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The presence of high-Z impurities in magnetically confined fusion devices has different influences on the confinement property of the plasma due to the high cooling rate of high-Z impurities. The first wall of EAST is equipped with molybdenum tiles, molybdenum particles sputtered from inevitable plasma-wall interaction enter into the plasma and become high-Z impurity. In this paper, four fast-time-response extreme ultraviolet (EUV) spectrometers, a system which is upgraded in the EAST 2021 campaign, are used to monitor the line emission from impurity ions in the 5–500 Å wavelength range simultaneously. The in-situ wavelength calibration is carried out accurately using several well-known emission lines of low- and medium-Z impurity ions. The observed spectral lines are carefully identified based on the National Institute of Standards Technology (NIST) database, previously published experimental data and the time evolution of the normalized line intensity of emission lines from impurity ions. At the lower electron temperature (Te0 = 1.5 keV), the EUV spectra emitted from molybdenum ions in the range of 5–485 Å are systematically identified in EAST discharges accompanied with spontaneous sputtering events. As a result, two unresolved transition arrays of molybdenum spectra composed of Mo19+-Mo24+ (Mo XX-Mo XXV) and Mo16+-Mo29+ (Mo XVII-Mo XXX) are observed in the ranges of 15–30 Å and 65–95 Å. In addition, several spectral lines of lower molybdenum ions of Mo4+-Mo17+ (Mo V-Mo XVIII) in the ranges of 27–60 Å and 120–485 Å are observed and identified on EAST for the first time, including a few strong and isolated forbidden and resonant lines, e.g. Mo XII at 329.414 Å, 336.639 Å and 381.125 Å, Mo XIII at 340.909 Å and 352.994 Å, Mo XIV at 373.647 Å and 423.576 Å, Mo XV at 50.448 Å, 57.927 Å and 58.832 Å. Six spectral lines are newly observed in the range of 27–32 Å, i.e. (27.21 ± 0.01) Å, (27.37 ± 0.01) Å, (28.99 ± 0.01) Å, (30.81 ± 0.01) Å, (31.54 ± 0.01) Å and (31.83 ± 0.01) Å, which may be Mo XV-Mo XVIII spectral lines. As a result, twelve strong and isolated spectral lines are chosen in routine observation for impurity transport physical study. The identification of these spectral lines not only enriches the molybdenum atom database, but also provides a solid experimental data base for magnetically confined devices to study the behavior and transport in core and edge plasmas of high-Z impurity.
1. 引 言
觉察物理相似性是前进的因素. 麦克斯韦善于从类比中悟出共性, 他写道: “为了不通过一种物理理论而获得物理思想, 我们就应当熟悉现存的物理相似性. 所谓物理相似性, 我认为是在一种科学定律和一些能够相互阐明的定律之间存在着的局部相似.” 从量子力学诞生日起, 它的经典对应(或类比)一直是物理学家关心的话题. 量子力学中的很多概念都有经典对应或类比, 如平移、转动和宇称等. 狄拉克认为量子幺正变换是经典正则变换的对应, 但也有不存在经典对应的例子, 如自旋. 如麦克斯韦所说, 物理类比是发展物理学的一个途径, 那么量子纠缠有没有经典对应(或类比)呢?
