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裂变产物衰变链设计

黄小龙 何璞昳 杨东 王香涵 金永利 李剑

黄小龙, 何璞昳, 杨东, 王香涵, 金永利, 李剑. 裂变产物衰变链设计[J]. 原子核物理评论, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020
引用本文: 黄小龙, 何璞昳, 杨东, 王香涵, 金永利, 李剑. 裂变产物衰变链设计[J]. 原子核物理评论, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020
Xiaolong HUANG, Puyi HE, Dong YANG, Xianghan WANG, Yongli JIN, Jian LI. Design of the Decay Chains for Fission Product[J]. Nuclear Physics Review, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020
Citation: Xiaolong HUANG, Puyi HE, Dong YANG, Xianghan WANG, Yongli JIN, Jian LI. Design of the Decay Chains for Fission Product[J]. Nuclear Physics Review, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020

裂变产物衰变链设计

doi: 10.11804/NuclPhysRev.39.2022020
基金项目: 国家基础科学公共科学数据中心“核物理主题数据库”资助项目(NBSDC-DB-08)
详细信息
    作者简介:

    黄小龙(1967−),男,四川广安人,博导,从事核结构和衰变数据评价研究; E-mail: huang@ciae.ac.cn

    通讯作者: 杨东,E-mail: dyang@jlu.edu.cn
  • 中图分类号: O571

Design of the Decay Chains for Fission Product

Funds: Database of Nuclear Physics in National Basic Science Data Center(NBSDC-DB-08)
More Information
    Corresponding author: E-mail: dyang@jlu.edu.cn
  • 摘要: 根据核科学参考文献库,对半衰期、缓发中子发射几率等进行了更新评价,采用系统学研究和理论研究相结合的评价方法对裂变产物中不确定的基态进行了自旋指定,对部分存在问题的数据进行了必要修正;对衰变子核存在同质异能态的放射性核素,根据衰变纲图和内转换系数重新计算得到退激至子核同质异能态和基态的分支比数据。在此基础上,结合现有核结构和衰变数据库,研制了裂变产物衰变链设计专用衰变数据库,按照衰变规律,建立了裂变产物衰变路径和衰变信息的完整衰变链,本工作为裂变产物分析和裂变产额研究提供了一个便利参考。
  • 图  1  102Y核的基态和同质异能态的能级信息(在线彩图)

    图  2  母核到129In的衰变关系以及129In衰变退激关系图

    图  3  process.py程序架构图(a)和draw.py程序架构图(b)

    图  4  A = 100质量链裂变产物衰变链设计示意图

    表  1  部分核建议的基态自旋修正及重新评价结果

    核素ENSDF数据库本工作评价值修正原因
    83Ga (5/2) 系统学、CDFT模型计算
    85As (3/2) (5/2) 系统学、CDFT模型计算
    89Br (3/2, 5/2) (5/2) 系统学
    97-103Rb (3/2+) (3/2) 系统学,nilsson轨道分析
    105,107Tc (3/2) (5/2+) 系统学
    125Ag (9/2+) (7/2+) 系统学
    147La (3/2+) (3/2) 系统学
    151La (1/2+) (3/2) 系统学
    161-167Eu (5/2+) (5/2+, 11/2) 系统学
    下载: 导出CSV

