An improved simple model for α decay half-lives

α decay is a significant decay process of unstable nuclei and was observed in the early days of nuclear physics. In 1896, Becquerel first observed this process as an unknown radiation. It was not defined until 1899 [1]. Subsequently, Rutherford explained it as the process of a parent nucleus releasing a $ ^{4}{\rm{He}} $ particle. In 1928, Gamow [2] and Condon and Gurney [3] independently explained α decay as a quantum tunneling process. Since then, α decay has been a popular topic in nuclear physics [4–29]. It is often studied to investigate nuclear forces, obtain information of nuclear structure including shell effects [22, 23], low-lying states [24], nuclear shape coexistences [25, 26], ground states [8], and energy levels [4] and particularly identify new superheavy elements and/or isotopes through the observation of α decay chains [14, 18, 27–29].

With the advancement of experimental technology, significant progress have been achieved in the experimental [30–36] and theoretical [37–66] fields for α decay. Experimentally, in recent years, a series of superheavy elements and/or isotopes have been successfully synthesized through warm, hot, and cold fusion reactions. For instance, in 2011, the superheavy element $ Z = 118 $ was successfully synthesized by conducting $ ^{48}{\rm{Ca}} $-induced hot fusion reactions using the actinide element $ {\rm{Cf}} $ as the target material [36]. More recently, a new α-emitting isotope, $ ^{214}{\rm{U}} $, was successfully identified in the fusion-evaporation reaction of $ ^{182}{\rm{W}} $ ($ ^{36}{\rm{Ar}} $, 4n) [34]. Theoretically, multiple models have been proposed to study α decay, including effective liquid drop model [38, 39], fission-like model [52], generalized liquid drop model (GLDM) [48, 49], density dependent M3Y (DDM3Y) effective interaction [43, 44], and several others [58–61]. Furthermore, many empirical formulas have been adopted to investigate α decay based on the Geiger-Nuttall (G-N) law and/or the quantum tunneling effect [67], such as the universal decay law (UDL) [68, 69], Viola-Seaborg-Sobiczewski (VSS) formula [70], Royer formula [45], Hatsukawa formula [71], Deng-Zhang-Royer formula (DUR) [72], Sobiczewski-Parkhomenko (SP) formula [73], and so forth [74–82].

In 2020, Bayrak proposed a phenomenological harmonic oscillator potential model (HOPM) [83] based on the Wentzel-Kramers-Brillouin (WKB) method and Bohr-Sommerfeld quantization condition. With this model, taking the α preformation probability $ P_{\alpha} $ as a constant and obtaining the depth parameter of nuclear potential $ V_0 $ by fitting the experimental data for the even-even nuclei of nuclear property table NUBASE2016 [84], the favored α decay half-lives of 263 nuclei including 136 even-even, 48 even-odd, 49 odd-even, and 30 odd-odd nuclei were calculated. Considering the increasing volume of experimental data and taking the preformation probabilities $ P_{\alpha} $ from Xu and Ren [77], which were derived by fitting experimental α decay half-lives, based on the HOPM, we obtain the parameter $ V_0=162.6 $ MeV by refitting 178 α decay half-lives of even-even nuclei obtained from the latest nuclear property table NUBASE2020 [85] with a corresponding root-mean-square (rms) deviation of $ \sigma=0.322 $. However, when applying the HOPM to calculate unfavored α decay half-lives, the emitted α particle carries a non-zero orbital angular momentum, i.e., $ l \neq 0 $, which means that the effect of centrifugal potential is introduced in the total interaction potential between the emitted α particle and the daughter nucleus. In favored α decay, the orbital angular momentum carried away by the emitted α particle is $ l=0 $; thus, the centrifugal potential is equal to zero. Under this condition, an analytical expression can be obtained for the logarithmic form of favored α decay half-lives with only one parameter. To extend the applicability of the analytical expression within the HOPM framework to consider the contribution of the centrifugal potential, adding a new term $ d\sqrt{l(l+1)} $ (d is the adjustable parameter) to the logarithmic form of favored α decay half-lives, we generalize this model to unfavored α decay and propose an improved simple model (ISM) for calculating favored and unfavored α decay half-lives. Fitting the experimental data of 205 unfavored α decay half-lives, we obtain $ d=0.381 $. Compared with the HOPM, the rms deviations of 128 unfavored odd-A and 77 unfavored odd-odd nuclei through the ISM are reduced from 1.292 and 1.339 to 0.592 and 0.621, respectively. Meanwhile, the rms deviation for all 693 nuclei is only 0.452. In addition, we further extend the ISM to predicting the α decay half-lives of 144 even-even, odd-A, and odd-odd nuclei with $ Z = 117,118,119, $ and $ 120 $. For comparison, the DUR and MUDL are also used. The corresponding predictions of these formulas are mostly consistent.

The remainder of this article is organized as follows. Section II briefly introduces the theoretical framework. Detailed numerical results and discussion are given in Section III. Finally, a summary is provided in Section IV.

The α decay half-life $ T_{1/2} $ is related to the decay width Γ as

where $ \hbar $ is the reduced Planck constant. Γ is the α-decay width including the α particle preformation probability $ P_\alpha $, the normalization factor F, and the penetration probability P. In the HOPM, it can be expressed as [57]

where $\mu={m_d m_{\alpha}}/(m_d +m_{\alpha})$ is the reduced mass of the α particle and daughter nucleus in the center-of-mass system with $ m_d $ and $ m_{\alpha} $ being the masses of the daughter nucleus and α particle, respectively, obtained from NUBASE2020 [85]. Owing to the complexity of nuclear potential and the many-body problem in nuclear physics, $ P_{\alpha} $ is a quantity that is challenging to ascertain. Referring the study of Xu and Ren [77], in this paper, the probability of α particle preformation is set as $ P_\alpha=0.43 $ for even-even nuclei, $ P_\alpha=0.35 $ for odd-A nuclei, and $ P_\alpha=0.18 $ for odd-odd nuclei.

The normalization factor F, describing the assault frequency or the collision probability of the α particle, can be expressed as

$P={\rm e}^{-2S}$, the barrier penetration probability of the α particle, is calculated using the semi-classical WKB approximation. S denotes the action integral. It is given by [83]

where $ k(r)=\sqrt{\dfrac{2\mu}{\hbar^2}(V(r)-Q_{\alpha})} $ is the wave number of the α particle, and r is the center-of-mass distance between the preformed α particle and the daughter nucleus. $ Q_{\alpha} $ and $ V(r) $ denote the α decay energy and total interaction potential between the emitted α particle and daughter nucleus, respectively. $ r_1 $ and $ r_2 $ denote the classical turning points, which satisfy the conditions $V(r_1)=V(r_2)= Q_{\alpha}$. $ Q_{\alpha} $ is calculated using

where $ M(A,Z) $, $ M(A-4,Z-2) $, and $M(^{4}{\rm He}$) represent the mass excesses of the parent nucleus, daughter nucleus, and α particle, respectively. The total interaction potential $ V(r) $ is expressed as

where $ V_N(r) $ is the nuclear potential. In this paper, it is selected as the modified harmonic oscillator form and can be expressed as [20, 83]

where $ V_1 $ and $ V_0 $ are the diffusivity and depth of nuclear potential, respectively. $ V_C $, the Coulomb potential, is taken as the potential of a uniformly charged sphere with sharp radius R. It is expressed as

where $ e^{2}=1.4399652 $ MeV$ \cdot $fm represents the square of the electronic elementary charge. $ Z_d $ and $ Z_{\alpha} $ are the proton numbers of the daughter nucleus and preformed α particle, respectively. The sharp radius R is calculated using the empirical radius formula $R=1.28A_d^{1/3}- 0.76+ 0.8A_d^{-1/3}$, where $ A_d $ is the mass numbers of the daughter nucleus [45]. $ V_l $ is the centrifugal potential and can be expressed as

where l denotes the orbital angular momentum carried away by the emitted α particle. For favored α decay, the total interaction potential $ V(r) $ can be expressed as [83]

where $ C_0=\dfrac{3Z_d\,Z_{\alpha}\,e^2}{2R} $, $ C_1=\dfrac{Z_d\,Z_{\alpha}\,e^2}{2R^3} $, and $ C_2=Z_d\,Z_{\alpha}e^2 $. Using $ ^{148}{\rm{Sm}} \to ^{144}{\rm{Nd}} + ^{4}{\rm{He}} $ as an example, the schematic diagram of the total interaction potential $ V(r) $ is shown in Fig. 1. Using the conditions $ V(r_1)=V(r_2)=Q_{\alpha} $, we obtain $ r_1=\sqrt{\dfrac{Q_{\alpha}+V_0-C_0}{V_1-C_1}} $ and $ r_2=\dfrac{C_2}{Q_{\alpha}} $.

Figure 1.  (color online) Variation in the total interaction potential $ V(r) $ for the parent nucleus $ ^{148}{\rm{Sm}} $ as a function of r.

The Bohr-Sommerfeld quantization condition, a crucial component of the WKB approximation, is employed to reduce the system's degrees of freedom. It is expressed as

where $ G_{\alpha} = 2n_r + l $ is the main quantum number of α decay, with $ n_r $ and l being the radial and angular momentum quantum numbers, respectively. It is given by [77]

where N is the neutron number of the parent nucleus.

Through the integral operation of Eq. (11), the analytical expression between $ V_0 $ and $ V_1 $ is obtained as follows:

where $ C_0<(Q_{\alpha}+V_0) $ and $ C_1< V_1 $. Using Eq. (13), the normalization factor F and action integral S can be analytical expressed as

Subsequently, the logarithmic form of favored α decay half-lives can be expressed as

Similar to the unfavored α decay, the emitted α particle carries a non-zero orbital angular momentum ($ l \neq 0 $); thus, the effect of centrifugal potential must be considered in the total interaction potential, which means that the total barrier is higher, resulting in a reduced penetration probability and consequently a longer α decay half-life. Under this condition, this effect must be considered for unfavored α decay. Generally, two methods can be used to solve this problem: directly adding the terms of orbital angular momentum $ d\,l(l+1) $ [61, 72, 78] or $ d\,\sqrt{l(l+1)} $ [74] to the corresponding models or empirical formulas. In this paper, if $ l \neq 0 $, the wave number $ k(r) $ under integration can not be determined using analytical solutions in the HOPM framework, then Eqs. (4), (11), and (14) can not be calculated analytically. Consequently, to generalize the applicability of the analytic expression within the framework of HOPM to study unfavored α decay half-lives, we have augmented the original analytic Eq. (16) with an additional term $ d\sqrt{l(l+1)} $, thereby proposing the ISM for calculating α decay half-lives. It can be expressed as

In 2020, Deng et al. presented an unitary Royer formula (DUR) for α decay half-lives. It can be expressed as [72]

where A and Z are the mass and proton numbers of the parent nucleus, respectively. The adjustable parameters are $ a=-26.8125 $, $ b=-1.1255 $, $ c=1.6057 $, and $d= 0.0513$, respectively. h is given by

In 2021, considering the effects of the orbital angular momentum and isospin, Soylu et al. modified the UDL formula for α decay and cluster radioactivity (MUDL). It can be expressed as [74]

where $ \mathcal{A}=A_{\alpha}A_d/(A_{\alpha}+A_d) $, with $ A_{\alpha} $ and $ A_d $ being the mass numbers of the emitted α particle and the daughter nucleus, respectively. The adjustable parameters are $ a=0.4392 $, $ b=-0.3944 $, $ c=-27.0649 $, and $ d=0.0052 $, respectively.

