eγJ
(2)

Consequently, with the changed sign for the η and ζ correction factors, the corrected hyper-fine constants in Table 3 from our article [3

3. Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ ion for nuclear magnetic octupole moment determination,” Opt. Express 20, 21379–21384 (2012) [CrossRef] [PubMed] .

] should read as in Table 1.

Table 1. Hyperfine coupling constants.

table-icon
View This Table

The recalculated octupole moment becomes
Ω(Ba+137)=0.04885(53)(μN×b).

The sign error is confirmed by our similar recent measurements on the D5/2 manifold of the same ion, which yield the value of the octupole moment independent from the D3/2 measurements. Despite this sign error which affected some of the presented values, all qualitative statements made in our article [3

3. Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ ion for nuclear magnetic octupole moment determination,” Opt. Express 20, 21379–21384 (2012) [CrossRef] [PubMed] .

] are unaffected.

References and links

1.

K. Beloy and A. Derevianko, “Second-order effects on the hyperfine structure of P states of alkali-metal atoms,” Phys. Rev. A 78, 032519 (2008) [CrossRef] .

2.

K. Beloy, A. Derevianko, and W. R. Johnson, “Hyperfine structure of the metastable 3P2 state of alkaline-earth-metal atoms as an accurate probe of nuclear magnetic octupole moments,” Phys. Rev. A 77, 012512 (2008) [CrossRef] .

3.

Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ ion for nuclear magnetic octupole moment determination,” Opt. Express 20, 21379–21384 (2012) [CrossRef] [PubMed] .

OCIS Codes
(020.2930) Atomic and molecular physics : Hyperfine structure
(300.6520) Spectroscopy : Spectroscopy, trapped ion

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: March 6, 2013
Published: March 13, 2013

Citation
Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett, "Spectroscopy on a single trapped 137Ba+ ion for nuclear magnetic octupole moment determination: erratum," Opt. Express 21, 7131-7132 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-7131


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References

  1. K. Beloy and A. Derevianko, “Second-order effects on the hyperfine structure of P states of alkali-metal atoms,” Phys. Rev. A78, 032519 (2008). [CrossRef]
  2. K. Beloy, A. Derevianko, and W. R. Johnson, “Hyperfine structure of the metastable 3P2 state of alkaline-earth-metal atoms as an accurate probe of nuclear magnetic octupole moments,” Phys. Rev. A77, 012512 (2008). [CrossRef]
  3. Nicholas C. Lewty, Boon Leng Chuah, Radu Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ ion for nuclear magnetic octupole moment determination,” Opt. Express20, 21379–21384 (2012). [CrossRef] [PubMed]

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