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  has an additional (−1)J−J′ factor in front compared to the corresponding equation from . 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 J − J′ = 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  have the wrong sign. Similarly, we believe that the equations for η and ζ (Eqs. (6) and (7) from ) have the wrong sign. These were used in this form in our article  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  for writing the two correction factors in terms of any (γJ,γ ′J′) electronic states
The recalculated octupole moment becomes
The sign error is confirmed by our similar recent measurements on the D 5/2 manifold of the same ion, which yield the value of the octupole moment independent from the D 3/2 measurements. Despite this sign error which affected some of the presented values, all qualitative statements made in our article  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] .