Based on WKB method and Bohr-Sommerfeld quantization condition, Bayrak proposed the HOPM to calculate the favored α decay half-lives of 263 nuclei. Considering the increase in experimental data and the effect of centrifugal potential, we generalize the HOPM to unfavored α decay and propose an ISM to calculate α decay half-lives. In this paper, to redetermine the only one adjustable parameter $ V_0 $ in HOPM, we use a genetic algorithm with the optimal solution of the standard deviation σ (The detailed definition of σ is given in following) as the objective function to obtain it. Fitting experimental α decay half-lives of 178 even-even nuclei, which are obtained from the latest nuclear property table NUBASE2020, we obtain the ideal value as $ V_0=162.6 $ MeV. Using the obtained $ V_0 $, based on Eq. (16), we first systemically calculate the favored α decay half-lives. The detail results for even-even, odd-A, and odd-odd nuclei are listed in Tables 2–4, respectively. These three tables share the same frameworks, the first three columns denote the α decay, experimental α decay energy, and minimum angular momentum carried away by the emitted α particle, respectively. The fourth and fifth columns represent the experimental α decay half-lives and those calculated using the HOPM in the logarithmic form, denoted as $ {\rm{log}}_{10}{T}_{1/2}^{\rm{\,exp}} $ and $ {\rm{log}}_{10}{T}_{1/2}^{\rm{\,HOPM}} $, respectively. These three tables show that our calculated results agree closely with the experimental data for most nuclei, with some exceptions, such as $ ^{268}{\rm{Hs}} $, $ ^{282}{\rm{Ds}} $, $ ^{185}{\rm{Pt}} $, $ ^{197}{\rm{Bi^{m}}} $, $ ^{231}{\rm{Pa}} $, $ ^{225}{\rm{Np}} $, $ ^{263}{\rm{Hs^{m}}} $, $ ^{196}{\rm{At^{m}}} $, and $ ^{198}{\rm{Fr^{m}}} $. For $ ^{268}{\rm{Hs}} $ and $ ^{282}{\rm{Ds}} $, the deformation around the region with $ N=184 $ and $ Z=108 $ may result in large deviations for these two nuclei [78, 88, 89]. For $ ^{197}{\rm{Bi^{m}}} $, $ ^{263}{\rm{Hs^{m}}} $, $ ^{196}{\rm{At^{m}}} $, and $ ^{198}{\rm{Fr^{m}}} $ in these excited state, the corresponding experimental data may have some uncertainty [90]. For a intuitive comparison, the differences between the experimental and calculated half-lives for even-even, odd-A, and odd-odd nuclei in the logarithmic form are plotted in Fig. 2. The figure clearly shows that the deviations between the experimental and calculated data are mostly within the range of $ \pm 0.5 $. This means our calculated results can reproduce the experimental data well.

α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
146Sm$ \to {}^{142}{\rm{Nd}} $	2.5288 ± 0.0028	0	$ 15.3316 ^{+ 0.0426 }_{- 0.0472 } $	$ 15.3856 ^{+ 0.0346 }_{- 0.0446 } $
148Sm$ \to {}^{144}{\rm{Nd}} $	1.9870 ± 0.0004	0	$ 23.2984 ^{+ 0.0815 }_{- 0.1004 } $	$ 23.4501 ^{+ 0.0072 }_{- 0.0173 } $
148Gd$ \to {}^{144}{\rm{Sm}} $	3.2713 ± 0.0003	0	$ 9.3522 ^{+ 0.0060 }_{- 0.0061 } $	$ 9.2179 ^{+ 0.0025 }_{- 0.0127 } $
150Gd$ \to {}^{146}{\rm{Sm}} $	2.8070 ± 0.0060	0	$ 13.7519 ^{+ 0.0190 }_{- 0.0199 } $	$ 13.7319 ^{+ 0.0653 }_{- 0.0757 } $
152Gd$ \to {}^{148}{\rm{Sm}} $	2.2038 ± 0.0010	0	$ 21.5325 ^{+ 0.0310 }_{- 0.0334 } $	$ 21.6542 ^{+ 0.0158 }_{- 0.0262 } $
150Dy$ \to {}^{146}{\rm{Gd}} $	4.3513 ± 0.0015	0	$ 2.6337 ^{+ 0.0030 }_{- 0.0030 } $	$ 2.8945 ^{+ 0.0086 }_{- 0.0185 } $
152Dy$ \to {}^{148}{\rm{Gd}} $	3.7270 ± 0.0040	0	$ 6.9329 ^{+ 0.0036 }_{- 0.0037 } $	$ 6.9305 ^{+ 0.0290 }_{- 0.0392 } $
154Dy$ \to {}^{150}{\rm{Gd}} $	2.9450 ± 0.0050	0	$ 13.9762 ^{+ 0.1761 }_{- 0.3010 } $	$ 13.7609 ^{+ 0.0523 }_{- 0.0628 } $
152Er$ \to {}^{148}{\rm{Dy}} $	4.9343 ± 0.0016	0	$ 1.0567 ^{+ 0.0042 }_{- 0.0042 } $	$ 0.8946 ^{+ 0.0077 }_{- 0.0178 } $
154Er$ \to {}^{150}{\rm{Dy}} $	4.2797 ± 0.0026	0	$ 4.6778 ^{+ 0.0104 }_{- 0.0106 } $	$ 4.4508 ^{+ 0.0157 }_{- 0.0260 } $
156Er$ \to {}^{152}{\rm{Dy}} $	3.4810 ± 0.0025	0	$ 9.9890 ^{+ 0.0217 }_{- 0.0229 } $	$ 10.1396 ^{+ 0.0209 }_{- 0.0314 } $
154Yb$ \to {}^{150}{\rm{Er}} $	5.4743 ± 0.0017	0	$ -0.3549 ^{+ 0.0021 }_{- 0.0021 } $	$ -0.5701 ^{+ 0.0072 }_{- 0.0173 } $
156Yb$ \to {}^{152}{\rm{Er}} $	4.8100 ± 0.0040	0	$ 2.4166 ^{+ 0.0115 }_{- 0.0118 } $	$ 2.5614 ^{+ 0.0208 }_{- 0.0312 } $
156Hf$ \to {}^{152}{\rm{Yb}} $	6.0260 ± 0.0030	0	$ -1.6383 ^{+ 0.0185 }_{- 0.0193 } $	$ -1.8568 ^{+ 0.0112 }_{- 0.0215 } $
158Hf$ \to {}^{154}{\rm{Yb}} $	5.4048 ± 0.0027	0	$ 0.8084 ^{+ 0.0105 }_{- 0.0108 } $	$ 0.6970 ^{+ 0.0120 }_{- 0.0225 } $
160Hf$ \to {}^{156}{\rm{Yb}} $	4.9019 ± 0.0026	0	$ 3.2884 ^{+ 0.0063 }_{- 0.0064 } $	$ 3.1354 ^{+ 0.0135 }_{- 0.0242 } $
162Hf$ \to {}^{158}{\rm{Yb}} $	4.4160 ± 0.0050	0	$ 5.6924 ^{+ 0.0098 }_{- 0.0100 } $	$ 5.8968 ^{+ 0.0306 }_{- 0.0415 } $
158W$ \to {}^{154}{\rm{Hf}} $	6.6125 ± 0.0026	0	$ -2.8447 ^{+ 0.0515 }_{- 0.0584 } $	$ -3.0775 ^{+ 0.0086 }_{- 0.0190 } $
160W$ \to {}^{156}{\rm{Hf}} $	6.0660 ± 0.0050	0	$ -0.9853 ^{+ 0.0235 }_{- 0.0248 } $	$ -1.1138 ^{+ 0.0191 }_{- 0.0296 } $
162W$ \to {}^{158}{\rm{Hf}} $	5.6783 ± 0.0024	0	$ 0.4204 ^{+ 0.0417 }_{- 0.0462 } $	$ 0.4647 ^{+ 0.0102 }_{- 0.0209 } $
164W$ \to {}^{160}{\rm{Hf}} $	5.2783 ± 0.0020	0	$ 2.2196 ^{+ 0.0136 }_{- 0.0140 } $	$ 2.2821 ^{+ 0.0095 }_{- 0.0203 } $
166W$ \to {}^{162}{\rm{Hf}} $	4.8560 ± 0.0040	0	$ 4.7392 ^{+ 0.0134 }_{- 0.0138 } $	$ 4.4509 ^{+ 0.0218 }_{- 0.0327 } $
168W$ \to {}^{164}{\rm{Hf}} $	4.5010 ± 0.0110	0	$ 6.2016 ^{+ 0.0159 }_{- 0.0165 } $	$ 6.5191 ^{+ 0.0673 }_{- 0.0786 } $
180W$ \to {}^{176}{\rm{Hf}} $	2.5153 ± 0.0010	0	$ 25.7005 ^{+ 0.1187 }_{- 0.1640 } $	$ 25.5606 ^{+ 0.0151 }_{- 0.0268 } $
162Os$ \to {}^{158}{\rm{W}} $	6.7678 ± 0.0029	0	$ -2.6778 ^{+ 0.0202 }_{- 0.0212 } $	$ -2.7616 ^{+ 0.0096 }_{- 0.0201 } $
164Os$ \to {}^{160}{\rm{W}} $	6.4790 ± 0.0050	0	$ -1.6619 ^{+ 0.0202 }_{- 0.0212 } $	$ -1.7578 ^{+ 0.0177 }_{- 0.0284 } $
166Os$ \to {}^{162}{\rm{W}} $	6.1430 ± 0.0030	0	$ -0.5928 ^{+ 0.0101 }_{- 0.0103 } $	$ -0.4993 ^{+ 0.0116 }_{- 0.0224 } $
Continued on next page

Table 2.  Calculations of α decay half-lives for even-even nuclei. The α decay energy and experimental half-lives are obtained from the latest evaluated nuclear properties table NUBASE2020 [85–87], with the units being MeV and s, respectively.

