Calculation of α Decay Half-Lives for Tl, Bi, and At Isotopes
Abstract
:1. Introduction
2. Theoretical Framework
2.1. Deformed Relativistic Hartree–Bogoliubov Theory in Continuum
2.2. Empirical Formula for Decay Half-Lives
2.2.1. Royer Formula
2.2.2. AKRA Formula
2.2.3. Viola–Seaborg–Sobiczewski (VSS) Formula
2.2.4. Parkhomenko–Sobiczewski (SP) Formula
2.2.5. Universal Decay Law (UDL) Formula
3. Results
4. Summary
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Transition | EXP | AKRA | Royer | SP | UDL | VSS | |
---|---|---|---|---|---|---|---|
184Bi →180Tl | 8.22 | −1.89 | −3.71 | −4.53 | −3.56 | −5.23 | −4.45 |
186Bi →182Tl | 7.76 | −1.83 | −2.21 | −3.13 | −2.15 | −3.85 | −3.12 |
187Bi →183Tl | 7.76 | −1.43 | −3.23 | −3.12 | −2.68 | −3.87 | −3.46 |
188Bi →184Tl | 7.26 | −1.22 | −0.47 | −1.49 | −0.49 | −2.23 | −1.57 |
189Bi →185Tl | 7.27 | −0.16 | −1.56 | −1.60 | −1.10 | −2.26 | −1.92 |
191At →187Bi | 7.82 | −2.77 | −2.55 | −2.57 | −2.07 | −3.27 | −2.87 |
192At →188Bi | 7.70 | −1.94 | −1.17 | −2.13 | −1.12 | −2.87 | −2.14 |
193At →189Bi | 7.57 | −1.55 | −1.74 | −1.82 | −1.27 | −2.47 | −2.09 |
194At →190Bi | 7.45 | −0.54 | −0.25 | −1.33 | −0.29 | −2.09 | −1.37 |
195At →191Bi | 7.34 | −0.51 | −0.97 | −1.11 | −0.50 | −1.72 | −1.35 |
212At →208Bi | 7.82 | −0.50 | −0.25 | −2.94 | −1.51 | −3.62 | −2.51 |
213At →209Bi | 9.25 | −6.90 | −7.48 | −6.93 | −6.00 | −7.75 | −6.70 |
214At →210Bi | 8.99 | −6.25 | −3.49 | −6.46 | −4.91 | −7.08 | −5.71 |
215At →211Bi | 8.18 | −4.43 | −4.41 | −4.14 | −3.15 | −4.81 | −3.91 |
216At →212Bi | 7.95 | −3.52 | −0.35 | −3.45 | −1.94 | −4.12 | −2.91 |
217At →213Bi | 7.20 | −1.49 | −1.04 | −1.07 | −0.01 | −1.58 | −0.87 |
218At →214Bi | 6.88 | 0.11 | 3.59 | 0.36 | 1.85 | −0.36 | 0.63 |
standard deviation | 1.55 | 1.11 | 1.09 | 1.61 | 1.16 |
Transition | EXP | AKRA | Royer | SP | UDL | VSS | |
---|---|---|---|---|---|---|---|
184Bi →180Tl | 8.04 | −1.89 | −3.18 | −3.98 | −3.02 | −4.69 | −3.94 |
186Bi →182Tl | 7.15 | −1.83 | −0.16 | −1.03 | −0.08 | −1.79 | −1.19 |
187Bi →183Tl | 6.75 | −1.43 | 0.52 | 0.28 | 0.76 | −0.31 | −0.13 |
188Bi →184Tl | 6.77 | −1.22 | 1.36 | 0.38 | 1.36 | −0.39 | 0.15 |
189Bi →185Tl | 6.27 | −0.16 | 2.57 | 2.15 | 2.70 | 1.66 | 1.75 |
191At →187Bi | 8.00 | −2.77 | −3.15 | −3.11 | −2.62 | −3.84 | −3.40 |
192At →188Bi | 7.76 | −1.94 | −1.37 | −2.33 | −1.32 | −3.08 | −2.33 |
193At →189Bi | 7.92 | −1.55 | −2.94 | −2.91 | −2.37 | −3.62 | −3.16 |
194At →190Bi | 7.77 | −0.54 | −1.30 | −2.41 | −1.35 | −3.14 | −2.36 |
195At →191Bi | 7.83 | −0.51 | −2.69 | −2.67 | −2.08 | −3.35 | −2.88 |
212At →208Bi | 7.67 | −0.50 | 0.22 | −2.46 | −1.04 | −3.15 | −2.07 |
213At →209Bi | 10.27 | −6.90 | −9.97 | −9.19 | −8.27 | −10.11 | −8.91 |
214At →210Bi | 9.86 | −6.25 | −5.61 | −8.63 | −7.01 | −9.21 | −7.71 |
215At →211Bi | 9.18 | −4.43 | −7.34 | −6.79 | −5.82 | −7.59 | −6.52 |
216At →212Bi | 7.96 | −3.52 | −0.37 | −3.48 | −1.96 | −4.14 | −2.93 |
217At →213Bi | 7.46 | −1.49 | −2.03 | −1.97 | −0.91 | −2.52 | −1.75 |
218At →214Bi | 6.33 | 0.11 | 5.86 | 2.68 | 4.15 | 1.93 | 2.77 |
standard deviation | 2.33 | 1.77 | 1.75 | 2.11 | 1.62 | ||
standard deviation (+) | 6.07 | 6.62 | 5.59 | 7.38 | 6.24 | ||
standard deviation (−) | 11.12 | 9.81 | 10.98 | 9.29 | 9.26 |
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Mun, M.-H.; Heo, K.; Cheoun, M.-K. Calculation of α Decay Half-Lives for Tl, Bi, and At Isotopes. Particles 2025, 8, 42. https://doi.org/10.3390/particles8020042
Mun M-H, Heo K, Cheoun M-K. Calculation of α Decay Half-Lives for Tl, Bi, and At Isotopes. Particles. 2025; 8(2):42. https://doi.org/10.3390/particles8020042
Chicago/Turabian StyleMun, Myeong-Hwan, Kyoungsu Heo, and Myung-Ki Cheoun. 2025. "Calculation of α Decay Half-Lives for Tl, Bi, and At Isotopes" Particles 8, no. 2: 42. https://doi.org/10.3390/particles8020042
APA StyleMun, M.-H., Heo, K., & Cheoun, M.-K. (2025). Calculation of α Decay Half-Lives for Tl, Bi, and At Isotopes. Particles, 8(2), 42. https://doi.org/10.3390/particles8020042