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

WANG Lide; ZHANG Junyao; LU Xiaoyong

doi:10.7498/aps.74.20250262

Abstract

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 IS_23,148 ≥ 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.

Keywords:

Authors and contacts

1.
National Key Laboratory of Particle Transport and Separation Technology, Tianjin 300180, China
2.
Research Institute of Physical and Chemical Engineering of Nuclear Industry, Tianjin 300180, China

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).

FullText HTML

References

[1]	Akhmedzhanov R A, Gushchin L A, Nizov N A, Nizov V A, Sobgayda D A, Zelensky I V 2024 JETP Lett. 119 834 Google Scholar
[2]	Liang P J, Liu X, Li P Y, Zhou Z Q, Li C F, Guo G C 2020 J. Opt. Soc. Am. B 37 1653 Google Scholar
[3]	Broderick K, Lusk R, Hinderer J, Griswold J, Boll R, Garland M, Heilbronn L, Mirzadeh S 2019 Appl. Radiat. Isot. 144 54 Google Scholar
[4]	Hu F, Cutler C S, Hoffman T, Sieckman G, Volkert W A, Jurisson S S 2002 Nucl. Med. Biol. 29 423 Google Scholar
[5]	Committee A 2015 Standard Practice for Analysis of Spent Nuclear Fuel to Determine Selected Isotopes and Estimate Fuel Burnup
[6]	Suryanarayana M V 2022 Sci. Rep. 12 11471 Google Scholar
[7]	Barabash A S, Belli P, Bernabei R, Boiko R S, Cappella F, Caracciolo V, Cerulli R, Danevich F A, Fang D L, Ferella F, Incicchitti A, Kobychev V V, Konovalov S I, Laubenstein M, Leoncini A, Merlo V, Nisi S, Niţescu O, Poda D V, Polischuk O G, Shcherbakov I B K, Šimkovic F, Timonina A, Tinkova V S, Tretyak V I, Umatov V I 2025 Eur. Phys. J. C 85 174 Google Scholar
[8]	https://www.isotopes.gov/products/neodymium
[9]	Letokhov V, Ryabov E (Trigg G L ed) 2004 Encyclopedia of Applied Physics (New York: Wiley) pp1015–1028
[10]	Babichev A P, Grigoriev I S, Grigoriev A I, Dorovskii A P, D'Yachkov A B, Kovalevich S K, Kochetov V A, Kuznetsov V A, Labozin V P, Matrakhov A V, Mironov S M, Nikulin S A, Pesnya A V, Timofeev N I, Firsov V A, Tsvetkov G O, Shatalova G G 2005 Quantum Electron. 35 879 Google Scholar
[11]	Grigoriev I, Diachkov A, Kovalevich S, Labosin V, Mironov S, Nikulin S, Pesnia A, Firsov V, Shatalova G, Tsvetkov G 2003 Proc. SPIE Int. Soc. Opt. Eng. 5121 406
[12]	D'Yachkov A B, Kovalevich S K, Labozin V P, Mironov S M, Panchenko V Y, Firsov V A, Tsvetkov G O, Shatalova G G 2012 Quantum Electron. 42 953 Google Scholar
[13]	Kramida A, Ralchenko Y, Reader J, (NIST ASD Team) 2024 NIST Atomic Spectra Database (Gaithersburg, MD: National Institute of Standards and Technology
[14]	Miyabe M, Iwata Y, Tomita H, Morita M, Sakamoto T 2024 Spectrochim. Acta Part B At. Spectrosc. 221 107036 Google Scholar
[15]	van Leeuwen K A H, Eliel E R, Post B H, Hogervorst W 1981 Z. Phys. A 301 95 Google Scholar
[16]	Zyuzikov A D, Mishin V I, Fedoseev V N 1988 Opt. Spectrosc. 64 287
[17]	D'Yachkov A B, Gorkunov A A, Labozin A V, Mironov S M, Panchenko V Y, Firsov V A, Tsvetkov G O 2018 Quantum Electron. 48 75 Google Scholar
[18]	张钧尧, 熊静逸, 魏少强, 李云飞, 卢肖勇 2023 72 193203 Google Scholar Zhang J Y, Xiong J Y, Wei S Q, Li Y F, Lu X Y 2023 Acta Phys. Sin. 72 193203 Google Scholar
[19]	Campbell P, Moore I D, Pearson M R 2016 Prog. Part. Nucl. Phys. 86 127 Google Scholar
[20]	Yang X F, Wang S J, Wilkins S G, Ruiz R F G 2023 Prog. Part. Nucl. Phys. 129 104005 Google Scholar
[21]	Lu X Y, Wang L D 2023 Chin. Phys. B 32 53204 Google Scholar
[22]	Lu X Y, Wang L D 2024 Appl. Radiat. Isot. 210 111334 Google Scholar
[23]	Demtröder W 2008 Laser Spectroscopy: Vol. 1 Basic Principles (Berlin: Springer) pp5–60
[24]	Greenland P T 1990 Contemp. Phys. 31 405 Google Scholar
[25]	Axner O, Gustafsson J, Omenetto N, Winefordner J D 2004 Spectrochim. Acta Part B At. Spectrosc. 59 1 Google Scholar
[26]	Agarwal G S 1970 Phys. Rev. A 1 1445 Google Scholar
[27]	Lambropoulos P, Lyras A 1989 Phys. Rev. A 40 2199 Google Scholar
[28]	Blagoev K B, Komarovskii V A 1994 At. Data Nucl. Data Tables 56 1 Google Scholar
[29]	Childs W J, Goodman L S 1972 Phys. Rev. A 6 1772 Google Scholar
[30]	Shen X P, Wang W L, Zhai L H, Deng H, Xu J, Yuan X L, Wei G Y, Wang W, Fang S, Su Y Y, Li Z M 2018 Spectrochim. Acta Part B At. Spectrosc. 145 96 Google Scholar
[31]	Lu X Y, Wang L D 2025 J. Phys. B: At. Mol. Opt. Phys. 58 025001 Google Scholar
[32]	Wakasugi M, Horiguchi T, Guo Jin W, Sakata H, Yoshizawa Y 1990 J. Phys. Soc. Jpn. 59 2700 Google Scholar