    表  2  专用衰变数据库中的所有核素

    所有核素列表
    V - 66, Cr- 66, Mn- 66, Fe- 66, Co- 66, Ni- 66, Cu- 66, Zn- 66, Ga- 66, Ge- 66;
    V - 67, Cr- 67, Mn- 67, Fe- 67, Co- 67, Co- 67m, Ni- 67, Cu- 67, Zn- 67, Ga- 67, Ge- 67;
    Cr- 68, Mn- 68, Fe- 68, Co- 68, Co- 68m, Ni- 68, Cu- 68, Cu- 68m, Zn- 68, Ga- 68, Ge- 68;
    Cr- 69, Mn- 69, Fe- 69, Co- 69, Co- 69m, Ni- 69, Ni- 69m, Cu- 69, Zn- 69, Zn- 69m, Ga- 69, Ge- 69, As- 69;
    Cr- 70, Mn- 70, Fe- 70, Co- 70, Co- 70m, Ni- 70, Cu- 70, Cu- 70m, Cu- 70n, Zn- 70, Ga- 70, Ge- 70, As- 70, Se- 70;
    Mn- 71, Fe- 71, Co- 71, Ni- 71, Ni- 71m, Cu-71, Zn- 71, Zn-71m, Ga- 71, Ge- 71, Ge- 71m, As- 71;
    Mn- 72, Fe- 72, Co- 72, Co- 72m, Ni- 72, Cu- 72, Zn- 72, Ga- 72, Ga- 72m, Ge- 72, As- 72, Se- 72;
    Mn- 73, Fe- 73, Co- 73, Ni- 73, Cu- 73, Zn- 73, Zn- 73m, Ga- 73, Ga- 73m, Ge- 73, Ge- 73m, As- 73, Se- 73, Se- 73m;
    Fe- 74, Co- 74, Ni- 74, Cu- 74, Zn- 74, Ga- 74, Ga- 74m, Ge- 74, As- 74, Se- 74, Br- 74, Br- 74m, Kr- 74;
    Fe- 75, Co- 75, Ni- 75, Cu- 75, Zn- 75, Zn- 75m, Ga- 75, Ge- 75, Ge- 75m, As- 75, As- 75m, Se- 75, Br- 75;
    Fe- 76, Co- 76, Co- 76m, Ni- 76, Cu- 76, Cu- 76m, Zn- 76, Ga- 76, Ge- 76, As- 76, Se- 76, Br- 76, Br- 76m, Kr- 76;
    Co- 77, Ni- 77, Cu- 77, Zn- 77, Zn- 77m, Ga- 77, Ge- 77, Ge- 77m, As- 77, Se- 77, Se- 77m, Br- 77, Br- 77m, Kr- 77;
    Co- 78, Ni- 78, Cu- 78, Zn- 78, Ga- 78, Ge- 78, As- 78, Se- 78, Br- 78, Kr- 78, Rb- 78, Rb- 78m, Sr- 78;
    Ni- 79, Cu- 79, Zn- 79, Zn- 79m, Ga- 79, Ge- 79, Ge- 79m, As- 79, Se- 79, Se- 79m, Br- 79, Br- 79m, Kr- 79, Kr- 79m, Rb- 79;
    Ni- 80, Cu- 80, Zn- 80, Ga- 80, Ga- 80m, Ge- 80, As- 80, Se- 80, Br- 80, Br- 80m, Kr- 80, Rb- 80, Sr- 80;
    Ni- 81, Cu- 81, Zn- 81, Ga- 81, Ge- 81, Ge- 81m, As- 81, Se- 81, Se- 81m, Br- 81, Kr- 81, Kr- 81m, Rb- 81, Rb- 81m, Sr- 81;
    Ni- 82, Cu- 82, Zn- 82, Ga- 82, Ge- 82, As- 82, As- 82m, Se- 82, Br- 82, Br- 82m, Kr- 82, Rb- 82, Rb- 82m, Sr- 82;
    Cu- 83, Zn- 83, Ga- 83, Ge- 83, As- 83, Se- 83, Se- 83m, Br- 83, Kr- 83, Kr- 83m, Rb- 83, Rb- 83m, Sr- 83, Sr- 83m;
    Cu- 84, Zn- 84, Ga- 84, Ga- 84m, Ge- 84, As- 84, As- 84m, Se- 84, Br- 84, Br- 84m, Kr- 84, Rb- 84, Rb- 84m, Sr- 84, Y - 84, Y - 84m, Zr- 84;
    Zn- 85, Ga- 85, Ge- 85, As- 85, Se- 85, Br- 85, Kr- 85, Kr- 85m, Rb- 85, Sr- 85, Sr- 85m, Y - 85, Y - 85m;
    Zn- 86, Ga- 86, Ge- 86, As- 86, Se- 86, Br- 86, Kr- 86, Rb- 86, Rb- 86m, Sr- 86, Y - 86, Y - 86m, Zr- 86;
    Ga- 87, Ge- 87, As- 87, Se- 87, Br- 87, Kr- 87, Rb- 87, Sr- 87, Sr- 87m, Y - 87, Y - 87m, Zr- 87, Zr- 87m;
    Ga- 88, Ge- 88, As- 88, Se- 88, Br- 88, Kr- 88, Rb- 88, Sr- 88, Y - 88, Y - 88m, Y - 88n, Zr- 88, Nb- 88, Nb- 88m;
    Ge- 89, As- 89, Se- 89, Br- 89, Kr- 89, Rb- 89, Sr- 89, Y - 89, Y - 89m, Zr- 89, Zr- 89m, Nb- 89, Nb- 89m;
    Ge- 90, As- 90, Se- 90, Br- 90, Kr- 90, Rb- 90, Rb- 90m, Sr- 90, Y - 90, Y - 90m, Zr- 90, Zr- 90m, Nb- 90, Nb- 90m, Nb- 90n, Mo- 90;
    As- 91, Se- 91, Br- 91, Kr- 91, Rb- 91, Sr- 91, Y - 91, Y - 91m, Zr- 91, Nb- 91, Nb- 91m, Mo- 91, Mo- 91m, Tc- 91, Tc- 91m;
    As- 92, Se- 92, Br- 92, Kr- 92, Rb- 92, Sr- 92, Y - 92, Zr- 92, Nb- 92, Nb- 92m, Mo- 92, Tc- 92, Ru- 92;
    Se- 93, Br- 93, Kr- 93, Rb- 93, Sr- 93, Y - 93, Y - 93m, Zr- 93, Nb- 93, Nb- 93m, Mo- 93, Mo- 93m, Tc- 93, Tc- 93m;
    Se- 94, Br- 94, Kr- 94, Rb- 94, Sr- 94, Y - 94, Zr- 94, Nb- 94, Nb- 94m, Mo- 94, Tc- 94, Tc- 94m, Ru- 94;
    Se- 95, Br- 95, Kr- 95, Rb- 95, Sr- 95, Y - 95, Zr- 95, Nb- 95, Nb- 95m, Mo- 95, Tc- 95, Tc- 95m, Ru- 95;
    Br- 96, Kr- 96, Rb- 96, Sr- 96, Y - 96, Y - 96m, Zr- 96, Nb- 96, Mo- 96, Tc- 96, Tc- 96m, Ru- 96, Rh- 96, Rh- 96m, Pd- 96;
    Br- 97, Kr- 97, Rb- 97, Sr- 97, Y - 97, Y - 97m, Y - 97n, Zr- 97, Nb- 97, Nb- 97m, Mo- 97, Tc- 97, Tc- 97m, Ru- 97, Rh- 97, Rh- 97m;
    Br- 98, Kr- 98, Rb- 98, Rb- 98m, Sr- 98, Y - 98, Y - 98m, Zr- 98, Nb- 98, Nb- 98m, Mo- 98, Tc- 98, Ru- 98, Rh- 98, Rh- 98m, Pd- 98;
    Kr- 99, Rb- 99, Sr- 99, Y - 99, Zr- 99, Nb- 99, Nb- 99m, Mo- 99, Tc- 99, Tc- 99m, Ru- 99, Rh- 99, Rh- 99m, Pd- 99;
    Kr-100, Rb-100, Sr-100, Y -100, Y -100m, Zr-100, Nb-100, Nb-100m, Mo-100, Tc-100, Ru-100, Rh-100, Rh-100m, Pd-100;
    Kr-101, Rb-101, Sr-101, Y -101, Zr-101, Nb-101, Mo-101, Tc-101, Ru-101, Rh-101, Rh-101m, Pd-101;
    Rb-102, Sr-102, Y -102, Y -102m, Zr-102, Nb-102, Nb-102m, Mo-102, Tc-102, Tc-102m, Ru-102, Rh-102, Rh-102m, Pd-102, Ag-102, Ag-102m,
    Cd-102;
    Rb-103, Sr-103, Y -103, Zr-103, Nb-103, Mo-103, Tc-103, Ru-103, Ru-103m, Rh-103, Rh-103m, Pd-103, Ag-103, Ag-103m;
    Rb-104, Sr-104, Y -104, Zr-104, Nb-104, Nb-104m, Mo-104, Tc-104, Ru-104, Rh-104, Rh-104m, Pd-104, Ag-104, Ag-104m, Cd-104;
    Sr-105, Y -105, Zr-105, Nb-105, Mo-105, Tc-105, Ru-105, Rh-105, Rh-105m, Pd-105, Ag-105, Ag-105m, Cd-105;
    Sr-106, Y -106, Zr-106, Nb-106, Nb-106m, Mo-106, Tc-106, Ru-106, Rh-106, Rh-106m, Pd-106, Ag-106, Ag-106m, Cd-106, In-106, In-106m,
    Sn-106;
    Sr-107, Y -107, Zr-107, Nb-107, Mo-107, Tc-107, Ru-107, Rh-107, Pd-107, Pd-107m, Ag-107, Ag-107m, Cd-107, In-107, In-107m;
    Y -108, Zr-108, Nb-108, Mo-108, Tc-108, Ru-108, Rh-108, Rh-108m, Pd-108, Ag-108, Ag-108m, Cd-108, In-108, In-108m, Sn-108;
    Y -109, Zr-109, Nb-109, Mo-109, Tc-109, Ru-109, Rh-109, Pd-109, Pd-109m, Ag-109, Ag-109m, Cd-109, In-109, In-109m, In-109n;
    Zr-110, Nb-110, Nb-110m, Mo-110, Tc-110, Ru-110, Rh-110, Rh-110m, Pd-110, Ag-110, Ag-110m, Cd-110, In-110, In-110m, Sn-110;
    Zr-111, Nb-111, Mo-111, Mo-111m, Tc-111, Ru-111, Rh-111, Pd-111, Pd-111m, Ag-111, Ag-111m, Cd-111, Cd-111m, In-111, In-111m, Sn-111;
    Zr-112, Nb-112, Mo-112, Tc-112, Ru-112, Rh-112, Rh-112m, Pd-112, Ag-112, Cd-112, In-112, In-112m, Sn-112, Sb-112, Te-112;
    Zr-113, Nb-113, Mo-113, Tc-113, Ru-113, Ru-113m, Rh-113, Pd-113, Pd-113m, Ag-113, Ag-113m, Cd-113, Cd-113m, In-113, In-113m, Sn-113,
    Sn-113m, Sb-113;
    Nb-114, Mo-114, Tc-114, Tc-114m, Ru-114, Rh-114, Rh-114m, Pd-114, Ag-114, Ag-114m, Cd-114, In-114, In-114m, In-114n, Sn-114, Sb-114,
    Te-114;
    Nb-115, Mo-115, Tc-115, Ru-115, Ru-115m, Rh-115, Pd-115, Pd-115m, Ag-115, Ag-115m, Cd-115, Cd-115m, In-115, In-115m, Sn-115, Sb-115,
    Te-115, Te-115m;
    Nb-116, Mo-116, Tc-116, Ru-116, Rh-116, Rh-116m, Pd-116, Ag-116, Ag-116m, Ag-116n, Cd-116, In-116, In-116m, In-116n, Sn-116, Sb-116,
    Sb-116m, Te-116;
    Mo-117, Tc-117, Ru-117, Rh-117, Pd-117, Pd-117m, Ag-117, Ag-117m, Cd-117, Cd-117m, In-117, In-117m, Sn-117, Sn-117m, Sb-117, Te-117,
    Te-117m;
    Mo-118, Tc-118, Ru-118, Rh-118, Rh-118m, Pd-118, Ag-118, Ag-118m, Cd-118, In-118, In-118m, In-118n, Sn-118, Sb-118, Sb-118m, Te-118;
    Mo-119, Tc-119, Ru-119, Rh-119, Pd-119, Pd-119m, Ag-119, Ag-119m, Cd-119, Cd-119m, In-119, In-119m, Sn-119, Sn-119m, Sb-119, Sb-119m,
    Te-119, Te-119m;
    Tc-120, Ru-120, Rh-120, Pd-120, Ag-120, Ag-120m, Ag-120n, Cd-120, In-120, In-120m, In-120n, Sn-120, Sb-120, Sb-120m, Te-120, I -120, I -120m, Xe-120;
    Tc-121, Ru-121, Rh-121, Pd-121, Ag-121, Cd-121, Cd-121m, In-121, In-121m, Sn-121, Sn-121m, Sb-121, Te-121, Te-121m, I -121;
