搜索

x

留言板

姓名
邮箱
手机号码
标题
留言内容
验证码

引用本文:
Citation:

王立德, 张钧尧, 卢肖勇
cstr: 32037.14.aps.74.20250262

Numerical studies of three-step selective photoionization of neodymium-150 isotope

WANG Lide, ZHANG Junyao, LU Xiaoyong
cstr: 32037.14.aps.74.20250262
Article Text (iFLYTEK Translation)
PDF
HTML
导出引用
  • 富集钕-150同位素在核工业、科学研究等领域具有重要应用. 基于高效高选择性多步电离路径, 原子蒸气激光同位素分离法能够实现钕同位素分离, 但现用路径第2步跃迁的同位素位移(isotope shift, IS)几乎为零, 导致产品中Nd-150丰度偏低. 本文基于密度矩阵理论建立了通用的三步电离路径选择性光电离模型, 模型中综合考虑了同位素位移、超精细结构等原子参数和频率、功率、线宽、偏振等激光参数, 可在磁子能级级别计算原子与激光的相互作用过程. 基于上述模型, 通过与文献数据对比获得了现用路径分支比的最优拟合值, 评估了现用路径在不同线宽下的Nd-150丰度水平; 在仅改变第2步跃迁的前提下构造假定电离路径, 开展所有钕同位素的电离率计算, 评估不同同位素位移、超精细结构下的Nd-150丰度, 指导后续原子光谱实验. 数值计算发现第二激发态角动量J3 = 6, 同位素位移IS23,148 ≥ 300 MHz时, 在b12 ≤ 0.5 GHz, b23 ≤ 1.0 GHz, 平行线偏振的典型激光参数下可实现与电磁法相当的Nd-150丰度(> 95%). 在此基础上压窄激光线宽, 能够在保持电离率的同时获得超过电磁法的Nd-150产品. 后续原子光谱实验应着重寻找IS23,148 ≥ 300 MHz, J3 = 6的第2步跃迁, 第2步跃迁的约化电偶极矩达到现用路径的30%即可满足丰度要求.
    The enriched neodymium-150 (Nd-150) isotope has important applications in fields such as nuclear industry and basic scientific research. The Nd isotope separation can be conducted by atomic vapor laser isotope separation (AVLIS), where the target isotope is selectively ionized through the λ1 = 596 nm → λ2 = 579 nm → λ3 = 640 nm photoionization scheme, and non-target isotopes remain neutral due to the frequency-detuned excitation. Subsequently, an external electric field is applied to extract the ions from the laser-produced plasma. The Nd-150 abundance in the product cannot meet the requirement of the application, attributed to the nearly negligible isotope shift of the λ2 = 579 nm transition, thus resulting in the excess ionization of non-target isotopes. A new high-selectivity photoionization scheme is desirable to address this limitation, and its expected parameter values can be determined through numerical calculations prior to the time-consuming atomic spectroscopy experiments. In this study, a three-step selective photoionization model is established based on the density matrix theory, with the consideration of the hyperfine structures and magnetic sublevels. This model allows the flexible adjustments of atomic parameters (e.g. branching ratio, isotope shift, hyperfine constant) and laser parameters (e.g. frequency, power density, bandwidth, polarization), while the ionization probabilities of magnetic sublevel transitions can be quantitatively predicted. For the existing schemes, the branching ratios are determined by comparing literature data with numerical results, and the Nd-150 abundance values under different laser bandwidths are evaluated. Further, an alternative scheme is numerically explored on the assumption that the first transition remains unchanged and the second transition has a more significant isotope shift and a smaller branching ratio, and the Nd-150 abundance values under different combinations of isotope shifts, hyperfine structures, and laser bandwidths are evaluated, with all the natural Nd isotopes included. From the numerical results, a scheme with the angular momentum of the second excited state J3 = 6, the isotope shift between Nd-148 and Nd-150 IS23,148 ≥ 300 MHz, and a lower reduced dipole matrix element of the second transition reaching approximately 30% of that of λ2 = 579 nm, can produce the high-abundance Nd-150 (>95%, equivalent to that of the electromagnetic separation method) under the bandwidths: b12 ≤ 0.5 GHz and b23 ≤ 1.0 GHz, and parallel linear-polarized lasers. Using the lasers with narrower bandwidth can achieve higher abundance, which is superior to the electromagnetic separation method. The expected high-abundance Nd-150 can be attributed to the combined effects of multi-factors: the larger isotope shift between Nd-150 and Nd-148 than that between other adjacent isotope pairs, the insignificant hyperfine splitting of odd isotopes, and the match between narrow-bandwidth lasers and Nd I spectroscopic parameters. These parameter values can serve as benchmarks helpful for experimental parameter selection in the forthcoming high-precision spectroscopy experiments.
      通信作者: 王立德, wld15@tsinghua.org.cn
    • 基金项目: 粒子输运与富集技术全国重点实验室稳定支持基金(基金号: SYSJJ-2022101)资助的课题.
      Corresponding author: WANG Lide, wld15@tsinghua.org.cn
    • Funds: Project supported by the National Key Laboratory of Particle Transport and Separation Technology (Grant No. SYSJJ-2022101).
    [1]

