搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

原子核β衰变寿命经验公式

夏金戈 李伟峰 方基宇 牛中明

引用本文:
Citation:

原子核β衰变寿命经验公式

夏金戈, 李伟峰, 方基宇, 牛中明

An empirical formula of nuclear β-decay half-lives

Xia Jin-Ge, Li Wei-Feng, Fang Ji-Yu, Niu Zhong-Ming
PDF
HTML
导出引用
  • 基于β衰变的费米理论, 提出一个计算原子核β衰变寿命且不含自由参数的经验公式. 通过引入奇偶效应、壳效应以及同位旋依赖, 新提出的经验公式显著改进了对原子核β 衰变寿命的预言精度. 对于寿命小于1 s的原子核, 新经验公式的预言结果与实验寿命常用对数的均方根偏差降至0.220, 这比不含自由参数的经验公式提高约54%, 甚至优于目前已有的其他经验公式和微观的准粒子无规相位近似方法. 在未知核区, 新经验公式预言的轻核区原子核的β衰变寿命一般短于各微观模型的预言结果, 而其预言的重核区原子核的β衰变寿命与各微观模型预言结果基本一致. 进一步采用新经验公式预言了核素图上丰中子原子核的β衰变寿命, 为r - 过程的模拟提供了寿命输入.
    Nuclear β-decay half-lives play an important role not only in nuclear physics, but also in astrophysics. The β-decay half-lives of many nuclei involved in the astrophysical rapid neutron-capture (r -process) still cannot be measured experimentally, so the theoretical predictions of nuclear β-decay half-lives are inevitable for r-process studies. Theoretical models for studying the nuclear β-decay half-lives include the empirical formula, the gross theory, the quasiparticle random phase approximation (QRPA), and the shell model. Compared with other theoretical models of β-decay half-lives, the empirical formula has high computational efficiency, and its prediction accuracy can be improved by introducing more and more physical information. In this work, an empirical formula without free parameters is proposed to calculate the nuclear β-decay half-lives based on the Fermi theory of β decay. By including the pairing effect, the shell effect, and the isospin dependence, the newly proposed empirical formula significantly improves the accuracy of predicting the nuclear β-decay half-life. For the nuclei with half-lives less than 1 second, the root-mean-square deviation of the common logarithms of the nuclear β-decay half-life predicted by the new empirical formula from the experimental data decreases to 0.220, which is improved by about 54% compared with that by the empirical formula without free parameters, even better than those by other existing empirical formulas and microscopic QRPA approaches. In the unknown region, the nuclear β-decay half-lives predicted by the new empirical formula are generally shorter than those predicted by the microscopic models in the light nuclear region, while those predicted by the new empirical formula in the heavy nuclear region are generally in agreement with those predicted by the microscopic models. The half-lives of neutron-rich nuclei on the nuclear chart are then predicted by the new empirical formula, providing nuclear β-decay half-life inputs for the r-process simulations.
      通信作者: 牛中明, zmniu@ahu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12375109, 11875070, 11935001)和安徽省高等学校自然科学研究重点项目(批准号: 2023AH050095)资助的课题.
      Corresponding author: Niu Zhong-Ming, zmniu@ahu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12375109, 11875070, 11935001) and the Key Research Foundation of Education Ministry of Anhui Province, China (Grant No. 2023AH050095).
    [1]

    Burbidge E M, Burbidge G R, Fowler W A, Hoyle F 1957 Rev. Mod. Phys. 29 547Google Scholar

    [2]

    Thielemann F K, Arcones A, Käappeli R, Liebendrfer M, Rauscher T, Winteler C, Fröhlichb C, Dillmannc I, Fischer T, Martinez-Pinedoc G, Langanke K, Farouqi K, Kratz K L, Panov I, Korneev I K 2011 Prog. Part. Nucl. Phys. 66 346Google Scholar

    [3]

    Cowan J J, Thielemann F K, Truran J W 1991 Phys. Rep. 208 267Google Scholar

    [4]

    Qian Y Z 2003 Prog. Part. Nucl. Phys. 50 153Google Scholar

    [5]