Cited By

图 1 三步电离路径示意图　(a) I_n = 0; (b) I_n ≠ 0

Figure 1. The three-step photoionization scheme: (a) I_n = 0; (b) I_n ≠ 0.

DownLoad: Full-Size Img PowerPoint

图 2 第2步饱和功率曲线实验值^[11]

Figure 2. The experimental saturated power density curve of the second transition^[11].

DownLoad: Full-Size Img PowerPoint

图 3 b₂₃ = 0.1 GHz时, 不同β₁₂, β₂₃下的第2步饱和功率曲线计算值　(a) β₁₂ = 0.05; (b) β₁₂ = 0.1; (c) β₁₂ = 0.15; (d) β₁₂ = 0.2

Figure 3. The numerical saturated power density curve of the second transition under b₂₃ = 0.1 GHz and different combinations of β₁₂, β₂₃: (a) β₁₂ = 0.05; (b) β₁₂ = 0.1; (c) β₁₂ = 0.15; (d) β₁₂ = 0.2.

DownLoad: Full-Size Img PowerPoint

图 4 b₂₃ = 1.5 GHz时, 不同β₁₂, β₂₃下的第2步饱和功率曲线计算值　(a) β₁₂ = 0.05; (b) β₁₂ = 0.1; (c) β₁₂ = 0.15; (d) β₁₂ = 0.2

Figure 4. The numerical saturated power density curve of the second transition under b₂₃ = 1.5 GHz and different combinations of β₁₂, β₂₃: (a) β₁₂ = 0.05; (b) β₁₂ = 0.1; (c) β₁₂ = 0.15; (d) β₁₂ = 0.2.

DownLoad: Full-Size Img PowerPoint

图 5 第2步饱和功率曲线的归一化Nd-150电离率计算值与实验值对比　(a) b₂₃ = 0.1 GHz; (b) b₂₃ = 1.5 GHz; (c) b₂₃ = 1.5 GHz, 纵轴[0.9, 1]的局部放大图

Figure 5. The numerical and experimental saturated power density curve of the second transition (shown as normalized ionization probability of Nd-150): (a) b₂₃ = 0.1 GHz; (b) b₂₃ = 1.5 GHz; (c) b₂₃ = 1.5 GHz, the partial enlarged view of the vertical axis in the range of [0.9, 1].