    [2]

    [3]

    [4]

    [5]

    [6]

    [7]

    [8]

    [9]

    [10]

    [11]

    [12]

    [13]

    [14]

    [15]

    [16]

    [17]

    [18]

    [19]

    [20]

    [21]

    [22]

    [23]

    [24]

    [25]

    [26]

    [27]

    [28]

    [29]

    [30]

    [31]

    [32]

  • 钕同位素 Nd-150 Nd-148 Nd-146 Nd-145 Nd-144 Nd-143 Nd-142
    天然丰度c0/% 5.62 5.73 17.22 8.30 23.85 12.17 27.11
    核自旋In 0 0 0 7/2 0 7/2 0
    衰变 2νββ 或 0νββ→Sm-150 α → Ce-140
    下载: 导出CSV

    电离路径λ1/nmλ2/nmλ3/nm
    路径一[10,11]596579640
    路径二[16]588597597
    路径三[17]628560597
    路径四[17]562627597
    下载: 导出CSV

    参数第1束激光第2束激光第3束激光
    时域线型高斯线型
    脉宽30 ns (FWHM)
    时序关系峰值时刻同步
    频域线型修正的洛伦兹线型
    截止系数κ12 = κ23 = 0.2
    频率与Nd-150共振, f12 = f23 = 0
    偏振平行线偏振0:1:00:1:0
    混合偏振1/3:1/3:1/31/3:1/3:1/3
    正交线偏振0:1:01/2:0:1/2
    下载: 导出CSV

    能级E/cm–1JA145/MHzA143/A145B145/MHzB143/B145τ/ns
    路径一E10 [13]4[29]–121.628[29]1.60860[29]64.634[29]1.897[29]
    路径一E216757.037 [13]5[15]–129.594[15]1.6099[15]90.6[15]1.91[15]600*
    路径一E334011.04 [11]6[30]0*0*0*0*100*
    注: “*”表示假定值.
    下载: 导出CSV

    跃迁IS148/MHzIS146/IS148IS145/IS148IS144/IS148IS143/IS148IS142/IS148
    路径一λ11126.9[15]1.78[15]2.20[15]2.51[15]2.93[15]3.28[15]
    路径一λ20*
    注: “*”表示假定值.
    下载: 导出CSV

    线宽/GHz1.0, 1.00.5, 1.00.3, 1.01.0, 0.51.0, 0.30.5, 0.50.3, 0.3
    C150/%49.8654.8155.8054.6458.8668.3561.00
    ρion,1500.38390.40710.41580.38480.38490.41440.4073
    下载: 导出CSV

    能级 E/cm–1 J A145/MHz A143/A145 B145/MHz B143/B145 τ/ns
    路径一E1 0 [13] 4[29] –121.628[29] 1.60860[29] 64.634[29] 1.897[29]
    路径一E2 16757.037 [13] 5[15] –129.594[15] 1.6099[15] 90.6[15] 1.91[15] 600*
    假定E3 34011.04* 可选 可调 1.6* 0* 1.9* 100*
    注: “*”表示假定值, “”表示在4, 5, 6范围内可选, “”表示在(–∞, 0] MHz范围内可调, 根据低能级超精细常数数值, 本文选取的范围为[–140, 0] MHz.
    下载: 导出CSV

    跃迁 IS148/MHz IS146/IS148 IS145/IS148 IS144/IS148 IS143/IS148 IS142/IS148 β $ \langle J_m | d_{mn}| J_n \rangle $/(×10–30 C·m)
    路径一λ1 1126.9[15] 1.78[15] 2.20[15] 2.51[15] 2.93[15] 3.28[15] 0.15 4.5535
    假定λ2 可调 1.66* 2* 2.32* 2.66* 3* 0.05* 6.7004
    注: “*”表示假定值, “”表示由理论模型得到的拟合值, “”表示在(–∞, ∞) GHz范围内可调, 根据第1步跃迁同位素位移数值, 本文选取的范围为[–1.5, 1.5] GHz.
    下载: 导出CSV