Table 2-continued from previous page
α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
168Os$ \to {}^{164}{\rm{W}} $	5.8156 ± 0.0027	0	$ 0.6888 ^{+ 0.0202 }_{- 0.0212 } $	$ 0.8372 ^{+ 0.0114 }_{- 0.0223 } $
170Os$ \to {}^{166}{\rm{W}} $	5.5369 ± 0.0027	0	$ 1.8897 ^{+ 0.0105 }_{- 0.0107 } $	$ 2.0747 ^{+ 0.0123 }_{- 0.0233 } $
172Os$ \to {}^{168}{\rm{W}} $	5.2240 ± 0.0070	0	$ 3.2078 ^{+ 0.0199 }_{- 0.0209 } $	$ 3.5841 ^{+ 0.0349 }_{- 0.0461 } $
174Os$ \to {}^{170}{\rm{W}} $	4.8710 ± 0.0100	0	$ 5.2632 ^{+ 0.0378 }_{- 0.0414 } $	$ 5.4643 ^{+ 0.0557 }_{- 0.0671 } $
186Os$ \to {}^{182}{\rm{W}} $	2.8212 ± 0.0009	0	$ 22.8001 ^{+ 0.1903 }_{- 0.3468 } $	$ 22.9093 ^{+ 0.0117 }_{- 0.0236 } $
166Pt$ \to {}^{162}{\rm{Os}} $	7.2920 ± 0.0070	0	$ -3.6716 ^{+ 0.0831 }_{- 0.1029 } $	$ -3.6097 ^{+ 0.0210 }_{- 0.0318 } $
168Pt$ \to {}^{164}{\rm{Os}} $	6.9900 ± 0.0030	0	$ -2.6946 ^{+ 0.0210 }_{- 0.0221 } $	$ -2.6525 ^{+ 0.0097 }_{- 0.0205 } $
170Pt$ \to {}^{166}{\rm{Os}} $	6.7070 ± 0.0030	0	$ -1.8560 ^{+ 0.0050 }_{- 0.0050 } $	$ -1.6924 ^{+ 0.0103 }_{- 0.0212 } $
172Pt$ \to {}^{168}{\rm{Os}} $	6.4630 ± 0.0040	0	$ -0.9928 ^{+ 0.0057 }_{- 0.0058 } $	$ -0.8089 ^{+ 0.0146 }_{- 0.0256 } $
174Pt$ \to {}^{170}{\rm{Os}} $	6.1830 ± 0.0030	0	$ 0.0610 ^{+ 0.0040 }_{- 0.0040 } $	$ 0.2698 ^{+ 0.0118 }_{- 0.0228 } $
176Pt$ \to {}^{172}{\rm{Os}} $	5.8848 ± 0.0020	0	$ 1.1993 ^{+ 0.0102 }_{- 0.0104 } $	$ 1.5059 ^{+ 0.0085 }_{- 0.0196 } $
178Pt$ \to {}^{174}{\rm{Os}} $	5.5730 ± 0.0220	0	$ 2.4295 ^{+ 0.0144 }_{- 0.0149 } $	$ 2.9079 ^{+ 0.1018 }_{- 0.1136 } $
180Pt$ \to {}^{176}{\rm{Os}} $	5.2760 ± 0.0050	0	$ 4.0322 ^{+ 0.0227 }_{- 0.0239 } $	$ 4.3638 ^{+ 0.0253 }_{- 0.0366 } $
182Pt$ \to {}^{178}{\rm{Os}} $	4.9510 ± 0.0050	0	$ 5.6249 ^{+ 0.0191 }_{- 0.0200 } $	$ 6.1098 ^{+ 0.0280 }_{- 0.0394 } $
184Pt$ \to {}^{180}{\rm{Os}} $	4.5990 ± 0.0080	0	$ 7.7857 ^{+ 0.0050 }_{- 0.0050 } $	$ 8.2131 ^{+ 0.0502 }_{- 0.0619 } $
186Pt$ \to {}^{182}{\rm{Os}} $	4.3200 ± 0.0180	0	$ 9.7282 ^{+ 0.0103 }_{- 0.0106 } $	$ 10.0701 ^{+ 0.1243 }_{- 0.1367 } $
188Pt$ \to {}^{184}{\rm{Os}} $	4.0070 ± 0.0050	0	$ 12.5284 ^{+ 0.0076 }_{- 0.0078 } $	$ 12.3854 ^{+ 0.0389 }_{- 0.0507 } $
190Pt$ \to {}^{186}{\rm{Os}} $	3.2686 ± 0.0006	0	$ 20.1830 ^{+ 0.0027 }_{- 0.0027 } $	$ 19.1251 ^{+ 0.0064 }_{- 0.0184 } $
170Hg$ \to {}^{166}{\rm{Pt}} $	7.7700 ± 0.0300	0	$ -3.5086 ^{+ 0.2568 }_{- 0.7132 } $	$ -4.2313 ^{+ 0.0835 }_{- 0.0948 } $
172Hg$ \to {}^{168}{\rm{Pt}} $	7.5240 ± 0.0060	0	$ -3.6364 ^{+ 0.0166 }_{- 0.0173 } $	$ -3.5099 ^{+ 0.0176 }_{- 0.0285 } $
174Hg$ \to {}^{170}{\rm{Pt}} $	7.2330 ± 0.0060	0	$ -2.6990 ^{+ 0.0792 }_{- 0.0969 } $	$ -2.6091 ^{+ 0.0188 }_{- 0.0298 } $
176Hg$ \to {}^{172}{\rm{Pt}} $	6.8970 ± 0.0060	0	$ -1.6467 ^{+ 0.0290 }_{- 0.0310 } $	$ -1.4965 ^{+ 0.0203 }_{- 0.0314 } $
178Hg$ \to {}^{174}{\rm{Pt}} $	6.5773 ± 0.0030	0	$ -0.5237 ^{+ 0.0039 }_{- 0.0039 } $	$ -0.3535 ^{+ 0.0110 }_{- 0.0222 } $
180Hg$ \to {}^{176}{\rm{Pt}} $	6.2585 ± 0.0023	0	$ 0.7321 ^{+ 0.0017 }_{- 0.0017 } $	$ 0.8778 ^{+ 0.0091 }_{- 0.0204 } $
182Hg$ \to {}^{178}{\rm{Pt}} $	5.9960 ± 0.0050	0	$ 1.8947 ^{+ 0.0024 }_{- 0.0024 } $	$ 1.9716 ^{+ 0.0212 }_{- 0.0326 } $
184Hg$ \to {}^{180}{\rm{Pt}} $	5.6600 ± 0.0040	0	$ 3.4442 ^{+ 0.0036 }_{- 0.0037 } $	$ 3.4823 ^{+ 0.0186 }_{- 0.0301 } $
186Hg$ \to {}^{182}{\rm{Pt}} $	5.2040 ± 0.0100	0	$ 5.7139 ^{+ 0.0185 }_{- 0.0193 } $	$ 5.7677 ^{+ 0.0531 }_{- 0.0649 } $
188Hg$ \to {}^{184}{\rm{Pt}} $	4.7090 ± 0.0150	0	$ 8.7218 ^{+ 0.0196 }_{- 0.0205 } $	$ 8.6312 ^{+ 0.0931 }_{- 0.1054 } $
178Pb$ \to {}^{174}{\rm{Hg}} $	7.7890 ± 0.0130	0	$ -3.6021 ^{+ 0.1206 }_{- 0.1675 } $	$ -3.5051 ^{+ 0.0371 }_{- 0.0483 } $
180Pb$ \to {}^{176}{\rm{Hg}} $	7.4190 ± 0.0050	0	$ -2.3872 ^{+ 0.0307 }_{- 0.0330 } $	$ -2.3876 ^{+ 0.0155 }_{- 0.0267 } $
182Pb$ \to {}^{178}{\rm{Hg}} $	7.0660 ± 0.0060	0	$ -1.2596 ^{+ 0.0378 }_{- 0.0414 } $	$ -1.2337 ^{+ 0.0201 }_{- 0.0314 } $
184Pb$ \to {}^{180}{\rm{Hg}} $	6.7740 ± 0.0030	0	$ -0.2129 ^{+ 0.0216 }_{- 0.0227 } $	$ -0.2043 ^{+ 0.0108 }_{- 0.0222 } $
186Pb$ \to {}^{182}{\rm{Hg}} $	6.4710 ± 0.0050	0	$ 1.0810 ^{+ 0.0027 }_{- 0.0027 } $	$ 0.9406 ^{+ 0.0193 }_{- 0.0308 } $
188Pb$ \to {}^{184}{\rm{Hg}} $	6.1090 ± 0.0030	0	$ 2.4703 ^{+ 0.0017 }_{- 0.0017 } $	$ 2.4218 ^{+ 0.0127 }_{- 0.0243 } $
190Pb$ \to {}^{186}{\rm{Hg}} $	5.6980 ± 0.0050	0	$ 4.2492 ^{+ 0.0061 }_{- 0.0062 } $	$ 4.2790 ^{+ 0.0237 }_{- 0.0354 } $
192Pb$ \to {}^{188}{\rm{Hg}} $	5.2220 ± 0.0050	0	$ 6.5462 ^{+ 0.0122 }_{- 0.0126 } $	$ 6.7095 ^{+ 0.0272 }_{- 0.0391 } $
194Pb$ \to {}^{190}{\rm{Hg}} $	4.7380 ± 0.0170	0	$ 9.9442 ^{+ 0.0237 }_{- 0.0251 } $	$ 9.5642 ^{+ 0.1073 }_{- 0.1200 } $
210Pb$ \to {}^{206}{\rm{Pb}} $	3.7920 ± 0.0200	0	$ 16.5667 ^{+ 0.0043 }_{- 0.0043 } $	$ 15.3018 ^{+ 0.1776 }_{- 0.1919 } $
186Po$ \to {}^{182}{\rm{Pb}} $	8.5010 ± 0.0140	0	$ -4.4685 ^{+ 0.1313 }_{- 0.1891 } $	$ -4.6712 ^{+ 0.0356 }_{- 0.0467 } $
188Po$ \to {}^{184}{\rm{Pb}} $	8.0820 ± 0.0150	0	$ -3.5686 ^{+ 0.0458 }_{- 0.0512 } $	$ -3.5430 ^{+ 0.0415 }_{- 0.0528 } $
190Po$ \to {}^{186}{\rm{Pb}} $	7.6930 ± 0.0070	0	$ -2.6108 ^{+ 0.0088 }_{- 0.0090 } $	$ -2.4058 ^{+ 0.0210 }_{- 0.0323 } $
Continued on next page

