## Lifetime (in ms) and transition rate (in s^{−1}) of the hyperfine level of 3d^{9}4s ^{3}D_{3} either with or without nuclear quadrupole HFI

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**Table 4.** Lifetime (in ms) and transition rate (in s^{−1}) of the hyperfine level of 3d^{9}4s ^{3}D_{3} either with or without nuclear quadrupole HFI. Notation *f* denotes the natural abundance of a different isotope with nuclear spin *I* and µ denotes the magnetic dipole moment in nuclear magnetons. Notation *Q* denotes the nuclear electric quadrupole moment in barns. Values of *I*, µ and *Q* are referred from [27], where the uncertainties of µ and *Q* values are quoted in parentheses. The values of *f* are referred from [28]. All lifetimes are given in ms (*a*[*b*] = *a* **×** 10^{b}).

**Abstract**

Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d^{9}4s ^{3}D_{3} in Ni-like ions (*Z* = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in ^{181}Ta, ^{185}Re and ^{187}Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.