    同位素 超精细常数 Nd-145超精细常数取值A'/MHz
    0 –20 –40 –60 –80 –100 –120 –140
    谱线分裂程度max(ν23, A, B) – min(ν23, A, B)/GHz
    Nd-145 B = –0.3A, A = A' 5.006 4.456 3.906 3.356 2.806 2.268 2.160 2.520
    B = –0.5A, A = A' 5.006 4.452 3.898 3.345 2.791 2.254 2.143 2.500
    B = –0.7A, A = A' 5.006 4.450 3.893 3.337 2.781 2.245 2.131 2.487
    B = –1.0A, A = A' 5.006 4.447 3.888 3.330 2.771 2.236 2.120 2.473
    Nd-143 B = –0.3A, A = 1.6A' 8.064 7.184 6.304 5.424 4.544 3.676 3.456 4.032
    B = –0.5A, A = 1.6A' 8.064 7.178 6.292 5.406 4.520 3.654 3.429 4.000
    B = –0.7A, A=1.6A' 8.064 7.174 6.284 5.394 4.504 3.639 3.410 3.979
    B= –1.0A, A=1.6A' 8.064 7.170 6.276 5.382 4.488 3.625 3.392 3.957
    下载: 导出CSV

    同位素 超精细常数 Nd-145超精细常数取值A'/MHz
    0 –20 –40 –60 –80 –100 –120 –140
    共振位置最大差异值max(|ν23, A, Bν23, A, 0|)/MHz
    Nd-145 B = –0.3A, A = A' 0 2.4 4.8 7.2 9.6 11.9 14.3 16.7
    B = –0.5A, A = A' 0 4.0 8.0 11.9 15.9 19.9 23.9 27.8
    B = –0.7A, A = A' 0 5.6 11.1 16.7 22.3 27.8 33.4 39.0
    B = –1.0A, A = A' 0 8.0 15.9 23.9 31.8 39.2 47.7 55.7
    Nd-143 B = –0.3A, A = 1.6A' 0 3.8 7.6 11.5 15.3 19.1 22.9 26.7
    B = –0.5A, A =1.6A' 0 6.4 12.7 19.1 25.5 31.8 38.2 44.6
    B = –0.7A, A=1.6A' 0 8.9 17.8 26.7 35.6 44.6 53.5 62.4
    B = –1.0A, A = 1.6A' 0 12.7 25.5 38.2 50.9 63.6 76.4 89.1
    下载: 导出CSV

    线宽/GHz 丰度/%
    Nd-150 Nd-148 Nd-146 Nd-145 Nd-144 Nd-143 Nd-142
    1.0, 1.0 47.45 24.25 2.66 6.69 0.54 18.26 0.14
    0.5, 1.0 52.04 20.13 1.76 5.41 0.39 20.17 0.11
    0.3, 1.0 53.16 19.23 1.64 5.20 0.37 20.30 0.10
    1.0, 0.5 51.22 20.98 1.80 5.42 0.40 20.08 0.11
    1.0, 0.3 52.23 20.14 1.69 5.21 0.38 20.24 0.10
    0.3, 0.3 64.99 6.85 0.71 3.01 0.22 24.14 0.08
    0.5, 0.5 60.70 11.03 0.93 3.60* 0.26 23.39 0.08
    注: 表中工况如图10(b)中的青色标记所示, f12 = f23 = 0, IS23,148 = –1000 MHz, A3,145 = –100 MHz; “*”, “”对应的奇同位素第二激发态布居率随时间的变化曲线分别与图12(a), (b)相对应.
    下载: 导出CSV

    共振位置 Nd-150 Nd-148 Nd-146 Nd-144 Nd-142
    ν12/MHz 0 1126.9 2009.2 2827.7 3700
    ν23/MHz 0 –1000 –1660 –2320 –3000
    ν12+ν23/MHz 0 126.9 349.2 507.7 700
    注: 表中工况如图10(b)中的青色标记所示, IS23,148 = –1000 MHz, A3,145 = –100 MHz.
    下载: 导出CSV
  • [1]

    [2]

    [3]

    [4]

    [5]

    [6]

    [7]

    [8]

    [9]

    [10]

    [11]

    [12]

    [13]

    [14]

    [15]

    [16]

    [17]

    [18]

    [19]

    [20]

    [21]

    [22]

    [23]

    [24]

    [25]

    [26]

    [27]

    [28]

    [29]

    [30]

    [31]

    [32]