Table 2-continued from previous page
α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
192Po$ \to {}^{188}{\rm{Pb}} $	7.3200 ± 0.0030	0	$ -1.4921 ^{+ 0.0040 }_{- 0.0041 } $	$ -1.2241 ^{+ 0.0098 }_{- 0.0212 } $
194Po$ \to {}^{190}{\rm{Pb}} $	6.9870 ± 0.0030	0	$ -0.4067 ^{+ 0.0044 }_{- 0.0045 } $	$ -0.0828 ^{+ 0.0105 }_{- 0.0221 } $
196Po$ \to {}^{192}{\rm{Pb}} $	6.6582 ± 0.0024	0	$ 0.7774 ^{+ 0.0054 }_{- 0.0054 } $	$ 1.1328 ^{+ 0.0091 }_{- 0.0207 } $
198Po$ \to {}^{194}{\rm{Pb}} $	6.3097 ± 0.0014	0	$ 2.2678 ^{+ 0.0059 }_{- 0.0060 } $	$ 2.5289 ^{+ 0.0058 }_{- 0.0175 } $
200Po$ \to {}^{196}{\rm{Pb}} $	5.9816 ± 0.0018	0	$ 3.7939 ^{+ 0.0030 }_{- 0.0030 } $	$ 3.9603 ^{+ 0.0081 }_{- 0.0200 } $
202Po$ \to {}^{198}{\rm{Pb}} $	5.7010 ± 0.0050	0	$ 5.1442 ^{+ 0.0039 }_{- 0.0039 } $	$ 5.2884 ^{+ 0.0243 }_{- 0.0363 } $
204Po$ \to {}^{200}{\rm{Pb}} $	5.4849 ± 0.0014	0	$ 6.2766 ^{+ 0.0015 }_{- 0.0015 } $	$ 6.3867 ^{+ 0.0072 }_{- 0.0192 } $
206Po$ \to {}^{202}{\rm{Pb}} $	5.3270 ± 0.0013	0	$ 7.1446 ^{+ 0.0049 }_{- 0.0050 } $	$ 7.2368 ^{+ 0.0070 }_{- 0.0191 } $
208Po$ \to {}^{204}{\rm{Pb}} $	5.2157 ± 0.0013	0	$ 7.9612 ^{+ 0.0003 }_{- 0.0003 } $	$ 7.8642 ^{+ 0.0073 }_{- 0.0193 } $
210Po$ \to {}^{206}{\rm{Pb}} $	5.4075 ± 0.0001	0	$ 7.0776 ^{+ 0.0000 }_{- 0.0000 } $	$ 6.8360 ^{+ 0.0005 }_{- 0.0122 } $
212Po$ \to {}^{208}{\rm{Pb}} $	8.9542 ± 0.0001	0	$ -6.5311 ^{+ 0.0117 }_{- 0.0120 } $	$ -6.9453 ^{+ 0.0002 }_{- 0.0112 } $
214Po$ \to {}^{210}{\rm{Pb}} $	7.8335 ± 0.0001	0	$ -3.7866 ^{+ 0.0000 }_{- 0.0000 } $	$ -4.0399 ^{+ 0.0003 }_{- 0.0114 } $
216Po$ \to {}^{212}{\rm{Pb}} $	6.9063 ± 0.0005	0	$ -0.8416 ^{+ 0.0018 }_{- 0.0018 } $	$ -1.0594 ^{+ 0.0018 }_{- 0.0135 } $
218Po$ \to {}^{214}{\rm{Pb}} $	6.1148 ± 0.0001	0	$ 2.2692 ^{+ 0.0017 }_{- 0.0017 } $	$ 2.0525 ^{+ 0.0002 }_{- 0.0127 } $
194Rn$ \to {}^{190}{\rm{Po}} $	7.8620 ± 0.0100	0	$ -3.1079 ^{+ 0.0810 }_{- 0.0997 } $	$ -2.1543 ^{+ 0.0297 }_{- 0.0413 } $
196Rn$ \to {}^{192}{\rm{Po}} $	7.6170 ± 0.0090	0	$ -2.3279 ^{+ 0.0913 }_{- 0.1158 } $	$ -1.3906 ^{+ 0.0282 }_{- 0.0398 } $
198Rn$ \to {}^{194}{\rm{Po}} $	7.3490 ± 0.0040	0	$ -1.1596 ^{+ 0.0107 }_{- 0.0109 } $	$ -0.5105 ^{+ 0.0133 }_{- 0.0250 } $
200Rn$ \to {}^{196}{\rm{Po}} $	7.0434 ± 0.0021	0	$ 0.0736 ^{+ 0.0595 }_{- 0.0689 } $	$ 0.5556 ^{+ 0.0075 }_{- 0.0193 } $
202Rn$ \to {}^{198}{\rm{Po}} $	6.7738 ± 0.0018	0	$ 1.0947 ^{+ 0.0045 }_{- 0.0045 } $	$ 1.5610 ^{+ 0.0068 }_{- 0.0187 } $
204Rn$ \to {}^{200}{\rm{Po}} $	6.5467 ± 0.0018	0	$ 2.0125 ^{+ 0.0080 }_{- 0.0081 } $	$ 2.4606 ^{+ 0.0072 }_{- 0.0191 } $
206Rn$ \to {}^{202}{\rm{Po}} $	6.3837 ± 0.0016	0	$ 2.7393 ^{+ 0.0128 }_{- 0.0132 } $	$ 3.1415 ^{+ 0.0067 }_{- 0.0187 } $
208Rn$ \to {}^{204}{\rm{Po}} $	6.2607 ± 0.0017	0	$ 3.3723 ^{+ 0.0025 }_{- 0.0025 } $	$ 3.6771 ^{+ 0.0073 }_{- 0.0193 } $
210Rn$ \to {}^{206}{\rm{Po}} $	6.1590 ± 0.0022	0	$ 3.9542 ^{+ 0.0177 }_{- 0.0185 } $	$ 4.1349 ^{+ 0.0097 }_{- 0.0217 } $
212Rn$ \to {}^{208}{\rm{Po}} $	6.3851 ± 0.0026	0	$ 3.1565 ^{+ 0.0036 }_{- 0.0036 } $	$ 3.1794 ^{+ 0.0108 }_{- 0.0228 } $
214Rn$ \to {}^{210}{\rm{Po}} $	9.2080 ± 0.0090	0	$ -6.5867 ^{+ 0.0050 }_{- 0.0051 } $	$ -6.8968 ^{+ 0.0203 }_{- 0.0315 } $
216Rn$ \to {}^{212}{\rm{Po}} $	8.1980 ± 0.0060	0	$ -4.5376 ^{+ 0.0561 }_{- 0.0645 } $	$ -4.3646 ^{+ 0.0165 }_{- 0.0280 } $
218Rn$ \to {}^{214}{\rm{Po}} $	7.2625 ± 0.0019	0	$ -1.4717 ^{+ 0.0019 }_{- 0.0019 } $	$ -1.5091 ^{+ 0.0064 }_{- 0.0183 } $
220Rn$ \to {}^{216}{\rm{Po}} $	6.4047 ± 0.0001	0	$ 1.7451 ^{+ 0.0008 }_{- 0.0008 } $	$ 1.6924 ^{+ 0.0006 }_{- 0.0125 } $
222Rn$ \to {}^{218}{\rm{Po}} $	5.5904 ± 0.0003	0	$ 5.5187 ^{+ 0.0000 }_{- 0.0000 } $	$ 5.4409 ^{+ 0.0015 }_{- 0.0142 } $
202Ra$ \to {}^{198}{\rm{Rn}} $	7.8800 ± 0.0070	0	$ -2.3872 ^{+ 0.1032 }_{- 0.1357 } $	$ -1.4246 ^{+ 0.0213 }_{- 0.0331 } $
204Ra$ \to {}^{200}{\rm{Rn}} $	7.6370 ± 0.0070	0	$ -1.2218 ^{+ 0.0607 }_{- 0.0706 } $	$ -0.6507 ^{+ 0.0224 }_{- 0.0343 } $
206Ra$ \to {}^{202}{\rm{Rn}} $	7.4150 ± 0.0040	0	$ -0.6198 ^{+ 0.0348 }_{- 0.0378 } $	$ 0.0928 ^{+ 0.0134 }_{- 0.0254 } $
208Ra$ \to {}^{204}{\rm{Rn}} $	7.2730 ± 0.0050	0	$ 0.1058 ^{+ 0.0173 }_{- 0.0180 } $	$ 0.5925 ^{+ 0.0173 }_{- 0.0293 } $
210Ra$ \to {}^{206}{\rm{Rn}} $	7.1510 ± 0.0030	0	$ 0.6021 ^{+ 0.0107 }_{- 0.0110 } $	$ 1.0362 ^{+ 0.0107 }_{- 0.0227 } $
214Ra$ \to {}^{210}{\rm{Rn}} $	7.2726 ± 0.0026	0	$ 0.3871 ^{+ 0.0028 }_{- 0.0029 } $	$ 0.6370 ^{+ 0.0090 }_{- 0.0209 } $
216Ra$ \to {}^{212}{\rm{Rn}} $	9.5260 ± 0.0070	0	$ -6.7645 ^{+ 0.0173 }_{- 0.0180 } $	$ -6.9906 ^{+ 0.0153 }_{- 0.0267 } $
218Ra$ \to {}^{214}{\rm{Rn}} $	8.5400 ± 0.0120	0	$ -4.5865 ^{+ 0.0023 }_{- 0.0024 } $	$ -4.6056 ^{+ 0.0316 }_{- 0.0434 } $
220Ra$ \to {}^{216}{\rm{Rn}} $	7.5940 ± 0.0050	0	$ -1.7423 ^{+ 0.0279 }_{- 0.0298 } $	$ -1.8429 ^{+ 0.0160 }_{- 0.0281 } $
222Ra$ \to {}^{218}{\rm{Rn}} $	6.6780 ± 0.0040	0	$ 1.5263 ^{+ 0.0051 }_{- 0.0052 } $	$ 1.4268 ^{+ 0.0158 }_{- 0.0283 } $
224Ra$ \to {}^{220}{\rm{Rn}} $	5.7889 ± 0.0002	0	$ 5.4966 ^{+ 0.0002 }_{- 0.0002 } $	$ 5.3737 ^{+ 0.0008 }_{- 0.0135 } $
226Ra$ \to {}^{222}{\rm{Rn}} $	4.8707 ± 0.0003	0	$ 10.7032 ^{+ 0.0019 }_{- 0.0019 } $	$ 10.6053 ^{+ 0.0016 }_{- 0.0149 } $
Continued on next page

