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-beta-decay half-lives are not only important parameters for studying the structures and decay properties of the exotic nucleus far from stability, but also basic parameters for understanding the astrophysical phenomenon. Astrophysicists need exact data of -decay half-lives as input to build nucleosynthesis models for understanding the elements abundances of our universe and solar system. For nuclei far from stability, experimental synthesis and further measurements on their half-lives are rather difficult due to the rarity and radioactivity of target material for synthesizing these nuclei. In theoretical respect, although there are many models such as finite-range droplet model plus quasi-particle random-phase approximation (QRPA), microscopic density functional theory plus QRPA, Hatree-Fock-Bogoliubov theory plus QRPA, and shell model etc., it is still a challenge to calculate -decay half-lives in a reliable way for nuclei far from the -stable line, partly because of the intrinsic complexity of nuclear multi-body problem. In empirical respect, Sargent made an empirical study of -decay half-lives in 1933 and discovered a law which is consistent with the Fermi -decay theory proposed one year later. From then on, there have been a few parametric models based on some of real physical behaviors, which describe complex quantum many-body systems, such as the Kratz-Herrmann formula and the gross theory. Recently, Zhang et al. discovered an exponential law describing -decay half-lives and the nucleon number (Z,N) of parent nuclei far from the stable line. A formula is proposed to calculate the -decay half-lives of nuclei far from stability, which can describe experimental data reasonably well. However, the differences between allowed transitions and forbidden transitions are not fully considered in this formula. Zhang et al. used a set of parameters to describe both allowed transitions and forbidden transitions. In this paper, we consider the different -decay half-lives of allowed transitions and forbidden transitions, and propose an updated parameterization of this formula. A set of parameters is obtained through fitting experimental data of different kinds of transitions with a least-square method. With these new parameters, the theoretical calculation results are in good agreement with the experimental values. The calculation accuracy is improved compared with previous version. By comparison with the complicated and time-consuming microscopic calculation, the improved exponential formula can give the results of -decay half-lives for the allowed transitions and the forbidden transitions in an effective and reliable way. According to the updated formula, we predict half-lives of --decay half-lives of some unknown nuclei far from the -stable line. These predictions are very useful references for the experimental study of --decay of nuclei far from stability and for astrophysical applications.
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Keywords:
- -decay half-lives /
- exponential law /
- allowed transitions /
- forbidden transitions
[1] Lee T D, Yang C N 1956 Phys. Rev. 104 254
[2] Feimi E 1934 Z. Phys. 88 161
[3] Feynman R P, Gell-Mann M 1958 Phys. Rev. 109 193
[4] Sudarshan E C G, Marshak R E 1958 Phys. Rev. 109 1860
[5] Mller P, Nix J R, Kratz K L 1997 At. Data Nucl. Data Tables 66 131
[6] Borzov I 2006 Nucl. Phys. A 777 645
[7] Engel J, Bender M, Dobaczewski J, Nazarewicz W, Surman R 1999 Phys. Rev. C 60 014302
[8] Ni D D, Ren Z Z, Zhi Q J 2011 Sci. China: Phys. Mech. Astron. 55 2397