  • [1] 刘鑫, 汶伟强, 李冀光, 魏宝仁, 肖君. 高电荷态类硼离子2P3/22P1/2跃迁的实验和理论研究进展. 必威体育下载 , 2024, 73(20): 203102. doi: 10.7498/aps.73.20241190
    [2] 钟振祥. 氢分子离子超精细结构理论综述. 必威体育下载 , 2024, 73(20): 203104. doi: 10.7498/aps.73.20241101
    [3] 计晨. 原子兰姆位移与超精细结构中的核结构效应. 必威体育下载 , 2024, 73(20): 202101. doi: 10.7498/aps.73.20241063
    [4] 陈润, 邵旭萍, 黄云霞, 杨晓华. BrF分子电磁偶极跃迁转动超精细微波谱模拟. 必威体育下载 , 2023, 72(4): 043301. doi: 10.7498/aps.72.20221957
    [5] 唐家栋, 刘乾昊, 程存峰, 胡水明. 磁场中HD分子振转跃迁的超精细结构. 必威体育下载 , 2021, 70(17): 170301. doi: 10.7498/aps.70.20210512
    [6] 张祥, 卢本全, 李冀光, 邹宏新. Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁同位素位移和超精细结构的理论研究. 必威体育下载 , 2019, 68(4): 043101. doi: 10.7498/aps.68.20182136
    [7] 余庚华, 颜辉, 高当丽, 赵朋义, 刘鸿, 朱晓玲, 杨维. 相对论多组态相互作用方法计算Mg+离子同位素位移. 必威体育下载 , 2018, 67(1): 013101. doi: 10.7498/aps.67.20171817
    [8] 裴栋梁, 何军, 王杰英, 王家超, 王军民. 铯原子里德伯态精细结构测量. 必威体育下载 , 2017, 66(19): 193701. doi: 10.7498/aps.66.193701
    [9] 余庚华, 刘鸿, 赵朋义, 徐炳明, 高当丽, 朱晓玲, 杨维. 采用相对论多组态Dirac-Hartree-Fock方法对Mg原子同位素位移的理论研究. 必威体育下载 , 2017, 66(11): 113101. doi: 10.7498/aps.66.113101
    [10] 任雅娜, 杨保东, 王杰, 杨光, 王军民. 铯原子7S1/2态磁偶极超精细常数的测量. 必威体育下载 , 2016, 65(7): 073103. doi: 10.7498/aps.65.073103
    [11] 杨保东, 高静, 王杰, 张天才, 王军民. 铯6S1/2 -6P3/2 -8S1/2阶梯型系统中超精细能级的多重电磁感应透明. 必威体育下载 , 2011, 60(11): 114207. doi: 10.7498/aps.60.114207
    [12] 陈兴鹏, 王楠. 相对论平均场理论对Rn同位素链原子核基态性质的研究. 必威体育下载 , 2011, 60(11): 112101. doi: 10.7498/aps.60.112101
    [13] 侯碧辉, 李 勇, 刘国庆, 张桂花, 刘凤艳, 陶世荃. 单晶LiNbO3:Mn2+的ESR谱研究. 必威体育下载 , 2005, 54(1): 373-378. doi: 10.7498/aps.54.373
    [14] 陈岁元, 刘常升, 李慧莉, 崔 彤. 非晶Fe73.5Cu1Nb3Si13.5B9合金激光纳米化的超精细结构研究. 必威体育下载 , 2005, 54(9): 4157-4163. doi: 10.7498/aps.54.4157
    [15] 王立军, 余慧莺. 窄带激光与能级具有超精细结构的二能级原子的相干激发. 必威体育下载 , 2004, 53(12): 4151-4156. doi: 10.7498/aps.53.4151
    [16] 马洪良, 陆 江, 王春涛. 141Pr+波长56908 nm谱线超精细结构测量. 必威体育下载 , 2003, 52(3): 566-569. doi: 10.7498/aps.52.566
    [17] 赵鹭明, 王立军. 超精细结构对激光与二能级原子相互作用的影响. 必威体育下载 , 2002, 51(6): 1227-1232. doi: 10.7498/aps.51.1227
    [18] 马洪良, 汤家镛. 142—146,148,150Nd+同位素位移的共线快离子束激光光谱学实验研究. 必威体育下载 , 2001, 50(3): 453-456. doi: 10.7498/aps.50.453
    [19] 黎光武, 马洪良, 李茂生, 陈志骏, 陈淼华, 陆福全, 彭先觉, 杨福家. LaⅡ5d2 1G4→4f5d 1F3超精 细结构光谱测量. 必威体育下载 , 2000, 49(7): 1256-1259. doi: 10.7498/aps.49.1256
    [20] 戴长建, 于长江. 脉冲激光场选择性光电离同位素原子. 必威体育下载 , 1994, 43(3): 356-368. doi: 10.7498/aps.43.356
计量
  • 文章访问数:  377
  • PDF下载量:  11
  • 被引次数: 0
出版历程
  • 收稿日期:  2025-03-02
  • 修回日期:  2025-04-03
  • 上网日期:  2025-04-18
  • 刊出日期:  2025-06-05

返回文章
返回