Table 2-continued from previous page
α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
208Th$ \to {}^{204}{\rm{Ra}} $	8.2000 ± 0.0300	0	$ -2.6198 ^{+ 0.1761 }_{- 0.3010 } $	$ -1.6203 ^{+ 0.0876 }_{- 0.1000 } $
210Th$ \to {}^{206}{\rm{Ra}} $	8.0960 ± 0.0060	0	$ -1.7959 ^{+ 0.0881 }_{- 0.1107 } $	$ -1.2980 ^{+ 0.0179 }_{- 0.0299 } $
212Th$ \to {}^{208}{\rm{Ra}} $	7.9580 ± 0.0050	0	$ -1.4989 ^{+ 0.0175 }_{- 0.0182 } $	$ -0.8651 ^{+ 0.0154 }_{- 0.0274 } $
214Th$ \to {}^{210}{\rm{Ra}} $	7.8270 ± 0.0050	0	$ -1.0605 ^{+ 0.0473 }_{- 0.0530 } $	$ -0.4425 ^{+ 0.0158 }_{- 0.0278 } $
216Th$ \to {}^{212}{\rm{Ra}} $	8.0720 ± 0.0040	0	$ -1.5804 ^{+ 0.0026 }_{- 0.0027 } $	$ -1.1834 ^{+ 0.0120 }_{- 0.0239 } $
218Th$ \to {}^{214}{\rm{Ra}} $	9.8490 ± 0.0090	0	$ -6.9136 ^{+ 0.0174 }_{- 0.0182 } $	$ -7.0891 ^{+ 0.0191 }_{- 0.0307 } $
220Th$ \to {}^{216}{\rm{Ra}} $	8.9730 ± 0.0110	0	$ -4.9914 ^{+ 0.0126 }_{- 0.0130 } $	$ -5.0586 ^{+ 0.0274 }_{- 0.0393 } $
222Th$ \to {}^{218}{\rm{Ra}} $	8.1326 ± 0.0029	0	$ -2.6498 ^{+ 0.0058 }_{- 0.0059 } $	$ -2.7726 ^{+ 0.0085 }_{- 0.0207 } $
224Th$ \to {}^{220}{\rm{Ra}} $	7.2990 ± 0.0060	0	$ 0.0170 ^{+ 0.0083 }_{- 0.0084 } $	$ -0.0859 ^{+ 0.0210 }_{- 0.0336 } $
226Th$ \to {}^{222}{\rm{Ra}} $	6.4525 ± 0.0010	0	$ 3.2653 ^{+ 0.0004 }_{- 0.0004 } $	$ 3.2039 ^{+ 0.0043 }_{- 0.0172 } $
228Th$ \to {}^{224}{\rm{Ra}} $	5.5202 ± 0.0002	0	$ 7.7807 ^{+ 0.0002 }_{- 0.0002 } $	$ 7.7299 ^{+ 0.0009 }_{- 0.0148 } $
230Th$ \to {}^{226}{\rm{Ra}} $	4.7700 ± 0.0015	0	$ 12.3765 ^{+ 0.0017 }_{- 0.0017 } $	$ 12.3551 ^{+ 0.0103 }_{- 0.0240 } $
232Th$ \to {}^{228}{\rm{Ra}} $	4.0816 ± 0.0014	0	$ 18.6452 ^{+ 0.0031 }_{- 0.0031 } $	$ 17.7276 ^{+ 0.0123 }_{- 0.0262 } $
218U$ \to {}^{214}{\rm{Th}} $	8.7750 ± 0.0090	0	$ -3.4510 ^{+ 0.0994 }_{- 0.1290 } $	$ -2.4735 ^{+ 0.0242 }_{- 0.0362 } $
222U$ \to {}^{218}{\rm{Th}} $	9.4800 ± 0.0500	0	$ -5.3279 ^{+ 0.0355 }_{- 0.0386 } $	$ -5.6497 ^{+ 0.1160 }_{- 0.1290 } $
224U$ \to {}^{220}{\rm{Th}} $	8.6280 ± 0.0070	0	$ -3.4023 ^{+ 0.0183 }_{- 0.0191 } $	$ -3.4880 ^{+ 0.0191 }_{- 0.0314 } $
226U$ \to {}^{222}{\rm{Th}} $	7.7010 ± 0.0040	0	$ -0.5702 ^{+ 0.0096 }_{- 0.0098 } $	$ -0.6968 ^{+ 0.0132 }_{- 0.0259 } $
228U$ \to {}^{224}{\rm{Th}} $	6.8000 ± 0.0090	0	$ 2.7482 ^{+ 0.0094 }_{- 0.0097 } $	$ 2.5962 ^{+ 0.0362 }_{- 0.0494 } $
230U$ \to {}^{226}{\rm{Th}} $	5.9925 ± 0.0005	0	$ 6.2425 ^{+ 0.0004 }_{- 0.0004 } $	$ 6.2069 ^{+ 0.0025 }_{- 0.0159 } $
232U$ \to {}^{228}{\rm{Th}} $	5.4136 ± 0.0001	0	$ 9.3373 ^{+ 0.0025 }_{- 0.0025 } $	$ 9.3132 ^{+ 0.0007 }_{- 0.0140 } $
234U$ \to {}^{230}{\rm{Th}} $	4.8575 ± 0.0007	0	$ 12.8891 ^{+ 0.0011 }_{- 0.0011 } $	$ 12.8325 ^{+ 0.0048 }_{- 0.0187 } $
236U$ \to {}^{232}{\rm{Th}} $	4.5730 ± 0.0009	0	$ 14.8687 ^{+ 0.0007 }_{- 0.0007 } $	$ 14.8945 ^{+ 0.0068 }_{- 0.0208 } $
238U$ \to {}^{234}{\rm{Th}} $	4.2699 ± 0.0021	0	$ 18.1487 ^{+ 0.0003 }_{- 0.0003 } $	$ 17.3210 ^{+ 0.0176 }_{- 0.0318 } $
230Pu$ \to {}^{226}{\rm{U}} $	7.1780 ± 0.0200	0	$ 2.0212 ^{+ 0.0395 }_{- 0.0435 } $	$ 1.9240 ^{+ 0.0754 }_{- 0.0890 } $
232Pu$ \to {}^{228}{\rm{U}} $	6.7160 ± 0.0100	0	$ 4.0048 ^{+ 0.0082 }_{- 0.0084 } $	$ 3.7802 ^{+ 0.0420 }_{- 0.0556 } $
234Pu$ \to {}^{230}{\rm{U}} $	6.3100 ± 0.0050	0	$ 5.7226 ^{+ 0.0049 }_{- 0.0050 } $	$ 5.5898 ^{+ 0.0232 }_{- 0.0369 } $
236Pu$ \to {}^{232}{\rm{U}} $	5.8672 ± 0.0001	0	$ 7.9552 ^{+ 0.0012 }_{- 0.0012 } $	$ 7.7850 ^{+ 0.0002 }_{- 0.0145 } $
238Pu$ \to {}^{234}{\rm{U}} $	5.5933 ± 0.0002	0	$ 9.4421 ^{+ 0.0005 }_{- 0.0005 } $	$ 9.2841 ^{+ 0.0009 }_{- 0.0151 } $
240Pu$ \to {}^{236}{\rm{U}} $	5.2558 ± 0.0001	0	$ 11.3161 ^{+ 0.0005 }_{- 0.0005 } $	$ 11.2939 ^{+ 0.0010 }_{- 0.0148 } $
242Pu$ \to {}^{238}{\rm{U}} $	4.9842 ± 0.0010	0	$ 13.0731 ^{+ 0.0023 }_{- 0.0023 } $	$ 13.0667 ^{+ 0.0067 }_{- 0.0209 } $
244Pu$ \to {}^{240}{\rm{U}} $	4.6656 ± 0.0010	0	$ 15.4097 ^{+ 0.0016 }_{- 0.0016 } $	$ 15.3452 ^{+ 0.0075 }_{- 0.0217 } $
234Cm$ \to {}^{230}{\rm{Pu}} $	7.3650 ± 0.0090	0	$ 2.2846 ^{+ 0.0693 }_{- 0.0825 } $	$ 2.0180 ^{+ 0.0334 }_{- 0.0469 } $
236Cm$ \to {}^{232}{\rm{Pu}} $	7.0670 ± 0.0050	0	$ 3.3554 ^{+ 0.0483 }_{- 0.0544 } $	$ 3.1757 ^{+ 0.0198 }_{- 0.0335 } $
238Cm$ \to {}^{234}{\rm{Pu}} $	6.6700 ± 0.0100	0	$ 5.3144 ^{+ 0.0207 }_{- 0.0217 } $	$ 4.8399 ^{+ 0.0435 }_{- 0.0574 } $
240Cm$ \to {}^{236}{\rm{Pu}} $	6.3978 ± 0.0006	0	$ 6.4194 ^{+ 0.0499 }_{- 0.0564 } $	$ 6.0796 ^{+ 0.0028 }_{- 0.0167 } $
242Cm$ \to {}^{238}{\rm{Pu}} $	6.2156 ± 0.0001	0	$ 7.1482 ^{+ 0.0005 }_{- 0.0005 } $	$ 6.9618 ^{+ 0.0005 }_{- 0.0142 } $
244Cm$ \to {}^{240}{\rm{Pu}} $	5.9016 ± 0.0000	0	$ 8.7570 ^{+ 0.0007 }_{- 0.0007 } $	$ 8.5707 ^{+ 0.0002 }_{- 0.0142 } $
246Cm$ \to {}^{242}{\rm{Pu}} $	5.4751 ± 0.0009	0	$ 11.1719 ^{+ 0.0037 }_{- 0.0037 } $	$ 10.9793 ^{+ 0.0054 }_{- 0.0196 } $
248Cm$ \to {}^{244}{\rm{Pu}} $	5.1618 ± 0.0003	0	$ 13.0787 ^{+ 0.0074 }_{- 0.0076 } $	$ 12.9485 ^{+ 0.0017 }_{- 0.0159 } $
238Cf$ \to {}^{234}{\rm{Cm}} $	8.1300 ± 0.3000	0	$ -0.0737 ^{+ 0.0260 }_{- 0.0276 } $	$ 0.1277 ^{+ 0.9415 }_{- 1.0136 } $
240Cf$ \to {}^{236}{\rm{Cm}} $	7.7110 ± 0.0040	0	$ 1.6119 ^{+ 0.0096 }_{- 0.0098 } $	$ 1.5564 ^{+ 0.0141 }_{- 0.0277 } $
Continued on next page

Table 2-continued from previous page
α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
242Cf$ \to {}^{238}{\rm{Cm}} $	7.5170 ± 0.0040	0	$ 2.5356 ^{+ 0.0183 }_{- 0.0191 } $	$ 2.2689 ^{+ 0.0147 }_{- 0.0284 } $
244Cf$ \to {}^{240}{\rm{Cm}} $	7.3290 ± 0.0018	0	$ 3.1931 ^{+ 0.0110 }_{- 0.0113 } $	$ 2.9882 ^{+ 0.0069 }_{- 0.0207 } $
246Cf$ \to {}^{242}{\rm{Cm}} $	6.8616 ± 0.0010	0	$ 5.1090 ^{+ 0.0060 }_{- 0.0061 } $	$ 4.8891 ^{+ 0.0043 }_{- 0.0182 } $
248Cf$ \to {}^{244}{\rm{Cm}} $	6.3610 ± 0.0050	0	$ 7.4596 ^{+ 0.0349 }_{- 0.0379 } $	$ 7.1669 ^{+ 0.0240 }_{- 0.0382 } $
250Cf$ \to {}^{246}{\rm{Cm}} $	6.1285 ± 0.0002	0	$ 8.6160 ^{+ 0.0030 }_{- 0.0030 } $	$ 8.3320 ^{+ 0.0010 }_{- 0.0152 } $
252Cf$ \to {}^{248}{\rm{Cm}} $	6.2170 ± 0.0000	0	$ 7.9352 ^{+ 0.0013 }_{- 0.0013 } $	$ 7.9004 ^{+ 0.0000 }_{- 0.0146 } $
254Cf$ \to {}^{250}{\rm{Cm}} $	5.9270 ± 0.0050	0	$ 9.2269 ^{+ 0.0014 }_{- 0.0014 } $	$ 9.4157 ^{+ 0.0269 }_{- 0.0412 } $
244Fm$ \to {}^{240}{\rm{Cf}} $	8.5500 ± 0.2000	0	$ -0.5058 ^{+ 0.0110 }_{- 0.0113 } $	$ -0.4594 ^{+ 0.5977 }_{- 0.6347 } $
246Fm$ \to {}^{242}{\rm{Cf}} $	8.3790 ± 0.0050	0	$ 0.2181 ^{+ 0.0111 }_{- 0.0114 } $	$ 0.0843 ^{+ 0.0157 }_{- 0.0294 } $
248Fm$ \to {}^{244}{\rm{Cf}} $	7.9950 ± 0.0080	0	$ 1.5378 ^{+ 0.0148 }_{- 0.0154 } $	$ 1.3549 ^{+ 0.0272 }_{- 0.0410 } $
250Fm$ \to {}^{246}{\rm{Cf}} $	7.5570 ± 0.0080	0	$ 3.2695 ^{+ 0.0151 }_{- 0.0157 } $	$ 2.9279 ^{+ 0.0298 }_{- 0.0438 } $
252Fm$ \to {}^{248}{\rm{Cf}} $	7.1537 ± 0.0010	0	$ 4.9610 ^{+ 0.0007 }_{- 0.0007 } $	$ 4.5128 ^{+ 0.0041 }_{- 0.0182 } $
254Fm$ \to {}^{250}{\rm{Cf}} $	7.3073 ± 0.0010	0	$ 4.0671 ^{+ 0.0003 }_{- 0.0003 } $	$ 3.9122 ^{+ 0.0039 }_{- 0.0180 } $
256Fm$ \to {}^{252}{\rm{Cf}} $	7.0253 ± 0.0019	0	$ 5.0658 ^{+ 0.0036 }_{- 0.0036 } $	$ 5.0715 ^{+ 0.0080 }_{- 0.0221 } $
252No$ \to {}^{248}{\rm{Fm}} $	8.5490 ± 0.0050	0	$ 0.5622 ^{+ 0.0028 }_{- 0.0028 } $	$ 0.2769 ^{+ 0.0156 }_{- 0.0294 } $
254No$ \to {}^{250}{\rm{Fm}} $	8.2260 ± 0.0080	0	$ 1.7550 ^{+ 0.0034 }_{- 0.0034 } $	$ 1.3296 ^{+ 0.0265 }_{- 0.0406 } $
256No$ \to {}^{252}{\rm{Fm}} $	8.5820 ± 0.0050	0	$ 0.4663 ^{+ 0.0074 }_{- 0.0075 } $	$ 0.2020 ^{+ 0.0155 }_{- 0.0293 } $
256Rf$ \to {}^{252}{\rm{No}} $	8.9260 ± 0.0150	0	$ 0.3282 ^{+ 0.0033 }_{- 0.0033 } $	$ -0.1738 ^{+ 0.0444 }_{- 0.0586 } $
258Rf$ \to {}^{254}{\rm{No}} $	9.1960 ± 0.0130	0	$ -0.5933 ^{+ 0.0170 }_{- 0.0177 } $	$ -0.9416 ^{+ 0.0367 }_{- 0.0506 } $
260Sg$ \to {}^{256}{\rm{Rf}} $	9.9010 ± 0.0100	0	$ -1.7678 ^{+ 0.0280 }_{- 0.0300 } $	$ -2.2001 ^{+ 0.0255 }_{- 0.0394 } $
266Hs$ \to {}^{262}{\rm{Sg}} $	10.3460 ± 0.0160	0	$ -2.4037 ^{+ 0.0792 }_{- 0.0969 } $	$ -2.6745 ^{+ 0.0387 }_{- 0.0528 } $
268Hs$ \to {}^{264}{\rm{Sg}} $	9.7600 ± 0.1000	0	$ 0.1461 ^{+ 0.2518 }_{- 0.6690 } $	$ -1.1695 ^{+ 0.2650 }_{- 0.2838 } $
270Hs$ \to {}^{266}{\rm{Sg}} $	9.0700 ± 0.0400	0	$ 0.9542 ^{+ 0.1597 }_{- 0.2553 } $	$ 0.8032 ^{+ 0.1202 }_{- 0.1356 } $
270Ds$ \to {}^{266}{\rm{Hs}} $	11.1170 ± 0.0280	0	$ -3.6882 ^{+ 0.0914 }_{- 0.1159 } $	$ -3.8611 ^{+ 0.0613 }_{- 0.0755 } $
282Ds$ \to {}^{278}{\rm{Hs}} $	9.1500 ± 0.4200	0	$ 2.4014 ^{+ 0.2518 }_{- 0.6690 } $	$ 1.2962 ^{+ 1.2293 }_{- 1.3403 } $
286Cn$ \to {}^{282}{\rm{Ds}} $	9.2400 ± 0.7600	0	$ 1.4771 ^{+ 0.3010 }_{- 0.3010 } $	$ 1.7006 ^{+ 2.1712 }_{- 2.5004 } $
286Fl$ \to {}^{282}{\rm{Cn}} $	10.3600 ± 0.0400	0	$ -0.6569 ^{+ 0.0099 }_{- 0.0101 } $	$ -0.8175 ^{+ 0.1026 }_{- 0.1181 } $
288Fl$ \to {}^{284}{\rm{Cn}} $	10.0760 ± 0.0120	0	$ -0.1851 ^{+ 0.0693 }_{- 0.0825 } $	$ -0.0558 ^{+ 0.0323 }_{- 0.0473 } $
290Lv$ \to {}^{286}{\rm{Fl}} $	11.0000 ± 0.0600	0	$ -2.0458 ^{+ 0.1249 }_{- 0.1761 } $	$ -1.7981 ^{+ 0.1419 }_{- 0.1580 } $
292Lv$ \to {}^{288}{\rm{Fl}} $	10.7910 ± 0.0120	0	$ -1.7959 ^{+ 0.1383 }_{- 0.2041 } $	$ -1.2802 ^{+ 0.0294 }_{- 0.0444 } $
294Og$ \to {}^{290}{\rm{Lv}} $	11.8700 ± 0.0300	0	$ -3.1549 ^{+ 0.1549 }_{- 0.2430 } $	$ -3.1857 ^{+ 0.0638 }_{- 0.0788 } $

Figure 2.  (color online) Deviations between the experimental half-lives and those calculated in logarithmic form using Eq. (16) for favored α decay for (a) even-even nuclei, (b) odd-A nuclei, and (c) odd-odd nuclei, respectively.