[9] Zhi Q J, Caurier E, Cuenca-Garca J J, Langanke K, Martnez-Pinedo G, Sieja K 2013 Phys. Rev. C 87 025803
[10] Nabi J U, Klapdor-Kleingrothaus H V 2004 At. Data Nucl. Data Tables 88 237
[11] Vogel P, Zirnbauer M R 1986 Phys. Rev. Lett. 57 3148
[12] Koonin S E 1991 Nature 354 468
[13] Haxton W C, Johnson C 1990 Phys. Rev. Lett. 65 1325
[14] Langanke K, Martnez R, Guerra E M 2005 Eur. Phys. J. A 24 193
[15] Sarriguren P, lavarez-Rodrguez R, Guerra E M 2005 Eur. Phys. J. A 24 193
[16] Pantis G, imkovic F, Vergados J D, Faessler A 1996 Phys. Rev. C 53 695
[17] Zhi Q J, Zheng Q 2011 Acta Phys. Sin. 60 102301 (in Chinese) [支启军, 郑强 2011 物理学报 60 102301]
[18] Zhang Y M, Xu F R 2008 Acta Phys. Sin. 57 4826 (in Chinese) [张玉美, 许甫荣 2008 物理学报 57 4826]
[19] Kratz K-L, Herrmann G 1973 Z. Phys. 263 435
[20] Pfeiffer B, Kratz K L, Mller P 2002 Prog. Nucl. Energy 41 39
[21] Takahashi K, Yamada M 1969 Prog. Theor. Phys. 41 1470
[22] Zhang X P, Ren Z Z 2006 Phys. Rev. C 73 014305
[23] Lu X T, Jiang D X, Ye Y L 2000 Nuclear Physics (Vol. 2)(Bijing: Atomic Energy Press) pp129-146 (in Chinese) [卢希庭, 江栋兴, 叶沿林 2000 原子核物理(北 京: 原子能出版社) 第129-146页]
[24] Smith C M H 1965 A Textbook of Nuclear Physics (Vol. 1)(Oxford: Pergamon) pp140-145
[25] Evans R D 1955 The Atomic Nucleus (Vol. 1)(New York: McGraw-Hill) pp200-210
[26] Zhang X P, Ren Z Z, Zhi Q J, Zhang Q 2007 J. Phys. G 34 2611
[27] National Nuclear Data Center On-line Retrieval System 2014 Nuclear Strucre -Decay Data (New York: Brookhaven National Laboratory)
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[1] Lee T D, Yang C N 1956 Phys. Rev. 104 254
[2] Feimi E 1934 Z. Phys. 88 161
[3] Feynman R P, Gell-Mann M 1958 Phys. Rev. 109 193
[4] Sudarshan E C G, Marshak R E 1958 Phys. Rev. 109 1860
[5] Mller P, Nix J R, Kratz K L 1997 At. Data Nucl. Data Tables 66 131
[6] Borzov I 2006 Nucl. Phys. A 777 645
[7] Engel J, Bender M, Dobaczewski J, Nazarewicz W, Surman R 1999 Phys. Rev. C 60 014302
[8] Ni D D, Ren Z Z, Zhi Q J 2011 Sci. China: Phys. Mech. Astron. 55 2397
[9] Zhi Q J, Caurier E, Cuenca-Garca J J, Langanke K, Martnez-Pinedo G, Sieja K 2013 Phys. Rev. C 87 025803
[10] Nabi J U, Klapdor-Kleingrothaus H V 2004 At. Data Nucl. Data Tables 88 237
[11] Vogel P, Zirnbauer M R 1986 Phys. Rev. Lett. 57 3148
[12] Koonin S E 1991 Nature 354 468
[13] Haxton W C, Johnson C 1990 Phys. Rev. Lett. 65 1325
[14] Langanke K, Martnez R, Guerra E M 2005 Eur. Phys. J. A 24 193
[15] Sarriguren P, lavarez-Rodrguez R, Guerra E M 2005 Eur. Phys. J. A 24 193
[16] Pantis G, imkovic F, Vergados J D, Faessler A 1996 Phys. Rev. C 53 695
[17] Zhi Q J, Zheng Q 2011 Acta Phys. Sin. 60 102301 (in Chinese) [支启军, 郑强 2011 物理学报 60 102301]
[18] Zhang Y M, Xu F R 2008 Acta Phys. Sin. 57 4826 (in Chinese) [张玉美, 许甫荣 2008 物理学报 57 4826]
[19] Kratz K-L, Herrmann G 1973 Z. Phys. 263 435
[20] Pfeiffer B, Kratz K L, Mller P 2002 Prog. Nucl. Energy 41 39
[21] Takahashi K, Yamada M 1969 Prog. Theor. Phys. 41 1470
[22] Zhang X P, Ren Z Z 2006 Phys. Rev. C 73 014305
[23] Lu X T, Jiang D X, Ye Y L 2000 Nuclear Physics (Vol. 2)(Bijing: Atomic Energy Press) pp129-146 (in Chinese) [卢希庭, 江栋兴, 叶沿林 2000 原子核物理(北 京: 原子能出版社) 第129-146页]
[24] Smith C M H 1965 A Textbook of Nuclear Physics (Vol. 1)(Oxford: Pergamon) pp140-145
[25] Evans R D 1955 The Atomic Nucleus (Vol. 1)(New York: McGraw-Hill) pp200-210
[26] Zhang X P, Ren Z Z, Zhi Q J, Zhang Q 2007 J. Phys. G 34 2611
[27] National Nuclear Data Center On-line Retrieval System 2014 Nuclear Strucre -Decay Data (New York: Brookhaven National Laboratory)
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