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.

Table 1. Hyperfine coupling constants.

View Table

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.