本文将要指出: 在介观电路量子化的框架中, 带有互感的两个介观电容-电感(
LC )回路, 其互感是产生量子纠缠的源头, 用量子力学方法可以求出其特征频率的公式, 该公式与如下描述的经典系统的小振动频率的表达式有相似之处, 可见两者有可比拟之处. 该经典系统如图1所示, 两个墙壁之间各连一个相同的弹簧, 弹簧系数是k, 两个弹簧之间接着一个可以在光滑的桌面上运动的滑动小车m1 , 小车挂有一根长为l的单摆, 摆球质量是m2 . 单摆的摆动会造成小车来回振动, 摆、小车和弹簧的互相牵制, 晃动效应反映了小车和摆的“纠缠”.在固态物理中, 当输运尺度与电荷非弹性相干长度可以比拟时, 电路中的量子效应必须被计入, 这种情形下的电路便称为介观电路. 集成电路向原子尺度的趋小化刺激了电路理论的研究进入量子领域[1,2]. 历史上, 一个单电容-电感(
LC )回路的状态, 作为一个电路的“元胞”, 被Louisell[3]在1973年量子化, 他认电荷q为正则坐标, 取电流I=dq/dt 乘上电感L为正则动量,p=Ldq/dt , 进一步将(q,p) 加上量子化条件[ˆq,ˆp]=iℏ , 则LC 电路被视为一个量子谐振子. 从那以后, 很多有关介观电路量子化的研究论文陆续发表[4-6].本文的内容安排如下: 先指出量子纠缠存在于带有互感m的两个介观电容-电感(
LC )回路中, 如图1所示. 给出这个系统的量子化形式. 然后得到系统哈密顿量的退纠缠算符并得到介观电路的量子纠缠态及其本征频率. 之后我们引入弹簧约束滑动小车-单摆系统的微振动系统并同时给出其振动频率, 最终得到两种体系相似点的类比.2. 带有互感的两个介观电容-电感(
LC )回路的量子化在分析力学中, 带有互感(系数
m) 的两个介观电容-电感(LC )回路的经典拉格朗日量为[7-9]L=12(l1I21+l2I22)+mI1I2−12(q21c1+q22c2), (1) 这里
mI1I2 代表两个单回路中的电流相互作用;l1 和l2 是两个单回路的电感, 在无漏磁情形下,0<m< √l1l2 . 取q1 ,q2 为正则坐标, 他们的共轭量为p1=∂L∂˙q1=l1I1+mI2, (2) p2=∂L∂˙q2=l2I2+mI1. (3) 相应的哈密顿量是
H=p1˙q1+p2˙q2−L=12(l1I21+l2I22)+mI1I2+12(q21c1+q22c2)=12A(p21l1+p22l2)−mAl1l2p1p2+12(q21c1+q22c2), (4) 其中定义了
A=1−m2l1l2,m2<l1l2. (5) 将
qi,pi 作为共轭对进行正则量子化为算符ˆqi,ˆpi , 加上量子化条件[ˆqi,ˆpj]=iℏδi,j, H→ˆH 是哈密顿算符.mAl1l2ˆp1ˆp2 是引起量子纠缠的项. 为什么如此说呢? 因为根据文献可知[10,11], 此项会导致双模压缩态的产生, 非简并参量放大器输出的双模压缩态的信号模和闲置模是纠缠在一起的.3. 哈密顿量
H 的退纠缠算符U为了在理论上化去
ˆH 含的耦合项, 本文试图找到一个幺正算符U, 将ˆH 对角化[12,13]. 采用坐标表象|qi⟩ , 记U为U=∬∞−∞dq1dq2|u(q1q2)⟩⟨(q1q2)|,detu=1, (6) 这里
⟨(q1q2)| ≡⟨q1,q2| 是双模坐标本征态,ˆqi|(q1q2)⟩=qi|(q1q2)⟩,u=(u11u12u21u22), (7) 其中, u是一个待定的
2×2 矩阵, 由对角化的要求决定. 方程(7)明显地体现了经典矩阵u映射为Hilbert空间中的量子幺正算符U. 用(6)式和(7)式得到ˆqi 的变换性质U(ˆq1ˆq2)U†=u−1(ˆq1ˆq2), (8) ∬∞−∞dp1dp2|(p1p2)⟩⟨(p1p2)|=1, (9) 和
⟨(p1p2)|u(q1q2)⟩=12πexp[−i(uTp)jqj] (10) (这里重复指标暗示求和)得到U的动量表示:
U=12π∬∞−∞dp1dp2∬∞−∞dq1dq2×|(p1p2)⟩⟨(q1q2)|exp[−i(uTp)jqj]=∬∞−∞dp1dp2|(p1p2)⟩⟨uT(p1p2)|, (11) 于是就得到
U(ˆp1ˆp2)U†=uT(ˆp1ˆp2). (12) 假设u的形式是
u=(1EGH), detu=H−EG=1, (13) 这里
H,E,G 是待定的, 则(uT)−1=(H−G−E1). (14) 在
U† 变换下,ˆq1→U†ˆq1U=ˆq1+Eˆq2,ˆq2→U†ˆq2U=Gˆq1+Hˆq2,ˆp1→U†ˆp1U=Hˆp1−Gˆp2,ˆp2→U†ˆp2U=−Eˆp1+ˆp2, (15) 故而
ˆH 在U† 变换下变成U†ˆHU=12A[(Hp1−Gp2)2l1+(−Ep1+p2)2l2]−mAl1l2(Hp1−Gp2)(−Ep1+p2)+12[(q1+Eq2)2c1+(Gq1+Hq2)2c2]. (16) 对角化要求(16)式中含有
