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    Energies are given in cm\(^{-1}\). See this link for conversion factors. Electric matrix elements are given in atomic units. Magnetic dipole matrix elements are given in Bohr magnetons, \(\mu_B\). The values of magnetic-dipole hyperfine constants A are listed in MHz. Dipole polarizabilities \(\alpha\) are given in atomic units, \(a_0^3\), where \(a_0\) is the Bohr radius. The atomic units for \(\alpha\) can be converted to SI units via \(\alpha /h \rm{[Hz/(V/m)^2]}\)\(=2.48832 \times 10^{-8} \alpha \) [a.u.], where the conversion coefficient is \( 4\pi \epsilon_0 a^3_0/h \) and the Planck constant \(h\) is factored out.

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    Data are taken from, “M. S. Safronova, V. A. Dzuba, V. V. Flambaum, U. I. Safronova, S. G. Porsev, and M. G. Kozlov, Phys. Rev. A 90, 052509 (2014), DOI: https://doi.org/10.1103/PhysRevA.90.052509", unless noted otherwise.
    Note:
    Transition types ‘M1’, ‘M2’, ’E1’, and ‘E2’ stand for magnetic dipole, magnetic quadrupole, electric dipole and electric quadrupole transition, respectively.
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    State Energy
    \(\ \lambda \)
    \( \alpha \)-variation sensitivity q Enhancement factor K Lifetime
    \(\ \) \(\ \rm{cm}^{-1} \) nm \(\ \rm{cm}^{-1} \) \(\ \) s
    $$4f^2 \ ^3H_4$$ 0 0 $$ $$ $$ $$
    $$5s4f \ ^3F_2$$ 2172(850) 4604(1300) -127720 -118 $$ 5.613 \times 10^{13}$$
    $$5s4f \ ^3F_3$$ 3826(840) 2614(470) -126746 -66 8.514
    $$4f^2 \ ^3H_5$$ 4939(100) 2025(40) 4917 2 0.331
    $$5s4f \ ^3F_4$$ 8463(810) 1182(100) -121952 -29 0.556
    $$4f^2 \ ^3F_2$$ 9207(50) 1086(6) 1324 0.3 0.373
    $$4f^2 \ ^3H_6$$ 9906(210) 1010(20) 9295 1.9 0.369
    $$4f^2 \ ^3F_3$$ 12532(90) 798(6) 4954 0.8 0.328
    $$4f^2 \ ^1G_4$$ 13108(110) 763(6) 4508 0.7 0.338
    $$5s4f \ ^1F_3$$ 14337(810) 698(40) -121525 -17 0.041
    $$4f^2 \ ^3F_4$$ 19717(200) 507(5) 10045 1 0.0648

    Transition Type Transition energy
    \(\ \lambda \) Matrix element
    Transition rate
    \(\ \) \(\ \) \(\ \rm{cm}^{-1} \) nm \(\ \) \(\ \rm{s}^{-1} \)
    $$ 4f5s\ ^3F_{2} - 4f^2\ ^3H_{4} $$ M2 2172 4604 0.03516 \(\ \mu_B \) 1.782\(\ \times 10^{-14} \)
    $$ 4f5s\ ^3F_{3} -4f^2\ ^3H_{4} $$ E1 3826 2614 0.00092 a.u. 1.366\(\ \times 10^{-2} \)
    $$ 4f5s\ ^3F_{3} - 4f5s \ ^3F_{2} $$ M1 1654 6046 2.43986 \(\ \mu_B \) 1.038\(\ \times 10^{-1} \)
    $$ 4f^2\ ^3H_{5} - 4f^2\ ^3H_{4} $$ M1 4939 2025 3.19913 \(\ \mu_B \) 3.024
    $$ 4f5s\ ^3F_{4} - 4f5s \ ^3F_{3} $$ M1 4637 2157 2.45429 \(\ \mu_B \) 1.8
    $$ 4f^2\ ^3F_{2} - 4f5s \ ^3F_{3} $$ E1 5381 1858 0.00652 a.u. 2.682
    $$ 4f^2\ ^3F_{2} - 4f^2 \ ^3H_{4} $$ E2 9207 1086 0.49808 a.u. 3.676\(\ \times 10^{-4} \)
    $$ 4f^2\ ^3H_{6} - 4f^2\ ^3H_{5} $$ M1 4967 2013 3.26426 \(\ \mu_B \) 2.709
    $$ 4f^2\ ^3F_{3} - 4f5s \ ^3F_{2} $$ E1 10360 965 0.00205 a.u. 1.351
    $$ 4f^2\ ^3F_{3} - 4f5s \ ^3F_{4} $$ E1 4069 2458 0.00601 a.u. 7.041\(\ \times 10^{-1} \)
    $$ 4f^2\ ^3F_{3} - 4f^2\ ^3F_{2} $$ M1 3325 3007 2.52457 \(\ \mu_B \) 9.028\(\ \times 10^{-1} \)
    $$ 4f^2\ ^3F_{3} - 4f^2\ ^3H_{4} $$ M1 12532 798 0.10761 \(\ \mu_B \) 8.782\(\ \times 10^{-2} \)
    $$ 4f^2\ ^1G_{4} - 4f5s \ ^3F_{3} $$ E1 9282 1077 0.00373 a.u. 2.506
    $$ 4f^2\ ^1G_{4} - 4f^2\ ^3H_{5} $$ M1 8169 1224 0.52656 \(\ \mu_B \) 4.530\(\ \times 10^{-1} \)
    $$ 4f^2\ ^1G_{4} - 4f^2\ ^3F_{3} $$ M1 576 17361 1.95991 \(\ \mu_B \) 2.200\(\ \times 10^{-3} \)
    $$ 4f5s\ ^1F_{3} - 4f^2\ ^3H_{4} $$ E1 14337 698 0.00475 a.u. 1.929\(\ \times 10^{1} \)
    $$ 4f5s\ ^1F_{3} - 4f5s \ ^3F_{2} $$ M1 12165 822 0.80183 \(\ \mu_B \) 4.46
    $$ 4f5s\ ^1F_{3} - 4f5s \ ^3F_{4} $$ M1 5874 1702 0.80877 \(\ \mu_B \) 5.108\(\ \times 10^{-1} \)
    $$ 4f5s\ ^1F_{3} - 4f^2\ ^3F_{4} $$ E1 1229 8137 0.01529 a.u. 1.255 \(\ \times 10^{-1} \)
    $$ 4f^2\ ^3F_{4} - 4f5s \ ^1F_{3} $$ E1 5380 1859 0.01635 a.u. 9.374
    $$ 4f^2\ ^3F_{4} - 4f5s \ ^3F_{3} $$ E1 15891 629 0.00120 a.u. 1.309
    $$ 4f^2\ ^3F_{4} - 4f^2\ ^3H_{5} $$ M1 14778 677 0.40844 \(\ \mu_B \) 1.614
    $$ 4f^2\ ^3F_{4} - 4f^2\ ^3F_{3} $$ M1 7185 1392 1.67986 \(\ \mu_B \) 3.137