    Arnould M, Goriely S, Takahashi K 2007 Phys. Rep. 450 97Google Scholar

    [6]

    Chen J, Fang J Y, Hao Y W, Niu Z M, Niu Y F 2023 Astrophys. J. 943 102Google Scholar

    [7]

    Mumpower M R, Surmana R, McLaughlin G C, Aprahamian A 2016 Prog. Part. Nucl. Phys. 86 86Google Scholar

    [8]

    Li Z, Niu Z M, Sun B H 2019 Sci. China. Phys. Mech. Astron. 62 982011Google Scholar

    [9]

    Niu Z, Sun B, Meng J 2009 Phys. Rev. C 80 065806Google Scholar

    [10]

    Surman R, Engel J, Bennett J R, Meyer B S 1997 Phys. Rev. Lett. 79 1809Google Scholar

    [11]

    Zhang X P, Ren Z Z 2006 Phys. Rev. C 73 014305Google Scholar

    [12]

    Zhang X P, Ren Z Z, Zhi Q J, Zheng Q 2007 J. Phys. G: Nucl. Part. Phys. 34 2611Google Scholar

    [13]

    Zhou Y, Li Z H, Wang Y B, Chen Y S, Guo B, Su J, Li Y J, Yan S Q, Li X Y, Han Z Y, Shen Y P, Gan L, Zeng S, Lian G, Liu W P 2017 Sci. China-Phys. Mech. Astron. 60 082012Google Scholar

    [14]

    Takahashi K, Yamada M 1969 Prog. Theor. Phys. 41 1470Google Scholar

    [15]

    Tachibana T, Yamada M, Yoshida Y 1990 Prog. Theor. Phys. 84 641Google Scholar

    [16]

    Nakata H, Tachibana T, Yamada M 1997 Nucl. Phys. A 625 521Google Scholar

    [17]

    Koura H, Chiba S 2017 Phys. Rev. C 95 064304Google Scholar

    [18]

    Engel J, Bender M, Dobaczewski J, Surman R 1999 Phys. Rev. C 60 014302Google Scholar

    [19]

    Minato F, Bai C L 2013 Phys. Rev. Lett. 110 122501Google Scholar

    [20]

    Niu Z M, Niu Y F, Liang H Z, Long W H, Nikšić T, Vretenar D, Meng J 2013 Phys. Lett. B 723 172Google Scholar

    [21]

    Borzov I N, Goriely S 2000 Phys. Rev. C 62 035501Google Scholar

    [22]

    Langanke K, Martínez-Pinedo G 2003 Rev. Mod. Phys. 75 819Google Scholar

    [23]

    Martínez-Pinedo G, Langanke K 1999 Phys. Rev. Lett. 83 4502Google Scholar

    [24]

    Suzuki T, Yoshida T, Kajino T, Otsuka T 2012 Phys. Rev. C 85 015802Google Scholar

    [25]

    Zhi Q, Caurier E, Cuenca-García J J, Langanke K, Martínez-Pinedo G, Sieja K 2013 Phys. Rev. C 87 025803Google Scholar

    [26]

    Möller P, Pfeiffer B, Kratz K L 2003 Phys. Rev. C 67 055802Google Scholar

    [27]

    Minato F, Niu Z, Liang H 2022 Phys. Rev. C 106 024306Google Scholar

    [28]

    Marketin T, Huther L, Martinez-Pinedo G 2016 Phys. Rev. C 93 025805Google Scholar

    [29]

    Niu Z M, Niu Y F, Liu Q, Liang H Z, Guo J Y 2013 Phys. Rev. C 87 051303Google Scholar

    [30]

    Wang Z Y, Niu Y F, Niu Z M, Guo J Y 2016 J. Phys. G: Nucl. Part. Phys. 43 045108Google Scholar

    [31]

    Nakatsukasa T, Inakura T, Yabana K 2007 Phys. Rev. C 76 024318Google Scholar

    [32]

    Liang H Z, Nakatsukasa T, Niu Z M, Meng J 2013 Phys. Rev. C 87 054310Google Scholar

    [33]

    Ney E M, Engel J, Li T, Schunck N 2020 Phys. Rev. C 102 034326Google Scholar

    [34]