ˆp1ˆp2 和ˆq1ˆq2 的项消失, 即要求l2HG+l1E+m(GE+H)=0, (17) c2E+c1GH=0. (18) 这意味着退纠缠, 联立
H−EG=1 可知H=c2/(c2+c1G2), (19) 于是
E=−Gc1/(c2+c1G2), (20) 接着有
HG=c2Gc2+c1G2=−c2c1E. (21) −l2c2c1E+l1E+m(2EG+1)=0, (22) mc1G2+G(l1c1−l2c2)−mc2=0. (23) 此方程的通解是
G=l2c2−l1c1±√(l1c1−l2c2)2+4m2c1c22mc1. (24) 不失一般性, (24)式中取负号, 并令
(c2l2−c1l1)2+4m2c2c1=Δ, (25) 可得
G=c2l2−c1l1−√Δ2mc1=−2mc2√Δ+c2l2−c1l1,E=c1m√Δ,H=√Δ−(c1l1−c2l2)2√Δ, (26) 于是相应的退纠缠算符为
U=∬∞−∞dq1dq2|(1EGH)(q1q2)⟩⟨(q1q2)|. (27) 4. 介观电路的量子纠缠态
用有序算符内的积分理论及双模坐标本征态的Fock表象[17-19]
⟨q1,q2|=√1π⟨00|exp{−12(q21+q22)+√2(q1a1+q2a2)−12a21−12a22}, (28) [ai,a†j]=δi,j, 以及真空投影算符的正规乘积表示[20-22]|00⟩⟨00|=:exp(−a†1a1−a†2a2): (29) 对U的表达式积分得到
U=∬∞−∞dq1dq2|(1EGH)(q1q2)⟩⟨(q1q2)|=1π∬∞−∞dq1dq2:exp{−12[(q1+Eq2)2+(Gq1+Hq2)2]−√2(q1+Eq2)a†1+√2(Gq1+Hq2)a†2−12(q21+q22)+√2(q1a1+q2a2)−12(a1+a†1)2−12(a2+a†2)2}:=2√Lexp{12L[(1+E2−G2−H2)(a†21−a†22)+4(G+EG)a†1a†2]}:exp{(a†1 a†2)(g−1)(a1a2)}:×exp{12L[(E2+H2−1−G2)(a21−a22)+4(G+EH)a1a2]}, (30) 其中
L=E2+G2+H2+3,g=2L(1+HE−GG−E1+H),1=(1001). (31) 可见
U|00⟩ 是一个双模压缩态U|00⟩=2√Lexp{12L[(1+E2−G2−H2)×(a†21−a†22)+4(G+EH)a†1a†2]}|00⟩, (32) 同时它也是一个纠缠态. 可见互感的存在导致量子纠缠. 该结果表示的是两个介观回路处于纠缠态, 注意到当前是在双模坐标表象下表示出来, 而此处的广义坐标
q1,q2 对应两个介观回路的电容各自携带的电量. 这就意味着测量其中一个回路电容上的电量后, 另外一个回路的电容电量也会塌缩到某个特定值上. 当然如果换成动量表象(对应两个回路中各自的电流), 也依然有纠缠的特性.5. 带互感的两个介观电容-电感(
LC )电路的特征频率去除含有
ˆp1ˆp2 和ˆq1ˆq2 的项后, 方程(18)变成U†ˆHU=p212Al1l2(l2H2+l1E2+2mHE)+p222Al1l2(l2G2+l1+2mG)+q212(1c1+G2c2)+q212(E2c1+H2c2). (33) 用(33)式算出
l2H2+l1E2+2mHE=m2c1G−mc2l2G√Δ, (34) l2G2+l1+2mG=−(l2G+m)√Δmc1, (35) 1c1+G2c2=c2+c1G2c1c2=−GEc2, (36) E2c1+H2c2=−mG√Δ, (37) 于是(33)式变成
U†ˆHU=(m2c1G−mc2l2)2Al1l2G√Δp21−G2Ec2q21−(l2G+m)√Δ2Al1l2mc1p22−m2G√Δq22. 与谐振子哈密顿量的标准形式
p22M+Mω2q22 比较, 可得两个特征频率为−GEc2m2c1G−mc2l2Al1l2G√Δ=c2l2+c1l1+√Δ2Al1l2c1c2≡ω2+ (38) 以及
mG√ΔAl1l2mc1(l2G+m)√Δ=c2l2+c1l1−√Δ2Al1l2c2c1≡ω2−. (39) 再用
A=1−m2/(l1l2), 可见ω2±=c2l2+c1l1±√(c2l2−c1l1)2+4m2c2c12c2c1(l1l2−m2), (40) 或
ω2±=c2l2+c1l1±√(c2l2+c1l1)2+4c2c1(m2−l2l1)2c2c1(l1l2−m2)=c2l2+c1l12c2c1(l1l2−m2)pm√[(c2l2+c1l1)2c2c1(l1l2−m2)]2−1c2c1(l1l2−m2), (41) 这是可以用实验验证的.