    Tc-122, Ru-122, Rh-122, Pd-122, Ag-122, Ag-122m, Ag-122n, Cd-122, In-122, In-122m, In-122n, Sn-122, Sb-122, Te-122, I -122, Xe-122;
    Ru-123, Rh-123, Pd-123, Pd-123m, Ag-123, Ag-123m, Cd-123, Cd-123m, In-123, In-123m, Sn-123, Sn-123m, Sb-123, Te-123, Te-123m, I -123,
    Xe-123;
    Ru-124, Rh-124, Pd-124, Ag-124, Ag-124m, Cd-124, In-124, In-124m, Sn-124, Sb-124, Sb-124m, Sb-124n, Te-124, I -124, Xe-124, Cs-124, Cs-124m, Ba-124;
    Ru-125, Rh-125, Pd-125, Pd-125m, Ag-125, Ag-125m, Cd-125, Cd-125m, In-125, In-125m, Sn-125, Sn-125m, Sb-125, Te-125, Te-125m, I -125,
    Xe-125, Xe-125m;
    Rh-126, Pd-126, Ag-126, Ag-126m, Cd-126, In-126, In-126m, Sn-126, Sb-126, Sb-126m, Sb-126n, Te-126, I -126, Xe-126, Cs-126, Ba-126;
    Rh-127, Pd-127, Ag-127, Ag-127m, Ag-127n, Cd-127, Cd-127m, In-127, In-127m, In-127n, Sn-127, Sn-127m, Sb-127, Te-127, Te-127m, I -127,
    Xe-127, Xe-127m, Cs-127;
    Rh-128, Pd-128, Ag-128, Cd-128, Cd-128m, In-128, In-128m, In-128n, Sn-128, Sn-128m, Sb-128, Sb-128m, Te-128, I -128, Xe-128, Cs-128, Ba-128;
    Pd-129, Ag-129, Ag-129m, Cd-129, Cd-129m, Cd-129n, In-129, In-129m, In-129n, Sn-129, Sn-129m, Sb-129, Sb-129m, Te-129, Te-129m, I -129,
    Xe-129, Xe-129m, Cs-129, Ba-129,
    Ba-129m;
    Pd-130, Ag-130, Cd-130, In-130, In-130m, In-130n, Sn-130, Sn-130m, Sb-130, Sb-130m, Te-130, I -130, I -130m, Xe-130, Cs-130, Cs-130m, Ba-130, Ba-130m, La-130, Ce-130;
    Pd-131, Ag-131, Cd-131, In-131, In-131m, In-131n, Sn-131, Sn-131m, Sb-131, Te-131, Te-131m, Te-131n, I -131, Xe-131, Xe-131m, Cs-131, Ba-131, Ba-131m, La-131;
    Ag-132, Cd-132, In-132, Sn-132, Sb-132, Sb-132m, Te-132, I -132, I -132m, Xe-132, Xe-132m, Cs-132, Ba-132, La-132, La-132m, Ce-132, Ce-132m;
    Ag-133, Cd-133, In-133, In-133m, Sn-133, Sb-133, Te-133, Te-133m, I -133, I -133m, Xe-133, Xe-133m, Cs-133, Ba-133, Ba-133m, La-133, Ce-133, Ce-133m;
    Cd-134, In-134, Sn-134, Sb-134, Sb-134m, Te-134, I -134, I -134m, Xe-134, Xe-134m, Cs-134, Cs-134m, Ba-134, La-134, Ce-134;
    Cd-135, In-135, Sn-135, Sb-135, Te-135, I -135, Xe-135, Xe-135m, Cs-135, Cs-135m, Ba-135, Ba-135m, Ba-135n, La-135, Ce-135, Ce-135m;
    In-136, Sn-136, Sb-136, Te-136, I -136, I -136m, Xe-136, Cs-136, Cs-136m, Ba-136, Ba-136m, La-136, La-136m, Ce-136, Pr-136, Nd-136;
    In-137, Sn-137, Sb-137, Te-137, I -137, Xe-137, Cs-137, Ba-137, Ba-137m, La-137, Ce-137, Ce-137m, Pr-137;
    Sn-138, Sb-138, Te-138, I -138, Xe-138, Cs-138, Cs-138m, Ba-138, La-138, Ce-138, Ce-138m, Pr-138, Pr-138m, Nd-138;
    Sn-139, Sb-139, Te-139, I -139, Xe-139, Cs-139, Ba-139, La-139, Ce-139, Ce-139m, Pr-139, Nd-139, Nd-139m;
    Sn-140, Sb-140, Te-140, I -140, Xe-140, Cs-140, Ba-140, La-140, Ce-140, Pr-140, Nd-140;
    Sb-141, Te-141, I -141, Xe-141, Cs-141, Ba-141, La-141, Ce-141, Pr-141, Nd-141, Nd-141m, Pm-141;
    Sb-142, Te-142, I -142, Xe-142, Cs-142, Ba-142, La-142, Ce-142, Pr-142, Pr-142m, Nd-142, Pm-142, Pm-142m, Sm-142;
    Te-143, I -143, Xe-143, Cs-143, Ba-143, La-143, Ce-143, Pr-143, Nd-143, Pm-143, Sm-143, Sm-143m, Sm-143n;
    Te-144, I -144, Xe-144, Cs-144, Cs-144m, Ba-144, La-144, Ce-144, Pr-144, Pr-144m, Nd-144, Pm-144, Sm-144, Eu-144, Gd-144;
    Te-145, I -145, Xe-145, Cs-145, Ba-145, La-145, Ce-145, Pr-145, Nd-145, Pm-145, Sm-145, Eu-145;
    I -146, Xe-146, Cs-146, Ba-146, La-146, La-146m, Ce-146, Pr-146, Nd-146, Pm-146, Sm-146, Eu-146, Gd-146;
    I -147, Xe-147, Cs-147, Ba-147, La-147, Ce-147, Pr-147, Nd-147, Pm-147, Sm-147, Eu-147, Gd-147, Tb-147, Tb-147m;
    Xe-148, Cs-148, Ba-148, La-148, Ce-148, Pr-148, Pr-148m, Nd-148, Pm-148, Pm-148m, Sm-148, Eu-148, Gd-148, Tb-148, Tb-148m, Dy-148;
    Xe-149, Cs-149, Ba-149, La-149, Ce-149, Pr-149, Nd-149, Pm-149, Sm-149, Eu-149, Gd-149, Tb-149, Tb-149m;
    Xe-150, Cs-150, Ba-150, La-150, Ce-150, Pr-150, Nd-150, Pm-150, Sm-150, Eu-150, Eu-150m, Gd-150, Tb-150, Tb-150m, Dy-150;
    Cs-151, Ba-151, La-151, Ce-151, Pr-151, Nd-151, Pm-151, Sm-151, Eu-151, Gd-151, Tb-151, Tb-151m;
    Cs-152, Ba-152, La-152, Ce-152, Pr-152, Nd-152, Pm-152, Pm-152m, Pm-152n, Sm-152, Eu-152, Eu-152m, Gd-152, Tb-152, Tb-152m, Dy-152;
    Ba-153, La-153, Ce-153, Pr-153, Nd-153, Pm-153, Sm-153, Sm-153m, Eu-153, Gd-153, Tb-153, Dy-153;
    Ba-154, La-154, Ce-154, Pr-154, Nd-154, Pm-154, Pm-154m, Sm-154, Eu-154, Eu-154m, Gd-154, Tb-154, Tb-154m, Tb-154n, Dy-154, Ho-154,
    Ho-154m, Er-154;
    La-155, Ce-155, Pr-155, Nd-155, Pm-155, Sm-155, Eu-155, Gd-155, Gd-155m, Tb-155, Dy-155, Ho-155;
    La-156, Ce-156, Pr-156, Nd-156, Pm-156, Pm-156m, Sm-156, Eu-156, Gd-156, Tb-156, Tb-156m, Tb-156n, Dy-156, Ho-156, Ho-156m, Ho-156n,
    Er-156;
    La-157, Ce-157, Pr-157, Nd-157, Pm-157, Sm-157, Eu-157, Gd-157, Tb-157, Dy-157, Dy-157m, Ho-157;
    Ce-158, Pr-158, Nd-158, Pm-158, Sm-158, Eu-158, Gd-158, Tb-158, Tb-158m, Dy-158, Ho-158, Ho-158m, Er-158;
    Ce-159, Pr-159, Nd-159, Pm-159, Sm-159, Eu-159, Gd-159, Tb-159, Dy-159, Ho-159, Ho-159m, Er-159;
    Pr-160, Nd-160, Pm-160, Pm-160m, Sm-160, Eu-160, Eu-160m, Gd-160, Tb-160, Dy-160, Ho-160, Ho-160m, Ho-160n, Er-160, Tm-160, Tm-160m;
    Pr-161, Nd-161, Pm-161, Sm-161, Eu-161, Gd-161, Tb-161, Dy-161, Ho-161, Ho-161m, Er-161, Tm-161, Tm-161m;
    Nd-162, Pm-162, Sm-162, Eu-162, Eu-162m, Gd-162, Tb-162, Tb-162m, Dy-162, Ho-162, Ho-162m, Er-162, Tm-162, Tm-162m, Yb-162;
    Nd-163, Pm-163, Sm-163, Eu-163, Gd-163, Gd-163m, Tb-163, Dy-163, Ho-163, Ho-163m, Er-163, Tm-163;
    Pm-164, Sm-164, Eu-164, Gd-164, Tb-164, Tb-164m, Dy-164, Ho-164, Ho-164m, Er-164, Tm-164, Tm-164m, Yb-164;
    Pm-165, Sm-165, Eu-165, Gd-165, Tb-165, Dy-165, Dy-165m, Ho-165, Er-165, Tm-165, Yb-165;
    Sm-166, Eu-166, Gd-166, Tb-166, Dy-166, Ho-166, Ho-166m, Er-166, Tm-166, Yb-166;
    Sm-167, Eu-167, Gd-167, Tb-167, Dy-167, Ho-167, Er-167, Er-167m, Tm-167, Yb-167, Lu-167, Lu-167m;
    Sm-168, Eu-168, Gd-168, Tb-168, Dy-168, Ho-168, Ho-168m, Er-168, Tm-168, Yb-168, Lu-168, Lu-168m, Hf-168;
    Eu-169, Gd-169, Tb-169, Dy-169, Ho-169, Er-169, Tm-169, Yb-169, Yb-169m, Lu-169, Lu-169m, Hf-169;
    Eu-170, Gd-170, Tb-170, Dy-170, Ho-170, Ho-170m, Er-170, Tm-170, Yb-170, Lu-170, Lu-170m, Hf-170, Ta-170;
    Gd-171, Tb-171, Dy-171, Ho-171, Er-171, Tm-171, Yb-171, Yb-171m, Lu-171, Lu-171m, Hf-171, Hf-171m, Ta-171;
    Gd-172, Tb-172, Dy-172, Dy-172m, Ho-172, Er-172, Tm-172, Yb-172, Lu-172, Lu-172m, Hf-172, Ta-172, W -172。
    下载: 导出CSV
  • [1] PRITYCHENKO B, BETAK E, SINGH B, et al. Nuclear Data Sheets, 2014, 120: 291. doi:  10.1016/j.nds.2014.07.070
    [2] Evaluated Nuclear Structure Data File (ENSDF)[EB/OL]. [2021-11-01]. https://www.nndc.bnl.gov/ensdf.
    [3] LIANG J, SINGH B, MCCUTCHAN E A, et al. Nuclear Data Sheets, 2020, 168: 1. doi:  10.1016/j.nds.2020.09.001
    [4] BIRCH M, SINGH B, DILLMANN I, et al. Nuclear Data Sheets, 2015, 128: 131. doi:  10.1016/j.nds.2015.08.002
    [5] KONDOV F G, WANG M, HUANG W J, et al. Chinese Physics C, 2021, 45(3): 030001-1. doi:  10.1088/1674-1137/abddae
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出版历程
  • 收稿日期:  2022-02-25
  • 修回日期:  2022-03-31
  • 刊出日期:  2022-09-20

