Lifetime (in ms) and transition rate (in s⁻¹) of the hyperfine level of 3d⁹4s ³D₃ either with or without nuclear quadrupole HFI

<p><b>Table 4.</b> Lifetime (in ms) and transition rate (in s⁻¹) of the hyperfine level of 3d⁹4s ³D₃ either with or without nuclear quadrupole HFI. Notation <em>f</em> denotes the natural abundance of a different isotope with nuclear spin <em>I</em> and µ denotes the magnetic dipole moment in nuclear magnetons. Notation <em>Q</em> denotes the nuclear electric quadrupole moment in barns. Values of <em>I</em>, µ and <em>Q</em> are referred from [<a href="http://iopscience.iop.org/0953-4075/46/14/145001/article#b467799bib27" target="_blank">27</a>], where the uncertainties of µ and <em>Q</em> values are quoted in parentheses. The values of <em>f</em> are referred from [<a href="http://iopscience.iop.org/0953-4075/46/14/145001/article#b467799bib28" target="_blank">28</a>]. All lifetimes are given in ms (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10^<em>b</em>).</p> <p><strong>Abstract</strong></p> <p>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 3d⁹4s ³D₃ in Ni-like ions (<em>Z</em> = 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 ¹⁸¹Ta, ¹⁸⁵Re and ¹⁸⁷Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.</p

Excitation energies of levels in the 3d⁹4s configuration for W⁴⁶⁺ from different theoretical approaches compared to experiment and other calculations

<p><b>Table 1.</b> Excitation energies of levels in the 3d⁹4s configuration for W⁴⁶⁺ from different theoretical approaches compared to experiment and other calculations.</p> <p><strong>Abstract</strong></p> <p>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 3d⁹4s ³D₃ in Ni-like ions (<em>Z</em> = 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 ¹⁸¹Ta, ¹⁸⁵Re and ¹⁸⁷Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.</p

Lifetimes of different hyperfine levels of 3d⁹4s ³D₃, <em>τ_F</em>, relative to the lifetime of 3d⁹4s ³D₃ which decays by the pure M3 transition, <em>τ_M3</em>

<p><strong>Figure 2.</strong> Lifetimes of different hyperfine levels of 3d⁹4s ³D₃, <em>τ_F</em>, relative to the lifetime of 3d⁹4s ³D₃ which decays by the pure M3 transition, <em>τ_M3</em>. Results for all hyperfine levels of different isotopes in table <a href="http://iopscience.iop.org/0953-4075/46/14/145001/article#b467799t4" target="_blank">4</a> are presented.</p> <p><strong>Abstract</strong></p> <p>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 3d⁹4s ³D₃ in Ni-like ions (<em>Z</em> = 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 ¹⁸¹Ta, ¹⁸⁵Re and ¹⁸⁷Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.</p

Convergence of the calculated transition rates for two E2 transitions and one M3 transition in W⁴⁶⁺

<p><b>Table 2.</b> Convergence of the calculated transition rates for two E2 transitions and one M3 transition in W⁴⁶⁺. All transition rates are given in s⁻¹. Each E2 transition rate is given in both Babushkin and Coulomb gauges (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10^<em>b</em>).</p> <p><strong>Abstract</strong></p> <p>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 3d⁹4s ³D₃ in Ni-like ions (<em>Z</em> = 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 ¹⁸¹Ta, ¹⁸⁵Re and ¹⁸⁷Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.</p

Calculated transition rates (in s⁻¹) of the M3 transition and two E2 transitions in ions along the Ni-like isoelectronic sequence

<p><b>Table 3.</b> Calculated transition rates (in s⁻¹) of the M3 transition and two E2 transitions in ions along the Ni-like isoelectronic sequence. Each E2 transition rate is given in both Babushkin and Coulomb gauges (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10^<em>b</em>).</p> <p><strong>Abstract</strong></p> <p>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 3d⁹4s ³D₃ in Ni-like ions (<em>Z</em> = 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 ¹⁸¹Ta, ¹⁸⁵Re and ¹⁸⁷Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.</p