6. 弹簧约束滑动小车-单摆系统的微振动频率
本节讨论自由滑动小车-单摆系统的微振动频率. 从分析力学观点出发, 可以根据摆线偏离竖直线的角度θ以及对滑块的坐标x写出系统的动能与势能. 其中动能为
T=12m1˙x2+m22[(˙x+l˙θcosθ)2+l2˙θ2sin2θ], (42) 其中第一项是滑动小车动能, 第二项是摆球动能, 反映了摆球同时参与滑动和摆动的速度合成规则, 即三角形余弦定理,
(˙x+l˙θcosθ)2+l2˙θ2sin2θ=˙x2+l2˙θ2+2˙xl˙θcosθ. (43) 势能是
V=−m2glcosθ+2×12kx2, (44) 从
L=T−V 以及ddt∂L∂˙x=∂L∂x, ddt∂L∂˙θ=∂L∂θ (45) 导出动力学方程
(m1+m2)¨x+m2l¨θcosθ−m2l˙θ2sinθ+2kx=0, (46) l¨θ+¨xcosθ+gsinθ=0. (47) 在小振动时,
cosθ≈1, sinθ≈θ, 故(46)式和(47)式分别约化为(m1+m2)¨x+m2l¨θ+2kx=0, (48) l¨θ+¨x+gθ=0, (49) 即
m1¨x=m2gθ−2kx, (50) m1l¨θ=2kx−g(m1+m2)θ. (51) 晃动过程中, 小车与摆有相同的频率, 故可令
x=Ysin(ωt), (52) θ=Zsin(ωt), (53) (ω2m1−2k)Y+m2gZ=0, (54) 2kY+[m1lω2−g(m1+m2)]Z=0, (55) 其系数行列式为零才有非平庸解, 即
|ω2m1−2km2g2k−g(m1+m2)+m1lω2|=0, (56) 也就是
m21lω4−m1[2kl+g(m1+m2)]ω2+2kgm1=0. (57) 由此解出
ω2=12lm21{m1[g(m1+m2)+2kl] ±√[g(m1+m2)+2kl]2m21−4lm212km1g}. (58) 所以弹簧约束滑动小车-单摆系统的微振动频率是
ω2=(m1+m2)g+2kl2m1l±√[(m1+m2)g+2kl2m1l]2−2kgm1l, (59) 这里的两个根都是正定的, 都是物理解,
2kgm1l= 2km1×gl 代表弹簧振子带动小车运动(以2km1 表征)与单摆运动(以gl 表征)之间的耦合, 是量子纠缠的经典类比.7. 量子纠缠的经典类比
将介观电路的本征频率(41)式改写为
ω2±=c2l2+c1l1±√(c2l2+c1l1)2+4c2c1(m2−l2l1)2c2c1(l1l2−m2)=c2l2+c1l12c2c1(l1l2−m2)±√[(c2l2+c1l1)2c2c1(l1l2−m2)]2−1c2c1(l1l2−m2), (60) 再和上述力学系统的频率(59)式作比较, 就可得到如下的对应:
(m1+m2)g+2kl2m1l→c1l1+c2l22c1c2(l1l2−m2), (61) 2kgm1l=2km1×gl→1c1c2(l1l2−m2). (62) 于是找到了一个鲜明的例子, 即量子纠缠可以有经典力学模拟或对应. 我们期望有更多的例子出现.
8 结 论
本文首次讨论了量子纠缠有没有经典类比(或对应) 的问题, 指出在介观电路量子化的框架中, 带有互感的两个介观电容-电感 (LC) 电路与两个弹簧之间夹一个小滑车在光滑的地面上附带一个单摆的运动可比拟. 先用有序算符内的积分理论证明第一个系统的互感是产生量子纠缠的源头, 再推导出求其特征频率的公式, 就发现它与第二个系统的小振动频率公式类似. 第二个系统中单摆的摆动会造成小车来回振动, 摆、小车和弹簧的互相牵制效应反映了小车和摆的“纠缠”. 从两个系统的振动频率对比中发现有类似, 这是严格数学推导的结果, 而不是哲学观点的逻辑推理. 时至今日, 我们还不能武断有量子纠缠的系统就不存在可以类比的经典力学系统, 真理是在探索讨论中渐渐显露的, 希望本文严密正确的推导能起抛砖引玉的作用.