裂变产物衰变链设计

doi: 10.11804/NuclPhysRev.39.2022020
    基金项目:  国家基础科学公共科学数据中心“核物理主题数据库”资助项目(NBSDC-DB-08)
    作者简介:

    黄小龙(1967−),男,四川广安人,博导,从事核结构和衰变数据评价研究; E-mail: huang@ciae.ac.cn

    通讯作者: 杨东,E-mail: dyang@jlu.edu.cn
  • 中图分类号: O571

摘要: 根据核科学参考文献库,对半衰期、缓发中子发射几率等进行了更新评价,采用系统学研究和理论研究相结合的评价方法对裂变产物中不确定的基态进行了自旋指定,对部分存在问题的数据进行了必要修正;对衰变子核存在同质异能态的放射性核素,根据衰变纲图和内转换系数重新计算得到退激至子核同质异能态和基态的分支比数据。在此基础上,结合现有核结构和衰变数据库,研制了裂变产物衰变链设计专用衰变数据库,按照衰变规律,建立了裂变产物衰变路径和衰变信息的完整衰变链,本工作为裂变产物分析和裂变产额研究提供了一个便利参考。

English Abstract

黄小龙, 何璞昳, 杨东, 王香涵, 金永利, 李剑. 裂变产物衰变链设计[J]. 原子核物理评论, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020
引用本文: 黄小龙, 何璞昳, 杨东, 王香涵, 金永利, 李剑. 裂变产物衰变链设计[J]. 原子核物理评论, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020
Xiaolong HUANG, Puyi HE, Dong YANG, Xianghan WANG, Yongli JIN, Jian LI. Design of the Decay Chains for Fission Product[J]. Nuclear Physics Review, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020
Citation: Xiaolong HUANG, Puyi HE, Dong YANG, Xianghan WANG, Yongli JIN, Jian LI. Design of the Decay Chains for Fission Product[J]. Nuclear Physics Review, 2022, 39(3): 405-412. doi: 10.11804/NuclPhysRev.39.2022020
    • 原子核裂变时首先生成具有一定质量的裂变碎片,这些碎片一般是丰中子的,很不稳定,在发射出瞬发中子和瞬发$ \gamma $射线后,由于仍然具有较高的中子-质子比,还是很不稳定,会继续进行一系列${\beta ^{\rm{ - }}}$衰变,直至它们变为稳定核素时为止。裂变碎片及其中子俘获和衰变子核统称为裂变产物,裂变产物核素质量数通常从66到172。

      通过$ {\beta ^{\rm{ - }}} $衰变,裂变产物放出$ {\beta } $粒子,转变为另一个核素,当处于激发态时会跃迁到基态,发射出缓发$ \gamma $射线。通过$ {\beta ^{\rm{ - }}} $衰变和电子俘获,核素原子序数或增或减,但质量数保持不变,这些质量数相同的核素就可以排成一排,构成一个衰变链。衰变链对裂变产物分析和裂变产额研究非常重要。

      每个衰变链由于核素衰变模式的不同造成每个链上的衰变路径也不同。对于简单的母子体衰变关系的衰变链,可采用手工方法进行计算并绘制,但当母子体衰变关系较复杂时,例如某一核素同时存在着$ {\beta ^{\rm{ - }}} $衰变、$ {\beta ^+ } $衰变、同质异能态跃迁、α衰变等多种衰变模式时,就会有多个衰变分支,相应形成多条衰变路径,这时若采用手工方法耗时繁琐且容易出错。为此,本文基于现有核结构和衰变数据库和最新实验测量数据,研制了裂变产物衰变链设计专用衰变数据库,按照衰变规律,建立了裂变产物的衰变路径和衰变信息的完整衰变链,以满足裂变产物分析的需要,为其实验设计提供指导。

    • 裂变产物衰变链设计时所需要的数据,常常会遇到这种情况:某个物理量有很多家测量数据,这些测量数据存在着严重的分歧。如果不经过评价,这些测量数据就无法使用。评价工作包括物理评价和数学处理两个过程,其主要流程是:(1) 物理评价,核数据评价最重要的基础是实验测量数据,在广泛收集有关实验数据的基础上,从物理角度出发,对测量进行筛选和权重评估,包括:半衰期、$ {\beta } $$ \gamma $射线的发射几率的测量和计算方法、能量和强度数据是否考虑结构数据、测量使用的仪器、研究组、完成时间等;对于同一组实验团队不同时期的测量数据,将采用其最新发表的结果。必要时可对实验数据特别是实验数据不确定度做出调整、修正或取舍从而达到统计意义上的一致。(2) 数学处理,确定了采用的实验数据后,对统计意义上一致的数据通过数学处理给出在统计意义上“最佳”的推荐值及推荐值不确定度,尽量不采用无不确定度的实验数据,但如遇到缺乏实验数据的特殊情况,则使用该类数据并予以说明。本工作采用的数学处理方法是常见的加权平均法。

    • 在下面讨论中,$ {x_i}(i = 1, \, 2,\, \cdot \cdot \cdot \cdot \cdot \cdot ,\, n) $是对某个物理量X所测的互不相关的测量数据,$ {\sigma _i} $为其不确定度,相应权重$ {w_i} = \frac{1}{{\sigma _i^2}} $n为总的测量次数。

      加权平均法以测量数据的不确定度作权,其加权平均值$ {x_w} $

      $$ {x_w} = \dfrac{{ \displaystyle \sum {{x_i}{w_i}} }}{{\displaystyle \sum {{w_i}} }} \text{,} $$ (1)

      相应的不确定度取${\sigma _{\rm inn}}$${\sigma _{\rm ext}}$二者之较大值:

      $$ {\sigma _{\rm inn}} = \sqrt {\frac{1}{{\displaystyle \sum {{w_i}} }}} \text{,} $$ (2)
      $$ {\sigma _{\rm ext}} = \sqrt {\sum\limits_i {\frac{{{{({x_i} - {x_w})}^2}}}{{\sigma _i^2 \times (n - 1)}}} } \times \sqrt {\frac{1}{{\displaystyle \sum\limits_i {{w_i}} }}} 。 $$ (3)

      根据核科学参考文献库NSR[1]和核结构数据库ENSDF [2],对半衰期、${\beta ^{\rm{ - }}}$n等实验测量数据进行了收集与整理(截止时间2021年月12月),若现有评价数据完成后没有新的实验数据,对存在缓发中子的先驱核,半衰期、$ {\beta ^{\rm{ - }}} $n等取自最新评价数据[3-4],其它核的半衰期取自ENSDF库;若现有评价数据完成后有新的实验数据,则对所有实验数据进行物理分析后,采用加权平均法给出新的评价数据。