DownLoad: Full-Size Img PowerPoint

图 6 偏振、J₃对第1步饱和功率曲线的影响

Figure 6. The influences of laser polarization and the angular momentum of the second excited state J₃ on the saturated power density curve of the first transition.

DownLoad: Full-Size Img PowerPoint

图 7 偏振、J₃对第2步饱和功率曲线的影响

Figure 7. The influences of laser polarization and the angular momentum of the second excited state J₃ on the saturated power density curve of the second transition.

DownLoad: Full-Size Img PowerPoint

图 8 偏振对超精细跃迁通道相对跃迁强度的影响　(a) J₁ = 4 → J₂ = 5; (b) J₂ = 5 → J₃ = 4; (c) J₂ = 5 → J₃ = 5; (d) J₂ = 5 → J₃ = 6　　　　

Figure 8. The influences of laser polarization on the relative strengths of the hyperfine transition paths: (a) J₁ = 4 → J₂ = 5; (b) J₂ = 5 → J₃ = 4; (c) J₂ = 5 → J₃ = 5; (d) J₂ = 5 → J₃ = 6.

DownLoad: Full-Size Img PowerPoint

图 9 第二激发态超精细常数A_3,145对钕奇同位素第2步跃迁超精细结构的影响, 以B_3,145 = 0 MHz, IS_23,148 = 0 GHz为示例　(a) Nd-145, A_3,145 = 0 MHz, –20 MHz, –40 MHz, –60 MHz; (b) Nd-145, A_3,145 = –80 MHz, –100 MHz, –120 MHz, –140 MHz; (c) Nd-143, A_{3, 143} = 1.6A_3,145, A_3,145 = 0 MHz, –20 MHz, –40 MHz, –60 MHz; (d) Nd-143, A_3,143 = 1.6A_3,145, A_3,145 = –80 MHz, –100 MHz, –120 MHz, –140 MHz

Figure 9. The influences of the second excited state’s hyperfine constant A_3,145 on the hyperfine structure of the second transition of Nd odd isotopes, taking B_3,145 = 0 MHz, IS_23,148 = 0 GHz as an example: (a) Nd-145, A_3,145 = 0 MHz, –20 MHz, –40 MHz, –60 MHz; (b) Nd-145, A_3,145 = –80 MHz, –100 MHz, –120 MHz, –140 MHz; (c) Nd-143, A_3,143 = 1.6A_3,145, A_3,145 = 0 MHz, –20 MHz, –40 MHz, –60 MHz; (d) Nd-143, A_{3, 143} = 1.6A_3,145, A_3,145 = –80 MHz, –100 MHz, –120 MHz, –140 MHz.

DownLoad: Full-Size Img PowerPoint

图 10 不同第2步跃迁同位素位移、第二激发态超精细结构下的钕同位素选择性光电离效果　(a) IS_23,148 = –1500 MHz; (b) IS_23,148 = –1000 MHz; (c) IS_23,148 = –500 MHz; (d) IS_23,148 = –300 MHz; (e) IS_23,148 = 0.0 MHz; (f) IS_23,148 = 300 MHz; (g) IS_23,148 = 500 MHz; (h) IS_23,148 = 1000 MHz; (i) IS_23,148 = 1500 MHz

Figure 10. The selective photoionization effects of Nd isotopes under different combinations of the second transition’s isotope shifts and the second excited state’s hyperfine structures: (a) IS_23,148 = –1500 MHz; (b) IS_23,148 = –1000 MHz; (c) IS_23,148 = –500 MHz; (d) IS_23,148 = –300 MHz; (e) IS_23,148 = 0.0 MHz; (f) IS_23,148 = 300 MHz; (g) IS_23,148 = 500 MHz; (h) IS_23,148 = 1000 MHz; (i) IS_23,148 = 1500 MHz.

DownLoad: Full-Size Img PowerPoint

图 11 钕奇同位素超精细跃迁通道　(a) 路径一λ₁, Nd-145; (b) 假定λ₂, Nd-145; (c) Nd-145第2步谱线和λ₁+λ₂双光子跃迁; (d) 路径一λ₁, Nd-143; (e) 假定λ₂, Nd-143; (f) Nd-143第2步谱线和λ₁+λ₂双光子跃迁

Figure 11. The hyperfine transition paths of Nd odd isotopes: (a) λ₁ of Scheme No. 1, Nd-145; (b) the imagined λ₂, Nd-145; (c) the second spectral line and λ₁+λ₂ two-photon transition of Nd-145; (d) λ₁ of Scheme No. 1, Nd-143; (e) the imagined λ₂, Nd-143; (f) the second spectral line and λ₁+λ₂ two-photon transition of Nd-143.