α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
105Te$ \to {}^{101}{\rm{Nb}} $	5.0680 ± 0.0030	0	$ -6.1986 ^{+ 0.0431 }_{- 0.0478 } $	$ -6.5162 ^{+ 0.0103 }_{- 0.0103 } $
107Te$ \to {}^{103}{\rm{Nb}} $	4.0100 ± 0.0050	0	$ -2.3372 ^{+ 0.0120 }_{- 0.0123 } $	$ -2.1065 ^{+ 0.0250 }_{- 0.0250 } $
113I$ \to {}^{109}{\rm{Sb}} $	2.7070 ± 0.0100	0	$ 7.2997 ^{+ 0.0130 }_{- 0.0134 } $	$ 7.5353 ^{+ 0.0939 }_{- 0.0944 } $
109Xe$ \to {}^{105}{\rm{Te}} $	4.2170 ± 0.0210	0	$ -1.8861 ^{+ 0.0621 }_{- 0.0726 } $	$ -1.9885 ^{+ 0.1008 }_{- 0.1016 } $
111Xe$ \to {}^{107}{\rm{Te}} $	3.7100 ± 0.0600	0	$ 0.8439 ^{+ 0.1039 }_{- 0.1368 } $	$ 0.7345 ^{+ 0.3492 }_{- 0.3581 } $
145Pm$ \to {}^{141}{\rm{Pr}} $	2.3210 ± 0.0290	0	$ 17.2999 ^{+ 0.0097 }_{- 0.0099 } $	$ 17.3786 ^{+ 0.3981 }_{- 0.4058 } $
147Sm$ \to {}^{143}{\rm{Nd}} $	2.3113 ± 0.0150	0	$ 18.5269 ^{+ 0.0020 }_{- 0.0020 } $	$ 18.3762 ^{+ 0.2119 }_{- 0.2140 } $
147Eu$ \to {}^{143}{\rm{Pm}} $	2.9910 ± 0.0005	0	$ 10.9644 ^{+ 0.0107 }_{- 0.0109 } $	$ 11.1826 ^{+ 0.0049 }_{- 0.0049 } $
149Gd$ \to {}^{145}{\rm{Sm}} $	3.0990 ± 0.0030	0	$ 11.2706 ^{+ 0.0047 }_{- 0.0047 } $	$ 10.8732 ^{+ 0.0281 }_{- 0.0281 } $
151Gd$ \to {}^{147}{\rm{Sm}} $	2.6522 ± 0.0029	0	$ 14.9882 ^{+ 0.0035 }_{- 0.0035 } $	$ 15.6039 ^{+ 0.0345 }_{- 0.0345 } $
151Dy$ \to {}^{147}{\rm{Gd}} $	4.1796 ± 0.0026	0	$ 4.2828 ^{+ 0.0072 }_{- 0.0073 } $	$ 4.0136 ^{+ 0.0158 }_{- 0.0158 } $
153Dy$ \to {}^{149}{\rm{Gd}} $	3.5590 ± 0.0040	0	$ 8.3887 ^{+ 0.0067 }_{- 0.0068 } $	$ 8.3050 ^{+ 0.0312 }_{- 0.0313 } $
151Ho$ \to {}^{147}{\rm{Tb}} $$ ^{\rm{m}} $	4.6950 ± 0.0018	0	$ 2.2041 ^{+ 0.0012 }_{- 0.0012 } $	$ 1.6715 ^{+ 0.0093 }_{- 0.0093 } $
151Ho$ ^{\rm{m}} $$ \to {}^{147}{\rm{Tb}} $	4.7400 ± 0.0002	0	$ 1.7875 ^{+ 0.0118 }_{- 0.0121 } $	$ 1.4417 ^{+ 0.0010 }_{- 0.0010 } $
153Ho$ \to {}^{149}{\rm{Tb}} $$ ^{\rm{m}} $	4.0250 ± 0.0040	0	$ 5.3717 ^{+ 0.0064 }_{- 0.0065 } $	$ 5.5780 ^{+ 0.0262 }_{- 0.0262 } $
153Ho$ ^{\rm{m}} $$ \to {}^{149}{\rm{Tb}} $	4.1200 ± 0.0003	0	$ 5.4914 ^{+ 0.0227 }_{- 0.0240 } $	$ 4.9667 ^{+ 0.0019 }_{- 0.0019 } $
153Er$ \to {}^{149}{\rm{Dy}} $	4.8024 ± 0.0014	0	$ 1.8451 ^{+ 0.0023 }_{- 0.0023 } $	$ 1.6542 ^{+ 0.0071 }_{- 0.0071 } $
155Er$ \to {}^{151}{\rm{Dy}} $	4.1180 ± 0.0050	0	$ 6.1600 ^{+ 0.0239 }_{- 0.0253 } $	$ 5.5677 ^{+ 0.0321 }_{- 0.0322 } $
153Tm$ \to {}^{149}{\rm{Ho}} $	5.2483 ± 0.0015	0	$ 0.2112 ^{+ 0.0029 }_{- 0.0029 } $	$ 0.0330 ^{+ 0.0067 }_{- 0.0067 } $
155Tm$ \to {}^{151}{\rm{Ho}} $	4.5720 ± 0.0050	0	$ 3.4154 ^{+ 0.0040 }_{- 0.0040 } $	$ 3.4093 ^{+ 0.0277 }_{- 0.0277 } $
157Tm$ \to {}^{153}{\rm{Ho}} $$ ^{\rm{m}} $	3.8780 ± 0.0280	0	$ 7.4630 ^{+ 0.0106 }_{- 0.0109 } $	$ 7.7996 ^{+ 0.1996 }_{- 0.2019 } $
153Tm$ ^{\rm{m}} $$ \to {}^{149}{\rm{Ho}} $$ ^{\rm{m}} $	5.2400 ± 0.0002	0	$ 0.4342 ^{+ 0.0334 }_{- 0.0362 } $	$ 0.0700 ^{+ 0.0009 }_{- 0.0009 } $
155Yb$ \to {}^{151}{\rm{Er}} $	5.3388 ± 0.0021	0	$ 0.3042 ^{+ 0.0048 }_{- 0.0049 } $	$ 0.1230 ^{+ 0.0092 }_{- 0.0093 } $
155Lu$ \to {}^{151}{\rm{Tm}} $	5.8016 ± 0.0022	0	$ -1.1217 ^{+ 0.0126 }_{- 0.0130 } $	$ -1.3425 ^{+ 0.0086 }_{- 0.0086 } $
155Lu$ ^{\rm{m}} $$ \to {}^{151}{\rm{Tm}} $$ ^{\rm{m}} $	5.7300 ± 0.0040	0	$ -0.7409 ^{+ 0.0274 }_{- 0.0293 } $	$ -1.0592 ^{+ 0.0160 }_{- 0.0160 } $
157Lu$ ^{\rm{m}} $$ \to {}^{153}{\rm{Tm}} $	5.1300 ± 0.0020	0	$ 1.7938 ^{+ 0.0107 }_{- 0.0110 } $	$ 1.5764 ^{+ 0.0095 }_{- 0.0095 } $
157Hf$ \to {}^{153}{\rm{Yb}} $	5.8800 ± 0.0030	0	$ -0.9124 ^{+ 0.0038 }_{- 0.0038 } $	$ -1.1911 ^{+ 0.0117 }_{- 0.0117 } $
159Hf$ \to {}^{155}{\rm{Yb}} $	5.2251 ± 0.0027	0	$ 1.1719 ^{+ 0.0083 }_{- 0.0084 } $	$ 1.6282 ^{+ 0.0127 }_{- 0.0127 } $
161Hf$ \to {}^{157}{\rm{Yb}} $	4.6790 ± 0.0250	0	$ 3.8024 ^{+ 0.0093 }_{- 0.0095 } $	$ 4.4473 ^{+ 0.1394 }_{- 0.1406 } $
157Ta$ \to {}^{153}{\rm{Lu}} $$ ^{\rm{m}} $	6.3550 ± 0.0060	0	$ -1.9820 ^{+ 0.0169 }_{- 0.0175 } $	$ -2.5163 ^{+ 0.0209 }_{- 0.0210 } $
157Ta$ ^{\rm{m}} $$ \to {}^{153}{\rm{Lu}} $	6.3900 ± 0.0050	0	$ -2.3665 ^{+ 0.0100 }_{- 0.0102 } $	$ -2.6379 ^{+ 0.0173 }_{- 0.0173 } $
159Ta$ \to {}^{155}{\rm{Lu}} $$ ^{\rm{m}} $	5.6810 ± 0.0240	0	$ 0.4856 ^{+ 0.0360 }_{- 0.0393 } $	$ 0.0744 ^{+ 0.1000 }_{- 0.1006 } $
159Ta$ ^{\rm{m}} $$ \to {}^{155}{\rm{Lu}} $	5.7500 ± 0.0050	0	$ 0.0078 ^{+ 0.0442 }_{- 0.0492 } $	$ -0.2112 ^{+ 0.0205 }_{- 0.0205 } $
161Ta$ ^{\rm{m}} $$ \to {}^{157}{\rm{Lu}} $$ ^{\rm{m}} $	5.2800 ± 0.0230	0	$ 1.6435 ^{+ 0.0152 }_{- 0.0158 } $	$ 1.8681 ^{+ 0.1076 }_{- 0.1084 } $
159W$ \to {}^{155}{\rm{Hf}} $	6.4510 ± 0.0040	0	$ -2.0862 ^{+ 0.0356 }_{- 0.0388 } $	$ -2.4217 ^{+ 0.0138 }_{- 0.0138 } $
161W$ \to {}^{157}{\rm{Hf}} $	5.9230 ± 0.0040	0	$ -0.2516 ^{+ 0.0167 }_{- 0.0174 } $	$ -0.4484 ^{+ 0.0159 }_{- 0.0159 } $
163W$ \to {}^{159}{\rm{Hf}} $	5.5200 ± 0.0600	0	$ 1.2738 ^{+ 0.0146 }_{- 0.0151 } $	$ 1.2610 ^{+ 0.2643 }_{- 0.2689 } $
167W$ \to {}^{163}{\rm{Hf}} $	4.7510 ± 0.0300	0	$ 4.6968 ^{+ 0.0108 }_{- 0.0111 } $	$ 5.1415 ^{+ 0.1682 }_{- 0.1698 } $
163Re$ \to {}^{159}{\rm{Ta}} $	6.0120 ± 0.0080	0	$ 0.0859 ^{+ 0.0717 }_{- 0.0859 } $	$ -0.3462 ^{+ 0.0314 }_{- 0.0315 } $
165Re$ \to {}^{161}{\rm{Ta}} $	5.6940 ± 0.0060	0	$ 1.0580 ^{+ 0.1383 }_{- 0.2041 } $	$ 0.9777 ^{+ 0.0257 }_{- 0.0258 } $
Continued on next page

Table 3.  Same as Table 2 but for the favored α decay of odd-A nuclei. The superscripts "n," "m," or "p" denote excited isomeric states, which are defined as higher states with half-lives exceeding 100 ns. The superscript “p” also presents nonisomeric levels as used in AME2020.