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图 3 发生钼杂质溅射的典型波形图 (a) 等离子体电流Ip; (b) 低杂波、离子回旋和中性束加热功率(PLHW, PICRF, PNBI); (c) 芯部弦平均电子密度ne; (d) 归一化的Mo V 258.069 Å和Mo XXIV 70.726 Å线辐射强度(IMo V, IMo XXIV); (e) 归一化的边界辐射和芯部辐射强度(Edge IAXUV, Core IAXUV)
Figure 3. Typical waveform of discharge with molybdenum impurity sputtering: (a) plasma current, Ip; (b) heating power of low hybrid wave, PLHW, ion cyclotron range of frequency heating, PICRF, and neutral beam injection, PNBI; (c) central line-averaged electron density, ne; (d) normalized intensities of Mo V at 258.069 Å, IMo V, and Mo XXIV at 70.726 Å, IMo XXIV; (e) normalized radiation intensities observed by fast AXUV system along an edge and central chord, Edge IAXUV, and Core IAXUV, respectively.
图 5 EAST #101700放电钼杂质爆发前325 ms(灰色线, t = 9.172 s)和爆发期间(蓝色线, t = 9.497 s)观测5—485 Å波段范围的EUV光谱 (a) 5—45 Å; (b) 45—165 Å; (c) 165—285 Å; (d) 285—485 Å
Figure 5. EUV spectra observed 325 ms before (grey lines, t = 9.172 s) and during (blue lines, t = 9.497 s) the molybdenum burst at the wavelength ranges of 5–485 Å in EAST discharge #101700: (a) 5–45 Å; (b) 45–165 Å; (c) 165–285 Å; (d) 285–485 Å.
图 6 EAST #101700放电中四条钼离子归一化谱线强度随时间的演化 (a) Mo VII 235.694 Å; (b) Mo XV 57.928 Å, 2nd Mo XV 115.856 Å; (c) Mo XXIV 70.726 Å
Figure 6. Time evolutions of the four molybdenum ions normalized line emission intensities in EAST #101700 discharge: (a) Mo VII at 235.694 Å; (b) Mo XV at 57.928 Å and 2nd Mo XV at 115.856 Å; (c) Mo XXIV at 70.726 Å.
表 1 在EUV波段识别的钼谱线
Table 1. Identified molybdenum lines in EUV range.
谱线 离子 电离能/eV 波长/Å 跃迁能级 实验值 参考值 Mo V Mo4+ 54.42 258.09 ± 0.03 258.069 4p54d3 3 → 4p64d2 1D2 324.98 ± 0.02 324.979 4p64d5f 3H°4 → 4p64d2 3F4 327.13 ± 0.01 327.167 4p54d3 3 → 4p64d2 3P2 Mo VI Mo5+ 68.83 227.75 ± 0.04 227.801 4p5(2P°)4d(3F)5s 2F°5/2→4p64d 2D5/2 229.20 ± 0.04 229.262 4p66f 2F°5/2 →4p64d 2D3/2 Mo VII Mo6+ 125.64 151.85 ± 0.04 151.747 4s24p5(2P°3/2)5d 2[1/2] °1 → 4s24p6 1S0 235.66 ± 0.05 235.694 4s24p5(2P°3/2)5f 2[3/2]1 → 4s24p5(2P°1/2)4d 2[3/2]°2 Mo VIII Mo7+ 143.6 133.18 ± 0.03 133.168 4s24p4(3P)5d 2P3/2→4s24p5 2P°3/2 134.34 ± 0.03 134.362 4s24p4(3P)5d 4F5/2→4s24p5 2P°3/2 136.83 ± 0.03 136.782 4s24p4(3P)5d 2D3/2→4s24p5 2P°3/2 Mo IX Mo8+ 164.12 132.03 ± 0.03 132.077 4s24p3(2P°)5d 3P°1→4s24p4 1S0 158.53 ± 0.03 158.641 4s24p3(2P°1/2)5s (1/2, 1/2)°1→4s24p4 3P2 176.67 ± 0.04 176.682 4s24p3(2D°3/2)5s (3/2, 1/2)°2→4s24p4 1D2 231.90 ± 0.05 231.991 4s24p3(2D°)4d 1F°3→4s24p4 1D2 237.76 ± 0.05 237.843 4s24p3(2D°)4d 1D°2→4s24p4 1D2 Mo X Mo9+ 186.3 152.54 ± 0.04 152.683 4s24p2(3P)5s 4P3/2 →4s24p3 4S°3/2 157.65 ± 0.04 157.624 4s24p2(3P)5s 2P3/2 →4s24p3 2D°5/2 159.07 ± 0.04 159.049 4s24p2(3P)5s 4P5/2 →4s24p3 2D°5/2 159.42 ± 0.04 159.219 4s24p2(3P)5s 4P3/2 →4s24p3 2D°3/2 231.07 ± 0.04 231.110 4s24p2(1D)4d 2F7/2 →4s24p3 2D°5/2 239.03 ± 0.06 239.017 4s24p2(1S)4d 2D5/2 →4s24p3 2P°3/2 243.05 ± 0.06 243.071 4s24p2(1D)4d 2D3/2→4s24p3 2D°5/2 Mo XI Mo10+ 209.3 146.65 ± 0.04 146.641 4s24p (2P°1/2)5s (1/2, 1/2)°1→4s24p2 3P2 322.12 ± 0.04 322.158 4s4p3 1P°1 → 4s24p2 1D2 Mo XII Mo11+ 230.28 131.37 ± 0.03 131.394 4s25s 2S1/2→4s24p 2P°1/2 250.09 ± 0.06 250.112 4s24d 2D5/2→4s24p 2P°3/2 329.53 ± 0.01 329.414 4s4p2 2P3/2→4s24p 2P°3/2 336.51 ± 0.01 336.639 4s4p2 2P1/2→4s24p 2P°3/2 381.13 ± 0.06 381.125 4s4p2 2D3/2→4s24p 2P°1/2 Mo XIII Mo12+ 279.1 53.56 ± 0.02 53.551 3d94s24p 3D°1→3d104s2 1S0 54.12 ± 0.02 54.101 3d94s24p 1P°1→3d104s2 1S0 340.88 ± 0.01 340.909 3d104s4p 1P°1→3d104s2 1S0 352.87 ± 0.03 352.994 3d104p2 3P1→3d104s4p 3P°0 Mo XIV Mo13+ 302.6 51.98 ± 0.02 52.000 3d9(2D)4p2(3P) 2P1/2→3d104p 2P°3/2 52.77 ± 0.02 52.753 3d9(2D)4s4p (3P°) 2P°3/2→3d104s 2S1/2 121.68 ± 0.02 121.647 3d105s 2S1/2→3d104p 2P°3/2 241.78 ± 0.06 241.609 3d104d 2D3/2→3d104p 2P°1/2 373.55 ± 0.05 373.647 3d104p 2P°3/2→3d104s 2S1/2 423.57 ± 0.07 423.576 3d104p 2P°1/2→3d104s 2S1/2 Mo XV Mo14+ 544 29.48 ± 0.01 29.458 3d95f 1P°1→3d10 1S0 29.81 ± 0.01 29.774 3d95f 3D°1→3d10 1S0 35.39 ± 0.01 35.368 3d94f 1P°1→3d10 1S0 50.43 ± 0.02 50.448 3d9(2D5/2)4p (5/2, 3/2)°1→3d10 1S0 58.04 ± 0.04 57.927 3d9(2D3/2)4s (3/2, 1/2) 2→3d10 1S0 58.86 ± 0.04 58.832 3d9(2D5/2)4s (5/2, 1/2) 2→3d10 1S0 347.47 ± 0.05 347.339 3d9(2D5/2)4p (5/2, 3/2)°3→3d9(2D5/2)4s (5/2, 1/2)3 365.77 ± 0.04 365.924 3d9(2D5/2)4p (5/2, 3/2)4→3d9(2D5/2)4s (5/2, 1/2)3 Mo XVI Mo15+ 591 32.92 ± 0.05 32.916 3p63d8(1G4)4f 2[1]°3/2→3p63d9 2D5/2 34.03 ± 0.01 33.992 3p63d8(3F2)4f 2[1]°3/2→3p63d9 2D3/2 54.46 ± 0.03 54.348 3p63d8(3F4)4s (4, 1/2) 9/2→3p63d9 2D5/2 Mo XVIII Mo17+ 702 38.81 ± 0.01 38.700a 3d64p→3d7 a 数据来源于文献[18], 其他数据来源于NIST数据库[25], 粗体表示可用于杂质诊断的谱线. -
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