DownLoad: Full-Size Img PowerPoint

图 12 钕奇同位素第二激发态布居率随作用时间的变化图　(a) Nd-145; (b) Nd-145, 纵轴[0, 2×10^–4]的局部放大图; (c) Nd-143; (d) Nd-143, 纵轴[0, 6×10^–5]的局部放大图

Figure 12. The population of the second excited state of Nd odd isotopes versus time: (a) Nd-145; (b) Nd-145, the partial enlarged view of the vertical axis in the range of [0, 2×10^–4]; (c) Nd-143; (d) Nd-143, the partial enlarged view of the vertical axis in the range of [0, 6×10^–5].

DownLoad: Full-Size Img PowerPoint

表 1 钕天然同位素

Table 1. Natural Nd isotopes.

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I_n	0	0	0	7/2	0	7/2	0
衰变	2νββ 或 0νββ→Sm-150	—	—	—	α → Ce-140	—	—

DownLoad: CSV

表 2 钕同位素三步电离路径

Table 2. The three-step photoionization scheme of Nd isotopes.

电离路径	λ₁/nm	λ₂/nm	λ₃/nm
路径一^[10,11]	596	579	640
路径二^[16]	588	597	597
路径三^[17]	628	560	597
路径四^[17]	562	627	597

DownLoad: CSV

表 3 数值计算中的激光参数取值

Table 3. The laser parameters adopted in the numerical calculation.

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	0:1:0	0:1:0	—
	混合偏振	1/3:1/3:1/3	1/3:1/3:1/3	—
	正交线偏振	0:1:0	1/2:0:1/2	—

DownLoad: CSV

表 4 路径一的能级参数

Table 4. The energy parameters of scheme No. 1.

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^*
路径一E₃	34011.04^[11]	6^[30]	0^*	0^*	0^*	0^*	100^*
注: “*”表示假定值.

DownLoad: CSV

表 5 路径一的同位素位移

Table 5. The isotope shifts of scheme No. 1.

跃迁	IS₁₄₈/MHz	IS₁₄₆/IS₁₄₈	IS₁₄₅/IS₁₄₈	IS₁₄₄/IS₁₄₈	IS₁₄₃/IS₁₄₈	IS₁₄₂/IS₁₄₈
路径一λ₁	1126.9^[15]	1.78^[15]	2.20^[15]	2.51^[15]	2.93^[15]	3.28^[15]
路径一λ₂	0^*	—	—	—	—	—
注: “*”表示假定值.

DownLoad: CSV

表 6 路径一选择性光电离效果

Table 6. The selective photoionization effects of scheme No. 1.

线宽/GHz	1.0, 1.0	0.5, 1.0	0.3, 1.0	1.0, 0.5	1.0, 0.3	0.5, 0.5	0.3, 0.3
C₁₅₀/%	49.86	54.81	55.80	54.64	58.86	68.35	61.00
ρ_ion,150	0.3839	0.4071	0.4158	0.3848	0.3849	0.4144	0.4073

DownLoad: CSV

表 7 钕同位素假定电离路径的能级参数

Table 7. The energy parameters of the imagined photoionization scheme of Nd isotope.

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.

DownLoad: CSV

表 8 钕同位素假定电离路径的跃迁参数

Table 8. The transition parameters of the imagined photoionization scheme of Nd isotope.

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.

DownLoad: CSV

表 9 第二激发态超精细常数B_3,145对钕奇同位素第2步跃迁谱线分裂程度的影响

Table 9. The influences of the second excited state’s hyperfine constant B_3,145 on the hyperfine splitting degree of the second transition of Nd odd isotopes.

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(ν_{23, A, B}) – min(ν_{23, 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

DownLoad: CSV

表 10 第二激发态超精细常数B_3,145对钕奇同位素第2步跃迁超精细跃迁通道共振位置的影响

Table 10. The influences of the second excited state’s hyperfine constant B_3,145 on the resonance frequencies of hyperfine transition paths of Nd odd isotopes’ the second transition.