    Mustonen M T, Engel J 2016 Phys. Rev. C 93 014304Google Scholar

    [35]

    Endo F, Koura H 2019 Phys. Rev. C 99 034303Google Scholar

    [36]

    Fang J Y, Chen J, Niu Z M 2022 Phys. Rev. C 106 054318Google Scholar

    [37]

    Sargent B W 1933 Proc. R. Soc. Lond. A 139 659Google Scholar

    [38]

    Shi M, Fang J Y, Niu Z M 2021 Chin. Phys. C 45 044103Google Scholar

    [39]

    Uyen N K, Chae K Y, Duy N N, Ly N D 2022 J. Phys. G: Nucl. Part. Phys. 49 025201Google Scholar

    [40]

    Kondev F G, Wang M, Huang W J, Naimi S, Audi G 2021 Chin. Phys. C 45 030001Google Scholar

    [41]

    Fermi E 1934 Z. Phys. 88 161Google Scholar

    [42]

    Wang N, Liu M, Wu X, Meng J 2014 Phys. Lett. B 734 215Google Scholar

    [43]

    Möller P, Mumpower M R, Kawano T, Myers W D 2019 At. Data Nucl. Data Tables 125 1Google Scholar

  • 图 1  表1均方根偏差$\sigma_{\rm{rms}}(\lg T_{1/2})$的柱状图

    Fig. 1.  Bar figure of the rms deviations $\sigma_{\rm{rms}}(\lg T_{1/2})$ in Table 1

    图 2  经验公式${\rm F}_1$, ${\rm F}_2$, ${\rm F}_3$, ${\rm F}_Z$的预测结果与实验数据的对数差随质子数Z和中子数N的变化. 竖线对应质子幻数$ Z=8, $$ 20, 28, 50, 82 $和中子幻数$ N=8, 20, 28, 50, 82, 126 $

    Fig. 2.  Logarithmic differences between the predictions by the empirical formulas ${\rm F}_1$, ${\rm F}_2$, ${\rm F}_3$, ${\rm F}_Z$ and the experimental data as the functions of proton number Z and neutron number N. The vertical lines correspond to the proton magic numbers $ Z=8, 20, 28, 50, 82 $ and the neutron magic numbers $ N=8, 20, 28, 50, 82, 126 $

    图 3  经验公式${\rm F}_1$, ${\rm F}_2$, ${\rm F}_3$, ${\rm F}_Z$的预测结果与实验数据的对数差

    Fig. 3.  Logarithmic differences between the predictions by the empirical formulas ${\rm F}_1$, ${\rm F}_2$, ${\rm F}_3$, ${\rm F}_Z$ and the experimental data

    图 4  ${\rm F}_1$, ${\rm F}_2$, ${\rm F}_3$预测的Ni, Sn, Pb同位素的$\beta$衰变寿命, 及其与${\rm F}_Z$计算结果的比较

    Fig. 4.  Nuclear $\beta$-decay half-lives of Ni, Sn and Pb isotopes predicted by the ${\rm F}_1$, ${\rm F}_2$ and ${\rm F}_3$, and their comparison with ${\rm F}_Z$ calculations

    图 5  图4一样, 但对应$N = 50$, $N = 82$, $N = 126$同中子素链

    Fig. 5.  Same to Fig. 4, but for $N = 50$, $N = 82$, and $N = 126$ isotones

    图 6  公式${\rm F}_3$预测的Zn, Zr, Sn, Nd, Pb同位素的$\beta$衰变寿命, 及其与FRDM + QRPA, HFB + FAM, HFB + QRPA理论结果的比较

    Fig. 6.  Nuclear $\beta$-decay half-lives of Zn, Zr, Sn, Nd and Pb isotopes predicted by formula ${\rm F}_3$, and the comparison with the theoretical results of FRDM + QRPA, HFB + FAM and HFB + QRPA models