    • 原子核的基态自旋是重要的原子核基础数据,它直接决定裂变产物衰变链上核素的衰变路径。目前远离稳定线的核素由于实验条件限制相当多的基态自旋数据并不确定或缺乏指定。图1给出了一个典型例子,从图1中可看出,102Y核的基态和同质异能态的自旋都缺乏指定,不同的自旋指定会给出不同的衰变路径,因此必须对数据不确定或缺乏指定的自旋进行重新评价。

      图  1  102Y核的基态和同质异能态的能级信息(在线彩图)

      采用系统学研究和理论研究相结合的评价方法。在整个裂变产物核区,区分已有准确自旋指定的原子核和自旋待定的候选核,考察同位素链和同中子素链中原子核基态自旋随中子和质子的变化,找出其一致性及随中子和质子的变化规律及导致这些现象的物理机制,提供自旋指定的系统性证据,为候选核基态自旋指定提供参考。利用成熟的壳模型和其他理论研究方法,对重要或者关键的原子核及附近同位素或同中异位素基态自旋进行研究,包括微观结构如组态等分析,与已有的实验结果比较,最终为基态自旋指定提供理论方面的物理依据。最终根据二者对裂变产物中不确定的基态进行自旋指定,对部分存在问题的数据进行必要修正。

      表1给出了部分核基态自旋重新评价结果,本次基态自旋重新评价结果考虑了以下信息:(1) 直接测量(磁矩、电四极矩);(2) 衰变数据的自洽;(3) 低激发态结构数据的自洽;(4) 系统学及附近Nilsson轨道;(5) 理论计算。

      表 1  部分核建议的基态自旋修正及重新评价结果

      核素ENSDF数据库本工作评价值修正原因
      83Ga (5/2) 系统学、CDFT模型计算
      85As (3/2) (5/2) 系统学、CDFT模型计算
      89Br (3/2, 5/2) (5/2) 系统学
      97-103Rb (3/2+) (3/2) 系统学,nilsson轨道分析
      105,107Tc (3/2) (5/2+) 系统学
      125Ag (9/2+) (7/2+) 系统学
      147La (3/2+) (3/2) 系统学
      151La (1/2+) (3/2) 系统学
      161-167Eu (5/2+) (5/2+, 11/2) 系统学
    • 若衰变子核存在同质异能态,在设计衰变链时就需要知道母核退激至子核同质异能态和基态的分支比,可根据衰变纲图和内转换系数进行计算得到。

      假定母核衰变到子核同质异能态的粒子的绝对强度为Bm,所有跃迁到该同质异能态的每条$ \gamma $射线的相对强度Ij(j=1, $ 2, \, \cdots $m),相对应的内转换系数为$\alpha_{\rm{j}} $,则跃迁到该同质异能态的总的绝对强度Pm=N×ΣIj(1+αj)+Bm,N为归一化因子;母核衰变到基态的粒子的绝对强度为Bg,所有跃迁到基态的每条$ \gamma $射线的相对强度Ii(i=1, 2$, \, \cdots $n),相对应的内转换系数为$\alpha_i $,则跃迁到基态的总的绝对强度Pg=N×ΣIi(1+αi)+Bg;此时衰变至子核同质异能态的衰变分支比Rm

      $$ {R}_{\mathrm{m}} = {P}_{\mathrm{m}}/({P}_{\mathrm{m}}+{P}_{\mathrm{g}}) 。 $$ (4)

      衰变至基态的衰变分支比Rg=100-Rm。对于实验测量数据不全或无测量数据的衰变,本工作取Rg=50,Rm=50。

    • 根据裂变产物的衰变路径和衰变信息等特点,研制了裂变产物衰变链设计专用衰变数据库,采用ENSDF数据格式,包含8种衰变类型的衰变数据,这些衰变类型有:$ {\beta ^{\rm{ - }}} $负衰变、伴随$ {\beta ^{\rm{ - }}} $负衰变的缓发中子衰变$ {\beta ^{\rm{ - }}} $n、$ {\beta ^{\rm{ - }}} $2n(由于目前实验上最多只观测到2个缓发中子,$ {\beta ^{\rm{ - }}} $3n及以上就没有涉及)、双$ {\beta } $负衰变2$ {\beta ^{\rm{ - }}} $$ {\beta ^ + } $/$ \varepsilon $轨道电子俘获、双$ {\beta } $正衰变2$ {\beta }^{+} $/2$\varepsilon$$\alpha $衰变、IT同核异能跃迁。数据库中的重要数据如半衰期、衰变分支比等,全部取自本工作更新评价、国际评价核结构和衰变数据库ENSDF [2]和NUBASE [5]数据库,其中,$ {\beta ^{\rm{ - }}} $n、$ {\beta ^{\rm{ - }}} $2n等取自最新评价数据[3-4]

      每个衰变链上除放射性核素外,还有稳定核素,为便于衰变链设计以及实际应用,将ENSDF数据格式的数据库转换成ENDF格式的数据库,并增加了稳定核素。在构建ENDF格式数据库时,主要考虑:(1) 核素ID,每个核素都对应一个核素识别,包括元素符号、质量数、原子序数以及中子数;(2) 核的状态,即基态g、第一同质异能态m以及第二同质异能态n(本工作最多考虑两个同质异能态);(3) 半衰期或稳定核素丰度;(4) 衰变方式;(5) 衰变分支比(包括退激至子核同质异能态的分支比)。这样在每个质量链上,就包括所有稳定核素、$ {\beta }^{-} $衰变核素以及少量$ {\beta } $+/$ \varepsilon $衰变核素,涵盖了裂变产物衰变链设计所需的全部数据信息。使用该库的数据,可完成A=66~172核区裂变产物衰变链设计。下面给出库中的数据内容。

      对于所有放射性核素的衰变数据,每个衰变母核的具体数据内容如下所示:

      · 母核特性El(能级),Jπ(自旋宇称),T1/2(半衰期),Q(总衰变能),α%, $ \varepsilon $%+$ { {\beta} ^+ } $%, ${ {\beta ^{\rm{ - }}} }$%, ${ {\beta ^{\rm{ - }}} } $n%, IT% (衰变分支比);

      · 子核特性El(能级),Jπ(自旋宇称),T1/2(半衰期);

      ·$ {\beta } $(或ε)衰变特性:$E_ {\beta } $Eε(平均衰变能量),$ I_{\beta } $±$ I_\varepsilon $(衰变强度);

      ·$ \gamma $衰变特性: $ E_{\gamma} $($ \gamma $能量),$I_{ \gamma } $($ \gamma $强度),αkαk/αL$\cdots ($内转换系数);

      · $ \alpha $衰变特性: Eα(能量),Iα(强度);

      · 其它伴随辐射:俄歇电子、内转换电子和X射线等辐射的能量及其强度;

      · 归一化因子:NR(相对$ \gamma $射线),NT($ \gamma $+ce的总$ \gamma $跃迁),NB($ {\beta } $衰变),BR(分支比)