Table 3-continued from previous page
α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
159Re$ ^{\rm{m}} $$ \to {}^{155}{\rm{Ta}} $	6.9700 ± 0.0500	0	$ -3.5740 ^{+ 0.0792 }_{- 0.0969 } $	$ -3.7233 ^{+ 0.1539 }_{- 0.1557 } $
161Re$ ^{\rm{m}} $$ \to {}^{157}{\rm{Ta}} $$ ^{\rm{m}} $	6.4300 ± 0.0013	0	$ -1.8012 ^{+ 0.0088 }_{- 0.0090 } $	$ -1.9210 ^{+ 0.0046 }_{- 0.0046 } $
163Re$ ^{\rm{m}} $$ \to {}^{159}{\rm{Ta}} $$ ^{\rm{m}} $	6.0700 ± 0.0050	0	$ -0.4891 ^{+ 0.0100 }_{- 0.0103 } $	$ -0.5726 ^{+ 0.0194 }_{- 0.0194 } $
165Re$ ^{\rm{m}} $$ \to {}^{161}{\rm{Ta}} $$ ^{\rm{m}} $	5.6600 ± 0.0220	0	$ 1.1266 ^{+ 0.0147 }_{- 0.0152 } $	$ 1.1243 ^{+ 0.0950 }_{- 0.0956 } $
161Os$ \to {}^{157}{\rm{W}} $	7.0690 ± 0.0110	0	$ -3.1938 ^{+ 0.0389 }_{- 0.0428 } $	$ -3.6288 ^{+ 0.0338 }_{- 0.0338 } $
163Os$ \to {}^{159}{\rm{W}} $	6.6730 ± 0.0070	0	$ -2.2441 ^{+ 0.0365 }_{- 0.0399 } $	$ -2.3368 ^{+ 0.0236 }_{- 0.0236 } $
165Os$ \to {}^{161}{\rm{W}} $	6.3350 ± 0.0060	0	$ -1.1030 ^{+ 0.0180 }_{- 0.0187 } $	$ -1.1301 ^{+ 0.0220 }_{- 0.0220 } $
167Os$ \to {}^{163}{\rm{W}} $	5.9800 ± 0.0600	0	$ 0.2162 ^{+ 0.0026 }_{- 0.0026 } $	$ 0.2519 ^{+ 0.2397 }_{- 0.2436 } $
169Os$ \to {}^{165}{\rm{W}} $	5.7130 ± 0.0030	0	$ 1.4024 ^{+ 0.0202 }_{- 0.0212 } $	$ 1.3843 ^{+ 0.0130 }_{- 0.0130 } $
171Os$ \to {}^{167}{\rm{W}} $	5.3710 ± 0.0040	0	$ 2.6638 ^{+ 0.0103 }_{- 0.0106 } $	$ 2.9577 ^{+ 0.0191 }_{- 0.0191 } $
173Os$ \to {}^{169}{\rm{W}} $	5.0550 ± 0.0060	0	$ 3.7482 ^{+ 0.0171 }_{- 0.0178 } $	$ 4.5595 ^{+ 0.0315 }_{- 0.0316 } $
167Ir$ \to {}^{163}{\rm{Re}} $	6.5049 ± 0.0026	0	$ -1.1716 ^{+ 0.0088 }_{- 0.0090 } $	$ -1.3141 ^{+ 0.0093 }_{- 0.0093 } $
169Ir$ \to {}^{165}{\rm{Re}} $	6.1410 ± 0.0040	0	$ -0.1765 ^{+ 0.0049 }_{- 0.0049 } $	$ 0.0635 ^{+ 0.0157 }_{- 0.0157 } $
171Ir$ \to {}^{167}{\rm{Re}} $$ ^{\rm{m}} $	5.9970 ± 0.0120	0	$ 1.3153 ^{+ 0.0401 }_{- 0.0442 } $	$ 0.6552 ^{+ 0.0487 }_{- 0.0489 } $
173Ir$ \to {}^{169}{\rm{Re}} $$ ^{\rm{m}} $	5.7160 ± 0.0090	0	$ 2.4102 ^{+ 0.0370 }_{- 0.0404 } $	$ 1.8601 ^{+ 0.0395 }_{- 0.0396 } $
177Ir$ \to {}^{173}{\rm{Re}} $	5.0800 ± 0.0300	0	$ 4.6961 ^{+ 0.0241 }_{- 0.0255 } $	$ 4.9612 ^{+ 0.1582 }_{- 0.1597 } $
165Ir$ ^{\rm{m}} $$ \to {}^{161}{\rm{Re}} $$ ^{\rm{m}} $	6.8800 ± 0.0500	0	$ -2.5673 ^{+ 0.0389 }_{- 0.0428 } $	$ -2.6105 ^{+ 0.1620 }_{- 0.1639 } $
167Ir$ ^{\rm{m}} $$ \to {}^{163}{\rm{Re}} $$ ^{\rm{m}} $	6.5600 ± 0.0021	0	$ -1.4945 ^{+ 0.0076 }_{- 0.0077 } $	$ -1.5095 ^{+ 0.0074 }_{- 0.0074 } $
169Ir$ ^{\rm{m}} $$ \to {}^{165}{\rm{Re}} $$ ^{\rm{m}} $	6.2700 ± 0.0220	0	$ -0.4505 ^{+ 0.0015 }_{- 0.0016 } $	$ -0.4334 ^{+ 0.0831 }_{- 0.0836 } $
165Pt$ \to {}^{161}{\rm{Os}} $	7.4530 ± 0.0140	0	$ -3.4318 ^{+ 0.1722 }_{- 0.2894 } $	$ -3.9938 ^{+ 0.0406 }_{- 0.0407 } $
167Pt$ \to {}^{163}{\rm{Os}} $	7.1600 ± 0.0600	0	$ -3.0386 ^{+ 0.0548 }_{- 0.0627 } $	$ -3.0981 ^{+ 0.1847 }_{- 0.1873 } $
169Pt$ \to {}^{165}{\rm{Os}} $	6.8580 ± 0.0050	0	$ -2.1555 ^{+ 0.0056 }_{- 0.0056 } $	$ -2.1118 ^{+ 0.0166 }_{- 0.0166 } $
171Pt$ \to {}^{167}{\rm{Os}} $	6.6070 ± 0.0030	0	$ -1.2765 ^{+ 0.0232 }_{- 0.0245 } $	$ -1.2348 ^{+ 0.0106 }_{- 0.0106 } $
173Pt$ \to {}^{169}{\rm{Os}} $	6.3600 ± 0.0600	0	$ -0.3524 ^{+ 0.0023 }_{- 0.0023 } $	$ -0.3183 ^{+ 0.2237 }_{- 0.2272 } $
177Pt$ \to {}^{173}{\rm{Os}} $	5.6429 ± 0.0027	0	$ 2.2441 ^{+ 0.0170 }_{- 0.0177 } $	$ 2.6791 ^{+ 0.0123 }_{- 0.0123 } $
181Pt$ \to {}^{177}{\rm{Os}} $	5.1500 ± 0.0050	0	$ 4.8468 ^{+ 0.0180 }_{- 0.0188 } $	$ 5.1229 ^{+ 0.0263 }_{- 0.0263 } $
183Pt$ \to {}^{179}{\rm{Os}} $	4.8220 ± 0.0090	0	$ 6.6088 ^{+ 0.0621 }_{- 0.0726 } $	$ 6.9559 ^{+ 0.0524 }_{- 0.0526 } $
185Pt$ \to {}^{181}{\rm{Os}} $$ ^{\rm{n}} $	4.2800 ± 0.0100	0	$ 7.9298 ^{+ 0.0145 }_{- 0.0150 } $	$ 10.4418 ^{+ 0.0701 }_{- 0.0704 } $
173Au$ \to {}^{169}{\rm{Ir}} $	6.8360 ± 0.0050	0	$ -1.5280 ^{+ 0.0134 }_{- 0.0138 } $	$ -1.6094 ^{+ 0.0170 }_{- 0.0170 } $
175Au$ \to {}^{171}{\rm{Ir}} $	6.5834 ± 0.0027	0	$ -0.6435 ^{+ 0.0065 }_{- 0.0066 } $	$ -0.7096 ^{+ 0.0097 }_{- 0.0097 } $
177Au$ \to {}^{173}{\rm{Ir}} $	6.2980 ± 0.0040	0	$ 0.5743 ^{+ 0.0057 }_{- 0.0058 } $	$ 0.3731 ^{+ 0.0155 }_{- 0.0155 } $
179Au$ \to {}^{175}{\rm{Ir}} $	5.9810 ± 0.0050	0	$ 1.5088 ^{+ 0.0180 }_{- 0.0187 } $	$ 1.6687 ^{+ 0.0210 }_{- 0.0210 } $
181Au$ \to {}^{177}{\rm{Ir}} $	5.7514 ± 0.0029	0	$ 2.7054 ^{+ 0.0423 }_{- 0.0468 } $	$ 2.6814 ^{+ 0.0130 }_{- 0.0130 } $
183Au$ \to {}^{179}{\rm{Ir}} $	5.4653 ± 0.0029	0	$ 3.8911 ^{+ 0.0100 }_{- 0.0103 } $	$ 4.0316 ^{+ 0.0141 }_{- 0.0141 } $
185Au$ \to {}^{181}{\rm{Ir}} $	5.1080 ± 0.0050	0	$ 4.9916 ^{+ 0.0061 }_{- 0.0062 } $	$ 5.8778 ^{+ 0.0270 }_{- 0.0270 } $
171Au$ ^{\rm{m}} $$ \to {}^{167}{\rm{Ir}} $$ ^{\rm{m}} $	7.1600 ± 0.0100	0	$ -2.7628 ^{+ 0.0067 }_{- 0.0068 } $	$ -2.6843 ^{+ 0.0314 }_{- 0.0315 } $
173Au$ ^{\rm{m}} $$ \to {}^{169}{\rm{Ir}} $$ ^{\rm{m}} $	6.9000 ± 0.0210	0	$ -1.8630 ^{+ 0.0035 }_{- 0.0036 } $	$ -1.8249 ^{+ 0.0700 }_{- 0.0703 } $
175Au$ ^{\rm{m}} $$ \to {}^{171}{\rm{Ir}} $$ ^{\rm{m}} $	6.5900 ± 0.0110	0	$ -0.7415 ^{+ 0.0032 }_{- 0.0032 } $	$ -0.7334 ^{+ 0.0395 }_{- 0.0396 } $
177Au$ ^{\rm{m}} $$ \to {}^{173}{\rm{Ir}} $$ ^{\rm{m}} $	6.2600 ± 0.0070	0	$ 0.2985 ^{+ 0.0049 }_{- 0.0050 } $	$ 0.5209 ^{+ 0.0273 }_{- 0.0274 } $
173Hg$ \to {}^{169}{\rm{Pt}} $	7.3780 ± 0.0040	0	$ -3.0969 ^{+ 0.0414 }_{- 0.0458 } $	$ -2.9648 ^{+ 0.0122 }_{- 0.0122 } $
175Hg$ \to {}^{171}{\rm{Pt}} $	7.0720 ± 0.0050	0	$ -1.9914 ^{+ 0.0126 }_{- 0.0130 } $	$ -1.9858 ^{+ 0.0163 }_{- 0.0163 } $
Continued on next page