    图 7  公式${\rm F}_3$预言的原子核$\beta$衰变寿命

    Fig. 7.  Nuclear $\beta$-decay half-lives predicted by formula ${\rm F}_3$

    表 1  经验公式${\rm F}_1$, ${\rm F}_2$, ${\rm F}_3$和${\rm F}_Z$预言的原子核衰变寿命的对数与实验数据的均方根偏差$\sigma_{\rm{rms}}(\lg T_{1/2})$, 其中第2—4列分别对应$T_{1/2}< 10^6\ {\rm{s}}$, $T_{1/2}< 10^3\ {\rm{s}}$和$T_{1/2}< 1\ {\rm{s}}$的原子核数据集

    Table 1.  The rms deviations $\sigma_{\rm{rms}}(\lg T_{1/2})$ of the logarithms of nuclear $\beta$-decay half-lives predicted by the empirical formulas ${\rm F}_1$, ${\rm F}_2$, ${\rm F}_3$, and ${\rm F}_Z$ with respective to the experimental data, where the 2nd–4th columns represent the data sets for nuclei with $T_{1/2}< 10^6\ {\rm{s}}$, $T_{1/2}< 10^3\ {\rm{s}}$, and $T_{1/2}< 1\ {\rm{s}}$, respectively

    Formula $ T_{1/2}< {10^6 \; {\rm{s}}}$ $T_{1/2}< {10^3 \; {\rm{s}}}$ $T_{1/2}< {1 \; {\rm{s}}}$
    ${\rm F}_1$ 1.096 0.732 0.478
    ${\rm F}_2$ 0.688 0.490 0.279
    ${\rm F}_3$ 0.609 0.403 0.220
    ${\rm F}_Z$ 0.664 0.408 0.221
    下载: 导出CSV
  • [1]

    Burbidge E M, Burbidge G R, Fowler W A, Hoyle F 1957 Rev. Mod. Phys. 29 547Google Scholar

    [2]

    Thielemann F K, Arcones A, Käappeli R, Liebendrfer M, Rauscher T, Winteler C, Fröhlichb C, Dillmannc I, Fischer T, Martinez-Pinedoc G, Langanke K, Farouqi K, Kratz K L, Panov I, Korneev I K 2011 Prog. Part. Nucl. Phys. 66 346Google Scholar

    [3]

    Cowan J J, Thielemann F K, Truran J W 1991 Phys. Rep. 208 267Google Scholar

    [4]

    Qian Y Z 2003 Prog. Part. Nucl. Phys. 50 153Google Scholar

    [5]

    Arnould M, Goriely S, Takahashi K 2007 Phys. Rep. 450 97Google Scholar

    [6]

    Chen J, Fang J Y, Hao Y W, Niu Z M, Niu Y F 2023 Astrophys. J. 943 102Google Scholar

    [7]

    Mumpower M R, Surmana R, McLaughlin G C, Aprahamian A 2016 Prog. Part. Nucl. Phys. 86 86Google Scholar

    [8]

    Li Z, Niu Z M, Sun B H 2019 Sci. China. Phys. Mech. Astron. 62 982011Google Scholar

    [9]

    Niu Z, Sun B, Meng J 2009 Phys. Rev. C 80 065806Google Scholar

    [10]

    Surman R, Engel J, Bennett J R, Meyer B S 1997 Phys. Rev. Lett. 79 1809Google Scholar

    [11]

    Zhang X P, Ren Z Z 2006 Phys. Rev. C 73 014305Google Scholar

    [12]

    Zhang X P, Ren Z Z, Zhi Q J, Zheng Q 2007 J. Phys. G: Nucl. Part. Phys. 34 2611Google Scholar

    [13]

    Zhou Y, Li Z H, Wang Y B, Chen Y S, Guo B, Su J, Li Y J, Yan S Q, Li X Y, Han Z Y, Shen Y P, Gan L, Zeng S, Lian G, Liu W P 2017 Sci. China-Phys. Mech. Astron. 60 082012Google Scholar

    [14]

    Takahashi K, Yamada M 1969 Prog. Theor. Phys. 41 1470Google Scholar

    [15]

    Tachibana T, Yamada M, Yoshida Y 1990 Prog. Theor. Phys. 84 641Google Scholar

    [16]

    Nakata H, Tachibana T, Yamada M 1997 Nucl. Phys. A 625 521Google Scholar

    [17]