      专用数据库中所有核素如表2所列。

      表 2  专用衰变数据库中的所有核素

      所有核素列表
      V - 66, Cr- 66, Mn- 66, Fe- 66, Co- 66, Ni- 66, Cu- 66, Zn- 66, Ga- 66, Ge- 66;
      V - 67, Cr- 67, Mn- 67, Fe- 67, Co- 67, Co- 67m, Ni- 67, Cu- 67, Zn- 67, Ga- 67, Ge- 67;
      Cr- 68, Mn- 68, Fe- 68, Co- 68, Co- 68m, Ni- 68, Cu- 68, Cu- 68m, Zn- 68, Ga- 68, Ge- 68;
      Cr- 69, Mn- 69, Fe- 69, Co- 69, Co- 69m, Ni- 69, Ni- 69m, Cu- 69, Zn- 69, Zn- 69m, Ga- 69, Ge- 69, As- 69;
      Cr- 70, Mn- 70, Fe- 70, Co- 70, Co- 70m, Ni- 70, Cu- 70, Cu- 70m, Cu- 70n, Zn- 70, Ga- 70, Ge- 70, As- 70, Se- 70;
      Mn- 71, Fe- 71, Co- 71, Ni- 71, Ni- 71m, Cu-71, Zn- 71, Zn-71m, Ga- 71, Ge- 71, Ge- 71m, As- 71;
      Mn- 72, Fe- 72, Co- 72, Co- 72m, Ni- 72, Cu- 72, Zn- 72, Ga- 72, Ga- 72m, Ge- 72, As- 72, Se- 72;
      Mn- 73, Fe- 73, Co- 73, Ni- 73, Cu- 73, Zn- 73, Zn- 73m, Ga- 73, Ga- 73m, Ge- 73, Ge- 73m, As- 73, Se- 73, Se- 73m;
      Fe- 74, Co- 74, Ni- 74, Cu- 74, Zn- 74, Ga- 74, Ga- 74m, Ge- 74, As- 74, Se- 74, Br- 74, Br- 74m, Kr- 74;
      Fe- 75, Co- 75, Ni- 75, Cu- 75, Zn- 75, Zn- 75m, Ga- 75, Ge- 75, Ge- 75m, As- 75, As- 75m, Se- 75, Br- 75;
      Fe- 76, Co- 76, Co- 76m, Ni- 76, Cu- 76, Cu- 76m, Zn- 76, Ga- 76, Ge- 76, As- 76, Se- 76, Br- 76, Br- 76m, Kr- 76;
      Co- 77, Ni- 77, Cu- 77, Zn- 77, Zn- 77m, Ga- 77, Ge- 77, Ge- 77m, As- 77, Se- 77, Se- 77m, Br- 77, Br- 77m, Kr- 77;
      Co- 78, Ni- 78, Cu- 78, Zn- 78, Ga- 78, Ge- 78, As- 78, Se- 78, Br- 78, Kr- 78, Rb- 78, Rb- 78m, Sr- 78;
      Ni- 79, Cu- 79, Zn- 79, Zn- 79m, Ga- 79, Ge- 79, Ge- 79m, As- 79, Se- 79, Se- 79m, Br- 79, Br- 79m, Kr- 79, Kr- 79m, Rb- 79;
      Ni- 80, Cu- 80, Zn- 80, Ga- 80, Ga- 80m, Ge- 80, As- 80, Se- 80, Br- 80, Br- 80m, Kr- 80, Rb- 80, Sr- 80;
      Ni- 81, Cu- 81, Zn- 81, Ga- 81, Ge- 81, Ge- 81m, As- 81, Se- 81, Se- 81m, Br- 81, Kr- 81, Kr- 81m, Rb- 81, Rb- 81m, Sr- 81;
      Ni- 82, Cu- 82, Zn- 82, Ga- 82, Ge- 82, As- 82, As- 82m, Se- 82, Br- 82, Br- 82m, Kr- 82, Rb- 82, Rb- 82m, Sr- 82;
      Cu- 83, Zn- 83, Ga- 83, Ge- 83, As- 83, Se- 83, Se- 83m, Br- 83, Kr- 83, Kr- 83m, Rb- 83, Rb- 83m, Sr- 83, Sr- 83m;
      Cu- 84, Zn- 84, Ga- 84, Ga- 84m, Ge- 84, As- 84, As- 84m, Se- 84, Br- 84, Br- 84m, Kr- 84, Rb- 84, Rb- 84m, Sr- 84, Y - 84, Y - 84m, Zr- 84;
      Zn- 85, Ga- 85, Ge- 85, As- 85, Se- 85, Br- 85, Kr- 85, Kr- 85m, Rb- 85, Sr- 85, Sr- 85m, Y - 85, Y - 85m;
      Zn- 86, Ga- 86, Ge- 86, As- 86, Se- 86, Br- 86, Kr- 86, Rb- 86, Rb- 86m, Sr- 86, Y - 86, Y - 86m, Zr- 86;
      Ga- 87, Ge- 87, As- 87, Se- 87, Br- 87, Kr- 87, Rb- 87, Sr- 87, Sr- 87m, Y - 87, Y - 87m, Zr- 87, Zr- 87m;
      Ga- 88, Ge- 88, As- 88, Se- 88, Br- 88, Kr- 88, Rb- 88, Sr- 88, Y - 88, Y - 88m, Y - 88n, Zr- 88, Nb- 88, Nb- 88m;
      Ge- 89, As- 89, Se- 89, Br- 89, Kr- 89, Rb- 89, Sr- 89, Y - 89, Y - 89m, Zr- 89, Zr- 89m, Nb- 89, Nb- 89m;
      Ge- 90, As- 90, Se- 90, Br- 90, Kr- 90, Rb- 90, Rb- 90m, Sr- 90, Y - 90, Y - 90m, Zr- 90, Zr- 90m, Nb- 90, Nb- 90m, Nb- 90n, Mo- 90;
      As- 91, Se- 91, Br- 91, Kr- 91, Rb- 91, Sr- 91, Y - 91, Y - 91m, Zr- 91, Nb- 91, Nb- 91m, Mo- 91, Mo- 91m, Tc- 91, Tc- 91m;
      As- 92, Se- 92, Br- 92, Kr- 92, Rb- 92, Sr- 92, Y - 92, Zr- 92, Nb- 92, Nb- 92m, Mo- 92, Tc- 92, Ru- 92;
      Se- 93, Br- 93, Kr- 93, Rb- 93, Sr- 93, Y - 93, Y - 93m, Zr- 93, Nb- 93, Nb- 93m, Mo- 93, Mo- 93m, Tc- 93, Tc- 93m;
      Se- 94, Br- 94, Kr- 94, Rb- 94, Sr- 94, Y - 94, Zr- 94, Nb- 94, Nb- 94m, Mo- 94, Tc- 94, Tc- 94m, Ru- 94;
      Se- 95, Br- 95, Kr- 95, Rb- 95, Sr- 95, Y - 95, Zr- 95, Nb- 95, Nb- 95m, Mo- 95, Tc- 95, Tc- 95m, Ru- 95;
      Br- 96, Kr- 96, Rb- 96, Sr- 96, Y - 96, Y - 96m, Zr- 96, Nb- 96, Mo- 96, Tc- 96, Tc- 96m, Ru- 96, Rh- 96, Rh- 96m, Pd- 96;
      Br- 97, Kr- 97, Rb- 97, Sr- 97, Y - 97, Y - 97m, Y - 97n, Zr- 97, Nb- 97, Nb- 97m, Mo- 97, Tc- 97, Tc- 97m, Ru- 97, Rh- 97, Rh- 97m;
      Br- 98, Kr- 98, Rb- 98, Rb- 98m, Sr- 98, Y - 98, Y - 98m, Zr- 98, Nb- 98, Nb- 98m, Mo- 98, Tc- 98, Ru- 98, Rh- 98, Rh- 98m, Pd- 98;
      Kr- 99, Rb- 99, Sr- 99, Y - 99, Zr- 99, Nb- 99, Nb- 99m, Mo- 99, Tc- 99, Tc- 99m, Ru- 99, Rh- 99, Rh- 99m, Pd- 99;
      Kr-100, Rb-100, Sr-100, Y -100, Y -100m, Zr-100, Nb-100, Nb-100m, Mo-100, Tc-100, Ru-100, Rh-100, Rh-100m, Pd-100;
      Kr-101, Rb-101, Sr-101, Y -101, Zr-101, Nb-101, Mo-101, Tc-101, Ru-101, Rh-101, Rh-101m, Pd-101;
      Rb-102, Sr-102, Y -102, Y -102m, Zr-102, Nb-102, Nb-102m, Mo-102, Tc-102, Tc-102m, Ru-102, Rh-102, Rh-102m, Pd-102, Ag-102, Ag-102m,
      Cd-102;
      Rb-103, Sr-103, Y -103, Zr-103, Nb-103, Mo-103, Tc-103, Ru-103, Ru-103m, Rh-103, Rh-103m, Pd-103, Ag-103, Ag-103m;
      Rb-104, Sr-104, Y -104, Zr-104, Nb-104, Nb-104m, Mo-104, Tc-104, Ru-104, Rh-104, Rh-104m, Pd-104, Ag-104, Ag-104m, Cd-104;
      Sr-105, Y -105, Zr-105, Nb-105, Mo-105, Tc-105, Ru-105, Rh-105, Rh-105m, Pd-105, Ag-105, Ag-105m, Cd-105;
      Sr-106, Y -106, Zr-106, Nb-106, Nb-106m, Mo-106, Tc-106, Ru-106, Rh-106, Rh-106m, Pd-106, Ag-106, Ag-106m, Cd-106, In-106, In-106m,
      Sn-106;
      Sr-107, Y -107, Zr-107, Nb-107, Mo-107, Tc-107, Ru-107, Rh-107, Pd-107, Pd-107m, Ag-107, Ag-107m, Cd-107, In-107, In-107m;
      Y -108, Zr-108, Nb-108, Mo-108, Tc-108, Ru-108, Rh-108, Rh-108m, Pd-108, Ag-108, Ag-108m, Cd-108, In-108, In-108m, Sn-108;
      Y -109, Zr-109, Nb-109, Mo-109, Tc-109, Ru-109, Rh-109, Pd-109, Pd-109m, Ag-109, Ag-109m, Cd-109, In-109, In-109m, In-109n;
      Zr-110, Nb-110, Nb-110m, Mo-110, Tc-110, Ru-110, Rh-110, Rh-110m, Pd-110, Ag-110, Ag-110m, Cd-110, In-110, In-110m, Sn-110;
      Zr-111, Nb-111, Mo-111, Mo-111m, Tc-111, Ru-111, Rh-111, Pd-111, Pd-111m, Ag-111, Ag-111m, Cd-111, Cd-111m, In-111, In-111m, Sn-111;
      Zr-112, Nb-112, Mo-112, Tc-112, Ru-112, Rh-112, Rh-112m, Pd-112, Ag-112, Cd-112, In-112, In-112m, Sn-112, Sb-112, Te-112;
      Zr-113, Nb-113, Mo-113, Tc-113, Ru-113, Ru-113m, Rh-113, Pd-113, Pd-113m, Ag-113, Ag-113m, Cd-113, Cd-113m, In-113, In-113m, Sn-113,
      Sn-113m, Sb-113;
      Nb-114, Mo-114, Tc-114, Tc-114m, Ru-114, Rh-114, Rh-114m, Pd-114, Ag-114, Ag-114m, Cd-114, In-114, In-114m, In-114n, Sn-114, Sb-114,
      Te-114;
      Nb-115, Mo-115, Tc-115, Ru-115, Ru-115m, Rh-115, Pd-115, Pd-115m, Ag-115, Ag-115m, Cd-115, Cd-115m, In-115, In-115m, Sn-115, Sb-115,
      Te-115, Te-115m;
      Nb-116, Mo-116, Tc-116, Ru-116, Rh-116, Rh-116m, Pd-116, Ag-116, Ag-116m, Ag-116n, Cd-116, In-116, In-116m, In-116n, Sn-116, Sb-116,
      Sb-116m, Te-116;
      Mo-117, Tc-117, Ru-117, Rh-117, Pd-117, Pd-117m, Ag-117, Ag-117m, Cd-117, Cd-117m, In-117, In-117m, Sn-117, Sn-117m, Sb-117, Te-117,
      Te-117m;
      Mo-118, Tc-118, Ru-118, Rh-118, Rh-118m, Pd-118, Ag-118, Ag-118m, Cd-118, In-118, In-118m, In-118n, Sn-118, Sb-118, Sb-118m, Te-118;
      Mo-119, Tc-119, Ru-119, Rh-119, Pd-119, Pd-119m, Ag-119, Ag-119m, Cd-119, Cd-119m, In-119, In-119m, Sn-119, Sn-119m, Sb-119, Sb-119m,