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(\|ν_{23, A, B} – ν_{23, 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

DownLoad: CSV

表 11 Nd-150丰度最低时的钕同位素选择性光电离效果

Table 11. The selective photoionization effects of Nd isotopes in the case of the lowest Nd-150 abundance.

线宽/GHz	丰度/%
线宽/GHz	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, IS_23,148 = –1000 MHz, A_3,145 = –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.

DownLoad: CSV

表 12 钕偶同位素共振位置

Table 12. The resonance frequency of Nd even isotopes.

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, IS_23,148 = –1000 MHz, A_3,145 = –100 MHz.

DownLoad: CSV

map

[1]	Akhmedzhanov R A, Gushchin L A, Nizov N A, Nizov V A, Sobgayda D A, Zelensky I V 2024 JETP Lett. 119 834 Google Scholar
[2]	Liang P J, Liu X, Li P Y, Zhou Z Q, Li C F, Guo G C 2020 J. Opt. Soc. Am. B 37 1653 Google Scholar
[3]	Broderick K, Lusk R, Hinderer J, Griswold J, Boll R, Garland M, Heilbronn L, Mirzadeh S 2019 Appl. Radiat. Isot. 144 54 Google Scholar
[4]	Hu F, Cutler C S, Hoffman T, Sieckman G, Volkert W A, Jurisson S S 2002 Nucl. Med. Biol. 29 423 Google Scholar
[5]	Committee A 2015 Standard Practice for Analysis of Spent Nuclear Fuel to Determine Selected Isotopes and Estimate Fuel Burnup
[6]	Suryanarayana M V 2022 Sci. Rep. 12 11471 Google Scholar
[7]	Barabash A S, Belli P, Bernabei R, Boiko R S, Cappella F, Caracciolo V, Cerulli R, Danevich F A, Fang D L, Ferella F, Incicchitti A, Kobychev V V, Konovalov S I, Laubenstein M, Leoncini A, Merlo V, Nisi S, Niţescu O, Poda D V, Polischuk O G, Shcherbakov I B K, Šimkovic F, Timonina A, Tinkova V S, Tretyak V I, Umatov V I 2025 Eur. Phys. J. C 85 174 Google Scholar
[8]	https://www.isotopes.gov/products/neodymium
[9]	Letokhov V, Ryabov E (Trigg G L ed) 2004 Encyclopedia of Applied Physics (New York: Wiley) pp1015–1028
[10]	Babichev A P, Grigoriev I S, Grigoriev A I, Dorovskii A P, D'Yachkov A B, Kovalevich S K, Kochetov V A, Kuznetsov V A, Labozin V P, Matrakhov A V, Mironov S M, Nikulin S A, Pesnya A V, Timofeev N I, Firsov V A, Tsvetkov G O, Shatalova G G 2005 Quantum Electron. 35 879 Google Scholar
[11]	Grigoriev I, Diachkov A, Kovalevich S, Labosin V, Mironov S, Nikulin S, Pesnia A, Firsov V, Shatalova G, Tsvetkov G 2003 Proc. SPIE Int. Soc. Opt. Eng. 5121 406