    Koura H, Chiba S 2017 Phys. Rev. C 95 064304Google Scholar

    [18]

    Engel J, Bender M, Dobaczewski J, Surman R 1999 Phys. Rev. C 60 014302Google Scholar

    [19]

    Minato F, Bai C L 2013 Phys. Rev. Lett. 110 122501Google Scholar

    [20]

    Niu Z M, Niu Y F, Liang H Z, Long W H, Nikšić T, Vretenar D, Meng J 2013 Phys. Lett. B 723 172Google Scholar

    [21]

    Borzov I N, Goriely S 2000 Phys. Rev. C 62 035501Google Scholar

    [22]

    Langanke K, Martínez-Pinedo G 2003 Rev. Mod. Phys. 75 819Google Scholar

    [23]

    Martínez-Pinedo G, Langanke K 1999 Phys. Rev. Lett. 83 4502Google Scholar

    [24]

    Suzuki T, Yoshida T, Kajino T, Otsuka T 2012 Phys. Rev. C 85 015802Google Scholar

    [25]

    Zhi Q, Caurier E, Cuenca-García J J, Langanke K, Martínez-Pinedo G, Sieja K 2013 Phys. Rev. C 87 025803Google Scholar

    [26]

    Möller P, Pfeiffer B, Kratz K L 2003 Phys. Rev. C 67 055802Google Scholar

    [27]

    Minato F, Niu Z, Liang H 2022 Phys. Rev. C 106 024306Google Scholar

    [28]

    Marketin T, Huther L, Martinez-Pinedo G 2016 Phys. Rev. C 93 025805Google Scholar

    [29]

    Niu Z M, Niu Y F, Liu Q, Liang H Z, Guo J Y 2013 Phys. Rev. C 87 051303Google Scholar

    [30]

    Wang Z Y, Niu Y F, Niu Z M, Guo J Y 2016 J. Phys. G: Nucl. Part. Phys. 43 045108Google Scholar

    [31]

    Nakatsukasa T, Inakura T, Yabana K 2007 Phys. Rev. C 76 024318Google Scholar

    [32]

    Liang H Z, Nakatsukasa T, Niu Z M, Meng J 2013 Phys. Rev. C 87 054310Google Scholar

    [33]

    Ney E M, Engel J, Li T, Schunck N 2020 Phys. Rev. C 102 034326Google Scholar

    [34]

    Mustonen M T, Engel J 2016 Phys. Rev. C 93 014304Google Scholar

    [35]

    Endo F, Koura H 2019 Phys. Rev. C 99 034303Google Scholar

    [36]

    Fang J Y, Chen J, Niu Z M 2022 Phys. Rev. C 106 054318Google Scholar

    [37]

    Sargent B W 1933 Proc. R. Soc. Lond. A 139 659Google Scholar

    [38]

    Shi M, Fang J Y, Niu Z M 2021 Chin. Phys. C 45 044103Google Scholar

    [39]

    Uyen N K, Chae K Y, Duy N N, Ly N D 2022 J. Phys. G: Nucl. Part. Phys. 49 025201Google Scholar

    [40]

    Kondev F G, Wang M, Huang W J, Naimi S, Audi G 2021 Chin. Phys. C 45 030001Google Scholar

    [41]

    Fermi E 1934 Z. Phys. 88 161Google Scholar

    [42]

    Wang N, Liu M, Wu X, Meng J 2014 Phys. Lett. B 734 215Google Scholar

    [43]

    Möller P, Mumpower M R, Kawano T, Myers W D 2019 At. Data Nucl. Data Tables 125 1Google Scholar