      Te-119, Te-119m;
      Tc-120, Ru-120, Rh-120, Pd-120, Ag-120, Ag-120m, Ag-120n, Cd-120, In-120, In-120m, In-120n, Sn-120, Sb-120, Sb-120m, Te-120, I -120, I -120m, Xe-120;
      Tc-121, Ru-121, Rh-121, Pd-121, Ag-121, Cd-121, Cd-121m, In-121, In-121m, Sn-121, Sn-121m, Sb-121, Te-121, Te-121m, I -121;
      Tc-122, Ru-122, Rh-122, Pd-122, Ag-122, Ag-122m, Ag-122n, Cd-122, In-122, In-122m, In-122n, Sn-122, Sb-122, Te-122, I -122, Xe-122;
      Ru-123, Rh-123, Pd-123, Pd-123m, Ag-123, Ag-123m, Cd-123, Cd-123m, In-123, In-123m, Sn-123, Sn-123m, Sb-123, Te-123, Te-123m, I -123,
      Xe-123;
      Ru-124, Rh-124, Pd-124, Ag-124, Ag-124m, Cd-124, In-124, In-124m, Sn-124, Sb-124, Sb-124m, Sb-124n, Te-124, I -124, Xe-124, Cs-124, Cs-124m, Ba-124;
      Ru-125, Rh-125, Pd-125, Pd-125m, Ag-125, Ag-125m, Cd-125, Cd-125m, In-125, In-125m, Sn-125, Sn-125m, Sb-125, Te-125, Te-125m, I -125,
      Xe-125, Xe-125m;
      Rh-126, Pd-126, Ag-126, Ag-126m, Cd-126, In-126, In-126m, Sn-126, Sb-126, Sb-126m, Sb-126n, Te-126, I -126, Xe-126, Cs-126, Ba-126;
      Rh-127, Pd-127, Ag-127, Ag-127m, Ag-127n, Cd-127, Cd-127m, In-127, In-127m, In-127n, Sn-127, Sn-127m, Sb-127, Te-127, Te-127m, I -127,
      Xe-127, Xe-127m, Cs-127;
      Rh-128, Pd-128, Ag-128, Cd-128, Cd-128m, In-128, In-128m, In-128n, Sn-128, Sn-128m, Sb-128, Sb-128m, Te-128, I -128, Xe-128, Cs-128, Ba-128;
      Pd-129, Ag-129, Ag-129m, Cd-129, Cd-129m, Cd-129n, In-129, In-129m, In-129n, Sn-129, Sn-129m, Sb-129, Sb-129m, Te-129, Te-129m, I -129,
      Xe-129, Xe-129m, Cs-129, Ba-129,
      Ba-129m;
      Pd-130, Ag-130, Cd-130, In-130, In-130m, In-130n, Sn-130, Sn-130m, Sb-130, Sb-130m, Te-130, I -130, I -130m, Xe-130, Cs-130, Cs-130m, Ba-130, Ba-130m, La-130, Ce-130;
      Pd-131, Ag-131, Cd-131, In-131, In-131m, In-131n, Sn-131, Sn-131m, Sb-131, Te-131, Te-131m, Te-131n, I -131, Xe-131, Xe-131m, Cs-131, Ba-131, Ba-131m, La-131;
      Ag-132, Cd-132, In-132, Sn-132, Sb-132, Sb-132m, Te-132, I -132, I -132m, Xe-132, Xe-132m, Cs-132, Ba-132, La-132, La-132m, Ce-132, Ce-132m;
      Ag-133, Cd-133, In-133, In-133m, Sn-133, Sb-133, Te-133, Te-133m, I -133, I -133m, Xe-133, Xe-133m, Cs-133, Ba-133, Ba-133m, La-133, Ce-133, Ce-133m;
      Cd-134, In-134, Sn-134, Sb-134, Sb-134m, Te-134, I -134, I -134m, Xe-134, Xe-134m, Cs-134, Cs-134m, Ba-134, La-134, Ce-134;
      Cd-135, In-135, Sn-135, Sb-135, Te-135, I -135, Xe-135, Xe-135m, Cs-135, Cs-135m, Ba-135, Ba-135m, Ba-135n, La-135, Ce-135, Ce-135m;
      In-136, Sn-136, Sb-136, Te-136, I -136, I -136m, Xe-136, Cs-136, Cs-136m, Ba-136, Ba-136m, La-136, La-136m, Ce-136, Pr-136, Nd-136;
      In-137, Sn-137, Sb-137, Te-137, I -137, Xe-137, Cs-137, Ba-137, Ba-137m, La-137, Ce-137, Ce-137m, Pr-137;
      Sn-138, Sb-138, Te-138, I -138, Xe-138, Cs-138, Cs-138m, Ba-138, La-138, Ce-138, Ce-138m, Pr-138, Pr-138m, Nd-138;
      Sn-139, Sb-139, Te-139, I -139, Xe-139, Cs-139, Ba-139, La-139, Ce-139, Ce-139m, Pr-139, Nd-139, Nd-139m;
      Sn-140, Sb-140, Te-140, I -140, Xe-140, Cs-140, Ba-140, La-140, Ce-140, Pr-140, Nd-140;
      Sb-141, Te-141, I -141, Xe-141, Cs-141, Ba-141, La-141, Ce-141, Pr-141, Nd-141, Nd-141m, Pm-141;
      Sb-142, Te-142, I -142, Xe-142, Cs-142, Ba-142, La-142, Ce-142, Pr-142, Pr-142m, Nd-142, Pm-142, Pm-142m, Sm-142;
      Te-143, I -143, Xe-143, Cs-143, Ba-143, La-143, Ce-143, Pr-143, Nd-143, Pm-143, Sm-143, Sm-143m, Sm-143n;
      Te-144, I -144, Xe-144, Cs-144, Cs-144m, Ba-144, La-144, Ce-144, Pr-144, Pr-144m, Nd-144, Pm-144, Sm-144, Eu-144, Gd-144;
      Te-145, I -145, Xe-145, Cs-145, Ba-145, La-145, Ce-145, Pr-145, Nd-145, Pm-145, Sm-145, Eu-145;
      I -146, Xe-146, Cs-146, Ba-146, La-146, La-146m, Ce-146, Pr-146, Nd-146, Pm-146, Sm-146, Eu-146, Gd-146;
      I -147, Xe-147, Cs-147, Ba-147, La-147, Ce-147, Pr-147, Nd-147, Pm-147, Sm-147, Eu-147, Gd-147, Tb-147, Tb-147m;
      Xe-148, Cs-148, Ba-148, La-148, Ce-148, Pr-148, Pr-148m, Nd-148, Pm-148, Pm-148m, Sm-148, Eu-148, Gd-148, Tb-148, Tb-148m, Dy-148;
      Xe-149, Cs-149, Ba-149, La-149, Ce-149, Pr-149, Nd-149, Pm-149, Sm-149, Eu-149, Gd-149, Tb-149, Tb-149m;
      Xe-150, Cs-150, Ba-150, La-150, Ce-150, Pr-150, Nd-150, Pm-150, Sm-150, Eu-150, Eu-150m, Gd-150, Tb-150, Tb-150m, Dy-150;
      Cs-151, Ba-151, La-151, Ce-151, Pr-151, Nd-151, Pm-151, Sm-151, Eu-151, Gd-151, Tb-151, Tb-151m;
      Cs-152, Ba-152, La-152, Ce-152, Pr-152, Nd-152, Pm-152, Pm-152m, Pm-152n, Sm-152, Eu-152, Eu-152m, Gd-152, Tb-152, Tb-152m, Dy-152;
      Ba-153, La-153, Ce-153, Pr-153, Nd-153, Pm-153, Sm-153, Sm-153m, Eu-153, Gd-153, Tb-153, Dy-153;
      Ba-154, La-154, Ce-154, Pr-154, Nd-154, Pm-154, Pm-154m, Sm-154, Eu-154, Eu-154m, Gd-154, Tb-154, Tb-154m, Tb-154n, Dy-154, Ho-154,
      Ho-154m, Er-154;
      La-155, Ce-155, Pr-155, Nd-155, Pm-155, Sm-155, Eu-155, Gd-155, Gd-155m, Tb-155, Dy-155, Ho-155;
      La-156, Ce-156, Pr-156, Nd-156, Pm-156, Pm-156m, Sm-156, Eu-156, Gd-156, Tb-156, Tb-156m, Tb-156n, Dy-156, Ho-156, Ho-156m, Ho-156n,
      Er-156;
      La-157, Ce-157, Pr-157, Nd-157, Pm-157, Sm-157, Eu-157, Gd-157, Tb-157, Dy-157, Dy-157m, Ho-157;
      Ce-158, Pr-158, Nd-158, Pm-158, Sm-158, Eu-158, Gd-158, Tb-158, Tb-158m, Dy-158, Ho-158, Ho-158m, Er-158;
      Ce-159, Pr-159, Nd-159, Pm-159, Sm-159, Eu-159, Gd-159, Tb-159, Dy-159, Ho-159, Ho-159m, Er-159;
      Pr-160, Nd-160, Pm-160, Pm-160m, Sm-160, Eu-160, Eu-160m, Gd-160, Tb-160, Dy-160, Ho-160, Ho-160m, Ho-160n, Er-160, Tm-160, Tm-160m;
      Pr-161, Nd-161, Pm-161, Sm-161, Eu-161, Gd-161, Tb-161, Dy-161, Ho-161, Ho-161m, Er-161, Tm-161, Tm-161m;
      Nd-162, Pm-162, Sm-162, Eu-162, Eu-162m, Gd-162, Tb-162, Tb-162m, Dy-162, Ho-162, Ho-162m, Er-162, Tm-162, Tm-162m, Yb-162;
      Nd-163, Pm-163, Sm-163, Eu-163, Gd-163, Gd-163m, Tb-163, Dy-163, Ho-163, Ho-163m, Er-163, Tm-163;
      Pm-164, Sm-164, Eu-164, Gd-164, Tb-164, Tb-164m, Dy-164, Ho-164, Ho-164m, Er-164, Tm-164, Tm-164m, Yb-164;
      Pm-165, Sm-165, Eu-165, Gd-165, Tb-165, Dy-165, Dy-165m, Ho-165, Er-165, Tm-165, Yb-165;
      Sm-166, Eu-166, Gd-166, Tb-166, Dy-166, Ho-166, Ho-166m, Er-166, Tm-166, Yb-166;
      Sm-167, Eu-167, Gd-167, Tb-167, Dy-167, Ho-167, Er-167, Er-167m, Tm-167, Yb-167, Lu-167, Lu-167m;
      Sm-168, Eu-168, Gd-168, Tb-168, Dy-168, Ho-168, Ho-168m, Er-168, Tm-168, Yb-168, Lu-168, Lu-168m, Hf-168;
      Eu-169, Gd-169, Tb-169, Dy-169, Ho-169, Er-169, Tm-169, Yb-169, Yb-169m, Lu-169, Lu-169m, Hf-169;
      Eu-170, Gd-170, Tb-170, Dy-170, Ho-170, Ho-170m, Er-170, Tm-170, Yb-170, Lu-170, Lu-170m, Hf-170, Ta-170;
      Gd-171, Tb-171, Dy-171, Ho-171, Er-171, Tm-171, Yb-171, Yb-171m, Lu-171, Lu-171m, Hf-171, Hf-171m, Ta-171;
      Gd-172, Tb-172, Dy-172, Dy-172m, Ho-172, Er-172, Tm-172, Yb-172, Lu-172, Lu-172m, Hf-172, Ta-172, W -172。
    • 这里以129In为例,介绍裂变产物衰变链是如何组成的并以此说明其复杂性,母体核素形成129In的衰变关系以及129In衰变退激关系如图2所示。