[12]	D'Yachkov A B, Kovalevich S K, Labozin V P, Mironov S M, Panchenko V Y, Firsov V A, Tsvetkov G O, Shatalova G G 2012 Quantum Electron. 42 953 Google Scholar
[13]	Kramida A, Ralchenko Y, Reader J, (NIST ASD Team) 2024 NIST Atomic Spectra Database (Gaithersburg, MD: National Institute of Standards and Technology
[14]	Miyabe M, Iwata Y, Tomita H, Morita M, Sakamoto T 2024 Spectrochim. Acta Part B At. Spectrosc. 221 107036 Google Scholar
[15]	van Leeuwen K A H, Eliel E R, Post B H, Hogervorst W 1981 Z. Phys. A 301 95 Google Scholar
[16]	Zyuzikov A D, Mishin V I, Fedoseev V N 1988 Opt. Spectrosc. 64 287
[17]	D'Yachkov A B, Gorkunov A A, Labozin A V, Mironov S M, Panchenko V Y, Firsov V A, Tsvetkov G O 2018 Quantum Electron. 48 75 Google Scholar
[18]	张钧尧, 熊静逸, 魏少强, 李云飞, 卢肖勇 2023 72 193203 Google Scholar Zhang J Y, Xiong J Y, Wei S Q, Li Y F, Lu X Y 2023 Acta Phys. Sin. 72 193203 Google Scholar
[19]	Campbell P, Moore I D, Pearson M R 2016 Prog. Part. Nucl. Phys. 86 127 Google Scholar
[20]	Yang X F, Wang S J, Wilkins S G, Ruiz R F G 2023 Prog. Part. Nucl. Phys. 129 104005 Google Scholar
[21]	Lu X Y, Wang L D 2023 Chin. Phys. B 32 53204 Google Scholar
[22]	Lu X Y, Wang L D 2024 Appl. Radiat. Isot. 210 111334 Google Scholar
[23]	Demtröder W 2008 Laser Spectroscopy: Vol. 1 Basic Principles (Berlin: Springer) pp5–60
[24]	Greenland P T 1990 Contemp. Phys. 31 405 Google Scholar
[25]	Axner O, Gustafsson J, Omenetto N, Winefordner J D 2004 Spectrochim. Acta Part B At. Spectrosc. 59 1 Google Scholar
[26]	Agarwal G S 1970 Phys. Rev. A 1 1445 Google Scholar
[27]	Lambropoulos P, Lyras A 1989 Phys. Rev. A 40 2199 Google Scholar
[28]	Blagoev K B, Komarovskii V A 1994 At. Data Nucl. Data Tables 56 1 Google Scholar
[29]	Childs W J, Goodman L S 1972 Phys. Rev. A 6 1772 Google Scholar
[30]	Shen X P, Wang W L, Zhai L H, Deng H, Xu J, Yuan X L, Wei G Y, Wang W, Fang S, Su Y Y, Li Z M 2018 Spectrochim. Acta Part B At. Spectrosc. 145 96 Google Scholar
[31]	Lu X Y, Wang L D 2025 J. Phys. B: At. Mol. Opt. Phys. 58 025001 Google Scholar
[32]	Wakasugi M, Horiguchi T, Guo Jin W, Sakata H, Yoshizawa Y 1990 J. Phys. Soc. Jpn. 59 2700 Google Scholar