  • [1] 陈泽, 张小平, 杨洪应, 郑强, 陈娜娜, 支启军. 等待点N=82附近核素β-衰变寿命的研究. 物理学报, 2014, 63(16): 162301. doi: 10.7498/aps.63.162301
    [2] 刘智惟, 包为民, 李小平, 刘东林. 一种考虑电磁波驱动效应的等离子碰撞频率分段计算方法. 物理学报, 2014, 63(23): 235201. doi: 10.7498/aps.63.235201
    [3] 张志荣, 吴边, 夏滑, 庞涛, 王高旋, 孙鹏帅, 董凤忠, 王煜. 基于可调谐半导体激光吸收光谱技术的气体浓度测量温度影响修正方法研究. 物理学报, 2013, 62(23): 234204. doi: 10.7498/aps.62.234204
    [4] 刘晓静, 张佰军, 华中, 肖利, 刘兵, 吴义恒, 王清才, 王岩, 张丙新. 关于B0→π-l+ν l衰变过程分支比的计算. 物理学报, 2011, 60(4): 041301. doi: 10.7498/aps.60.041301
    [5] 王文芳, 陈科, 邬静达, 文锦辉, 赖天树. 长寿命吸收过程对超快动力学过程测量的影响. 物理学报, 2011, 60(11): 117802. doi: 10.7498/aps.60.117802
    [6] 李明杰, 吴晔, 刘维清, 肖井华. 手机短信息传播过程和短信息寿命研究. 物理学报, 2009, 58(8): 5251-5258. doi: 10.7498/aps.58.5251
    [7] 王向丽, 董晨钟, 桑萃萃. Ne原子的1s光电离及其Auger衰变过程的理论研究. 物理学报, 2009, 58(8): 5297-5303. doi: 10.7498/aps.58.5297
    [8] 鲁公儒, 李 祥, 李培英. R-宇称破缺的相互作用研究. 物理学报, 2008, 57(2): 778-783. doi: 10.7498/aps.57.778
    [9] 吴向尧, 公丕锋, 苏希玉, 刘晓静, 范希会, 王 丽, 石宗华, 郭义庆. D→Klv~l衰变过程的研究. 物理学报, 2006, 55(7): 3375-3379. doi: 10.7498/aps.55.3375
    [10] 吴向尧, 尹新国, 郭义庆, 张晓波, 尹建华, 谢远亮. 关于B0→K0π0衰变过程研究. 物理学报, 2004, 53(4): 1015-1019. doi: 10.7498/aps.53.1015
    [11] 曹效文. 非晶态超导体转变温度Tc的经验公式. 物理学报, 1985, 34(5): 706-708. doi: 10.7498/aps.34.706
    [12] 谢毓章, 阮丽真. MBBA和CC混合物的螺距测量及螺距与温度关系经验公式. 物理学报, 1984, 33(7): 1031-1036. doi: 10.7498/aps.33.1031
    [13] 王晓光, 李虓林, 赵佩英, 程希有. 新粒子的电磁衰变过程与层子的性质. 物理学报, 1977, 26(6): 526-530. doi: 10.7498/aps.26.526
    [14] 李虓林, 王稼军, 王晓光. 新粒子J(3095)衰变过程的分析. 物理学报, 1977, 26(1): 1-8. doi: 10.7498/aps.26.1
    [15] 何祚庥, 黄涛. 场流关系和π+→e++ν+γ的衰变过程. 物理学报, 1976, 25(5): 409-414. doi: 10.7498/aps.25.409
    [16] 葛墨林. 衰变过程中G2U旋态的一个经验选择定则. 物理学报, 1966, 22(4): 503-506. doi: 10.7498/aps.22.503
    [17] 朱保如. 不稳定粒子η的衰变分支比R((η→ππγ)/(η→3π)). 物理学报, 1965, 21(1): 92-102. doi: 10.7498/aps.21.92
    [18] 高崇寿. 偶同位旋π-π共振态质量的经验公式. 物理学报, 1964, 20(7): 680-681. doi: 10.7498/aps.20.680
    [19] 超子及K介子衰变的分枝比和平均寿命间的比例. 物理学报, 1959, 15(2): 63-76. doi: 10.7498/aps.15.63
    [20] 胡宁, 于敏. β—衰变理论. 物理学报, 1951, 8(3): 260-269. doi: 10.7498/aps.8.260
计量
  • 文章访问数:  2203
  • PDF下载量:  69
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-10-16
  • 修回日期:  2023-12-08
  • 上网日期:  2024-01-03
  • 刊出日期:  2024-03-20

/

返回文章
返回