      图  2  母核到129In的衰变关系以及129In衰变退激关系图

      图2可看出,衰变到129In的母体核素包括:(1) 核材料裂变直接产生;(2) 由各前驱母体衰变而来,包括129mCd、129Cd、129mIn、129nIn。129In衰变退激的子体核素包括:(1) 129mSn;(2) 129Sn;(3) 128Sn。由此可见,129In的衰变链非常复杂,衰变路径多达7条,这部分的计算比较繁杂,需逐个计算每个前驱母核衰变到该核素以及退激至各个子核的衰变信息。

    • 衰变链每个衰变阶段的名称取决于它与前后阶段的关系,“母体核素”衰变后产生“子体核素”。子体核素有可能是稳定的,但也可以继续衰变形成下一个子体核素。

      在计算各母体核素对子体核素的形成过程中,需按照衰变路径逐个计算母体核素,但这样不可避免地会造成重复计算。为解决上述问题,本文采用如下方法:从专用衰变数据库产生每个质量链衰变路径的数据文件。每次在计算某条路径上的某母体核素对子体核素的贡献时,通过搜索数据文件,判断从该母体核素到指定子体核素的衰变路径片段是否已在前面的路径上出现过,是则不再计算,否则计算。同样,计算衰变退激到子体核素信息时,也按照这种思路进行。

      质量链衰变路径的数据库是按如下方式设计的:在1个衰变链中,如果1个核素的质子数最小,则以它为母核建立1个$ {\beta ^{\rm{ - }}} $基态链;如果1个核素的质子数最大,则以它为母核建立1个EC基态链;特别情况,少量核素存在α衰变、2$ {\beta ^{\rm{ - }}} $或2$ {\beta ^ + } $/2$\varepsilon$,须分别建立各自的衰变链;如果核素以激发态存在,则以它为母核建立激发态链。

    • 为方便绘制每个质量链的衰变链图,用Python语言开发了衰变链设计绘图程序包DecayChainDrawer,由两部分组成,process.py和draw.py,process.py主要功能是从专用衰变数据库读取每个核的衰变数据,产生draw.py的输入数据文件;draw.py的主要功能是计算原子核之间的衰变关系,确定每个核在衰变链上的相对位置,生成Tex格式数据文件,该Tex文件可用TexLive产生PDF格式的衰变链图。程序主要框架见图3(a)和(b)。应用DecayChainDrawer程序包可实现裂变产物核区A = 66~172每条质量链上的衰变链图绘制。

      图  3  process.py程序架构图(a)和draw.py程序架构图(b)

    • A = 100质量链为例,给出一条复杂裂变产物衰变链的设计示意图,见图4。从图2图4可看出,每个核素都具有特定的母体核素和复杂的衰变分支。

      图  4  A = 100质量链裂变产物衰变链设计示意图

    • 根据核科学参考文献库,对半衰期、缓发中子发射几率等进行了更新评价,对部分基态指定存在问题的数据利用系统学研究和理论研究相结合的方法进行了必要修正,并根据衰变纲图和内转换系数重新计算了退激至子核同质异能态和基态的衰变分支比数据。在此基础上,结合现有核结构和衰变数据库,研制了裂变产物衰变链设计专用衰变数据库,按照衰变规律,建立了裂变产物衰变路径和衰变信息的完整衰变链。

      衰变链上的所有核素都是已观测到的,理论预言存在但实验未观测到的暂不包括,实验测量截止时间是2021年12月。所有先驱核缓发中子数据都是实验测量数据,理论预言存在但实验未观测到数值的都认为该缓发中子发射途径不存在,因此链上没有画。对$ {\beta ^ + } $/$\varepsilon $衰变,最多考虑了两个核素,而同质异能态(IT)衰变同样最多只考虑了两个同质异能态。本工作完成的裂变产物核衰变链可为裂变产物分析和裂变产额研究提供一个便利的参考。

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