[1]	Liu Xin, Wen Wei-Qiang, Li Ji-Guang, Wei Bao-Ren, Xiao Jun. Experimental and theoretical research progress of ²P_1/2 – ²P_3/2 transitions of highly charged boron-like ions. Acta Physica Sinica, 2024, 73(20): 203102. doi: 10.7498/aps.73.20241190
[2]	Zhong Zhen-Xiang. Review of the hyperfine structure theory of hydrogen molecular ions. Acta Physica Sinica, 2024, 73(20): 203104. doi: 10.7498/aps.73.20241101
[3]	Ji Chen. Nuclear structure effects to atomic Lamb shift and hyperfine splitting. Acta Physica Sinica, 2024, 73(20): 202101. doi: 10.7498/aps.73.20241063
[4]	Chen Run, Shao Xu-Ping, Huang Yun-Xia, Yang Xiao-Hua. Simulation of hyperfine-rotational spectrum of electromagnetic dipole transition rotation of BrF molecules. Acta Physica Sinica, 2023, 72(4): 043301. doi: 10.7498/aps.72.20221957
[5]	Tang Jia-Dong, Liu Qian-Hao, Cheng Cun-Feng, Hu Shui-Ming. Hyperfine structure of ro-vibrational transition of HD in magnetic field. Acta Physica Sinica, 2021, 70(17): 170301. doi: 10.7498/aps.70.20210512
[6]	Zhang Xiang, Lu Ben-Quan, Li Ji-Guang, Zou Hong-Xin. Theoretical investigation on hyperfine structure and isotope shift for 5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2 clock transition in Hg⁺. Acta Physica Sinica, 2019, 68(4): 043101. doi: 10.7498/aps.68.20182136
[7]	Yu Geng-Hua, Yan Hui, Gao Dang-Li, Zhao Peng-Yi, Liu Hong, Zhu Xiao-Ling, Yang Wei. Calculationof isotope shift of Mg+ ion by using the relativistic multi-configuration interaction method. Acta Physica Sinica, 2018, 67(1): 013101. doi: 10.7498/aps.67.20171817
[8]	Pei Dong-Liang, He Jun, Wang Jie-Ying, Wang Jia-Chao, Wang Jun-Min. Measurement of the fine structure of cesium Rydberg state. Acta Physica Sinica, 2017, 66(19): 193701. doi: 10.7498/aps.66.193701
[9]	Yu Geng-Hua, Liu Hong, Zhao Peng-Yi, Xu Bing-Ming, Gao Dang-Li, Zhu Xiao-Ling, Yang Wei. Theoretical calculations on isotope shifts of Mg I by using relativistic multiconfiguration Dirac-Hartree-Fock method. Acta Physica Sinica, 2017, 66(11): 113101. doi: 10.7498/aps.66.113101
[10]	Ren Ya-Na, Yang Bao-Dong, Wang Jie, Yang Guang, Wang Jun-Min. Measurement of the magnetic dipole hyperfine constant Ahfs of cesium 7S1/2 state. Acta Physica Sinica, 2016, 65(7): 073103. doi: 10.7498/aps.65.073103
[11]	Yang Bao-Dong, Gao Jing, Wang Jie, Zhang Tian-Cai, Wang Jun-Min. Multiple electromagnetically-induced transparency of hyperfine levels in cesium 6S1/2 -6P3/2 -8S1/2 ladder-type system. Acta Physica Sinica, 2011, 60(11): 114207. doi: 10.7498/aps.60.114207
[12]	Chen Xing-Peng, Wang Nan. Ground state properties of Rn isotopes within the relativistic mean field theory. Acta Physica Sinica, 2011, 60(11): 112101. doi: 10.7498/aps.60.112101
[13]	Hou Bi-Hui, Li Yong, Liu Guo-Qing, Zhang Gui-Hua, Liu Feng-Yan, Tao Shi-Quan. ESR study of the Mn2+ center in LiNbO3. Acta Physica Sinica, 2005, 54(1): 373-378. doi: 10.7498/aps.54.373
[14]	Chen Sui-Yuan, Liu Chang-Sheng, Li Hui-Li, Cui Tong. Hyperfine stucture during nanocrystallization of amorphous Fe73.5Cu1Nb3Si13.5B9 alloy irradiated by laser. Acta Physica Sinica, 2005, 54(9): 4157-4163. doi: 10.7498/aps.54.4157
[15]	Wang Li－Jun, Yu Hui-Ying. The coherent excitation property of a two-level atom w itha hyperfine structure in narrow band laser field. Acta Physica Sinica, 2004, 53(12): 4151-4156. doi: 10.7498/aps.53.4151
[16]	Ma Hong-Liang, Lu Jiang, Wang Chun-Tao. Measurement of hyperfine structure spectrum in 56908 nm line of 141Pr+. Acta Physica Sinica, 2003, 52(3): 566-569. doi: 10.7498/aps.52.566
[17]	Zhao Lu-Ming, Wang Li-Jun. . Acta Physica Sinica, 2002, 51(6): 1227-1232. doi: 10.7498/aps.51.1227
[18]	MA HONG-LIANG, TANG JIA-YONG. MEASUREMENT OF ISOTOPE SHIFTS AMONG 142—146,148,150Nd+ BY USING COLLINEAR FAST-ION-BEAM LASER SPECTROSCOPY. Acta Physica Sinica, 2001, 50(3): 453-456. doi: 10.7498/aps.50.453
[19]	LI GUANG-WU, MA HONG-LIANG, LI MAO-SHENG, CHEN ZHI-JUN, CHEN MIAO-HUA, LU FU-QUAN, PENG XIAN-JUE, YANG FU-JIA. HYPERFINE STRUCTURE MEASUREMENT IN LaⅡ5d2 1Ｇ4 →4f5d 1F3. Acta Physica Sinica, 2000, 49(7): 1256-1259. doi: 10.7498/aps.49.1256
[20]	DAI CHANG-JIAN, XU CHANG-JIANG. SELECTIVE PHOTOIONIZATION OF ISOTOPIC ATOMS WITH PULSED LASERS. Acta Physica Sinica, 1994, 43(3): 356-368. doi: 10.7498/aps.43.356

Catalog

Vol. 74, Issue 11 - 2025-06-05

Metrics

Abstract views: 365
PDF Downloads: 11
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板