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 Optical Society of America
We recently became aware that Eq. (4) from [1] has an additional (−1)J−J′ factor in front compared to the corresponding equation from [2]. 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 [1] have the wrong sign. Similarly, we believe that the equations for η and ζ (Eqs. (6) and (7) from [2]) have the wrong sign. These were used in this form in our article [3] 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] for writing the two correction factors in terms of any (γJ,γ ′J′) electronic states
Consequently, with the changed sign for the η and ζ correction factors, the corrected hyper-fine constants in Table 3 from our article [3] should read as in Table 1.
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 [3] 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] .