Table 3-continued from previous page
α decay	$ Q_{\alpha} $	l	$ \log_{10}{T}_{1/2}^{\rm{\,exp}} $	$ \log_{10}{T}_{1/2}^{\rm{\,HOPM}} $
179Hg$ \to {}^{175}{\rm{Pt}} $	6.3500 ± 0.0300	0	$ 0.1461 ^{+ 0.0122 }_{- 0.0126 } $	$ 0.6115 ^{+ 0.1158 }_{- 0.1167 } $
183Hg$ \to {}^{179}{\rm{Pt}} $	6.0390 ± 0.0040	0	$ 1.9049 ^{+ 0.0312 }_{- 0.0336 } $	$ 1.8988 ^{+ 0.0168 }_{- 0.0168 } $
185Hg$ \to {}^{181}{\rm{Pt}} $	5.7730 ± 0.0040	0	$ 2.9129 ^{+ 0.0088 }_{- 0.0089 } $	$ 3.0732 ^{+ 0.0180 }_{- 0.0181 } $
177Tl$ \to {}^{173}{\rm{Au}} $	7.0670 ± 0.0070	0	$ -1.6081 ^{+ 0.1065 }_{- 0.1413 } $	$ -1.5657 ^{+ 0.0231 }_{- 0.0232 } $
179Tl$ \to {}^{175}{\rm{Au}} $	6.7091 ± 0.0026	0	$ -0.1377 ^{+ 0.0089 }_{- 0.0090 } $	$ -0.3152 ^{+ 0.0093 }_{- 0.0094 } $
181Tl$ \to {}^{177}{\rm{Au}} $	6.3220 ± 0.0040	0	$ 1.5279 ^{+ 0.0147 }_{- 0.0152 } $	$ 1.1615 ^{+ 0.0158 }_{- 0.0158 } $
177Tl$ ^{\rm{m}} $$ \to {}^{173}{\rm{Au}} $$ ^{\rm{m}} $	7.6600 ± 0.0180	0	$ -3.3285 ^{+ 0.0696 }_{- 0.0830 } $	$ -3.4017 ^{+ 0.0521 }_{- 0.0523 } $
179Tl$ ^{\rm{m}} $$ \to {}^{175}{\rm{Au}} $$ ^{\rm{m}} $	7.3700 ± 0.0100	0	$ -2.8508 ^{+ 0.0061 }_{- 0.0062 } $	$ -2.5178 ^{+ 0.0309 }_{- 0.0309 } $
185Pb$ ^{\rm{m}} $$ \to {}^{181}{\rm{Hg}} $$ ^{\rm{m}} $	6.5600 ± 0.0500	0	$ 0.9106 ^{+ 0.0157 }_{- 0.0163 } $	$ 0.6931 ^{+ 0.1879 }_{- 0.1902 } $
187Pb$ ^{\rm{m}} $$ \to {}^{183}{\rm{Hg}} $$ ^{\rm{m}} $	6.2100 ± 0.0100	0	$ 2.1833 ^{+ 0.0071 }_{- 0.0072 } $	$ 2.0922 ^{+ 0.0412 }_{- 0.0413 } $
189Pb$ ^{\rm{m}} $$ \to {}^{185}{\rm{Hg}} $$ ^{\rm{m}} $	5.8500 ± 0.0040	0	$ 4.1012 ^{+ 0.0177 }_{- 0.0184 } $	$ 3.6672 ^{+ 0.0182 }_{- 0.0182 } $
191Pb$ ^{\rm{m}} $$ \to {}^{187}{\rm{Hg}} $$ ^{\rm{m}} $	5.4000 ± 0.0100	0	$ 5.8156 ^{+ 0.0157 }_{- 0.0162 } $	$ 5.8605 ^{+ 0.0515 }_{- 0.0516 } $
185Bi$ ^{\rm{m}} $$ \to {}^{181}{\rm{Tl}} $	8.2200 ± 0.0800	0	$ -3.2366 ^{+ 0.0290 }_{- 0.0310 } $	$ -4.1870 ^{+ 0.2109 }_{- 0.2143 } $
187Bi$ ^{\rm{m}} $$ \to {}^{183}{\rm{Tl}} $	7.8900 ± 0.0080	0	$ -3.4318 ^{+ 0.0229 }_{- 0.0241 } $	$ -3.2649 ^{+ 0.0227 }_{- 0.0228 } $
189Bi$ ^{\rm{m}} $$ \to {}^{185}{\rm{Tl}} $	7.4500 ± 0.0050	0	$ -2.2201 ^{+ 0.0086 }_{- 0.0088 } $	$ -1.9388 ^{+ 0.0156 }_{- 0.0156 } $
191Bi$ \to {}^{187}{\rm{Tl}} $$ ^{\rm{m}} $	6.4500 ± 0.0030	0	$ 1.3859 ^{+ 0.0104 }_{- 0.0106 } $	$ 1.5833 ^{+ 0.0118 }_{- 0.0118 } $
191Bi$ ^{\rm{m}} $$ \to {}^{187}{\rm{Tl}} $	7.0200 ± 0.0250	0	$ -0.7356 ^{+ 0.0269 }_{- 0.0287 } $	$ -0.5146 ^{+ 0.0857 }_{- 0.0862 } $
193Bi$ \to {}^{189}{\rm{Tl}} $$ ^{\rm{m}} $	6.0200 ± 0.0050	0	$ 3.2594 ^{+ 0.0200 }_{- 0.0210 } $	$ 3.3889 ^{+ 0.0220 }_{- 0.0220 } $
193Bi$ ^{\rm{m}} $$ \to {}^{189}{\rm{Tl}} $	6.6100 ± 0.0060	0	$ 0.5809 ^{+ 0.0186 }_{- 0.0194 } $	$ 0.9806 ^{+ 0.0227 }_{- 0.0228 } $
195Bi$ \to {}^{191}{\rm{Tl}} $$ ^{\rm{m}} $	5.5400 ± 0.0050	0	$ 5.7853 ^{+ 0.0094 }_{- 0.0096 } $	$ 5.6596 ^{+ 0.0251 }_{- 0.0251 } $
195Bi$ ^{\rm{m}} $$ \to {}^{191}{\rm{Tl}} $	6.2300 ± 0.0060	0	$ 2.4210 ^{+ 0.0050 }_{- 0.0050 } $	$ 2.5056 ^{+ 0.0250 }_{- 0.0250 } $
197Bi$ ^{\rm{m}} $$ \to {}^{193}{\rm{Tl}} $	5.9000 ± 0.0120	0	$ 2.7402 ^{+ 0.0136 }_{- 0.0140 } $	$ 3.9566 ^{+ 0.0544 }_{- 0.0546 } $
191Po$ \to {}^{187}{\rm{Pb}} $	7.4930 ± 0.0050	0	$ -1.6576 ^{+ 0.0193 }_{- 0.0202 } $	$ -1.6837 ^{+ 0.0157 }_{- 0.0157 } $
193Po$ \to {}^{189}{\rm{Pb}} $	7.0940 ± 0.0040	0	$ -0.3990 ^{+ 0.0355 }_{- 0.0387 } $	$ -0.3607 ^{+ 0.0137 }_{- 0.0137 } $
195Po$ \to {}^{191}{\rm{Pb}} $	6.7497 ± 0.0028	0	$ 0.6934 ^{+ 0.0083 }_{- 0.0085 } $	$ 0.8827 ^{+ 0.0104 }_{- 0.0104 } $
197Po$ \to {}^{193}{\rm{Pb}} $	6.4110 ± 0.0030	0	$ 2.0857 ^{+ 0.0072 }_{- 0.0074 } $	$ 2.2086 ^{+ 0.0121 }_{- 0.0121 } $
199Po$ \to {}^{195}{\rm{Pb}} $	6.0743 ± 0.0019	0	$ 3.6411 ^{+ 0.0117 }_{- 0.0121 } $	$ 3.6414 ^{+ 0.0083 }_{- 0.0084 } $
201Po$ \to {}^{197}{\rm{Pb}} $	5.7993 ± 0.0017	0	$ 4.9182 ^{+ 0.0028 }_{- 0.0028 } $	$ 4.9107 ^{+ 0.0080 }_{- 0.0080 } $
205Po$ \to {}^{201}{\rm{Pb}} $	5.3250 ± 0.0100	0	$ 7.1948 ^{+ 0.0195 }_{- 0.0204 } $	$ 7.3415 ^{+ 0.0541 }_{- 0.0542 } $
207Po$ \to {}^{203}{\rm{Pb}} $	5.2159 ± 0.0025	0	$ 7.9975 ^{+ 0.0015 }_{- 0.0015 } $	$ 7.9571 ^{+ 0.0140 }_{- 0.0140 } $
209Po$ \to {}^{205}{\rm{Pb}} $$ ^{\rm{m}} $	4.9800 ± 0.0014	0	$ 9.5945 ^{+ 0.0104 }_{- 0.0106 } $	$ 9.3406 ^{+ 0.0084 }_{- 0.0084 } $
213Po$ \to {}^{209}{\rm{Pb}} $	8.5361 ± 0.0026	0	$ -5.4312 ^{+ 0.0001 }_{- 0.0001 } $	$ -5.8339 ^{+ 0.0065 }_{- 0.0065 } $
215Po$ \to {}^{211}{\rm{Pb}} $	7.5263 ± 0.0008	0	$ -2.7493 ^{+ 0.0012 }_{- 0.0012 } $	$ -3.0161 ^{+ 0.0025 }_{- 0.0025 } $
217Po$ \to {}^{213}{\rm{Pb}} $	6.6621 ± 0.0024	0	$ 0.1957 ^{+ 0.0140 }_{- 0.0144 } $	$ -0.0592 ^{+ 0.0090 }_{- 0.0090 } $
219Po$ \to {}^{215}{\rm{Pb}} $	5.9100 ± 0.0500	0	$ 3.3407 ^{+ 0.0402 }_{- 0.0444 } $	$ 3.0699 ^{+ 0.2266 }_{- 0.2297 } $
187Po$ ^{\rm{m}} $$ \to {}^{183}{\rm{Pb}} $$ ^{\rm{m}} $	7.8900 ± 0.0270	0	$ -3.3010 ^{+ 0.0000 }_{- 0.0000 } $	$ -2.9076 ^{+ 0.0776 }_{- 0.0780 } $
191Po$ ^{\rm{m}} $$ \to {}^{187}{\rm{Pb}} $$ ^{\rm{m}} $	7.5400 ± 0.0110	0	$ -1.0315 ^{+ 0.0138 }_{- 0.0142 } $	$ -1.8304 ^{+ 0.0341 }_{- 0.0342 } $
193Po$ ^{\rm{m}} $$ \to {}^{189}{\rm{Pb}} $$ ^{\rm{m}} $	7.1500 ± 0.0060	0	$ -0.6108 ^{+ 0.0191 }_{- 0.0200 } $	$ -0.5513 ^{+ 0.0203 }_{- 0.0203 } $
195Po$ ^{\rm{m}} $$ \to {}^{191}{\rm{Pb}} $$ ^{\rm{m}} $	6.8411 ± 0.0090	0	$ 0.2833 ^{+ 0.0045 }_{- 0.0045 } $	$ 0.5470 ^{+ 0.0327 }_{- 0.0327 } $
197Po$ ^{\rm{m}} $$ \to {}^{193}{\rm{Pb}} $$ ^{\rm{m}} $	6.5200 ± 0.0120	0	$ 1.4873 ^{+ 0.0017 }_{- 0.0017 } $	$ 1.7749 ^{+ 0.0470 }_{- 0.0472 } $
199Po$ ^{\rm{m}} $$ \to {}^{195}{\rm{Pb}} $$ ^{\rm{m}} $	6.1800 ± 0.0027	0	$ 3.0181 ^{+ 0.0052 }_{- 0.0052 } $	$ 3.1832 ^{+ 0.0115 }_{- 0.0115 } $
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