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本文使用组态相互作用加多体微扰理论方法对Al +光钟态3s 2 1S 0和3s3p 3P 0的“幻零”波长进行了理论计算. 3s 2 1S 0态的“幻零”波长为266.994(1) nm, 3s3p 3P 0态的“幻零”波长为184.56(7) nm, 174.4(1) nm, 121.5(1) nm和119.7(2) nm. 精确测量这些“幻零”波长, 有助于高精度确定光钟态相关跃迁的振子强度或者约化矩阵元, 进而降低Al +光钟黑体辐射频移评估的不确定度. 同时, 对这些“幻零”波长的精密测量, 对研究Al +原子结构具有重要意义.In quantum optical experiments, the polarizabilities of atomic systems play a very important role, which can be used to describe the interactions of atomic systems with external electromagnetic fields. When subjected to a specific electric field such as a laser field with a particular frequency, the frequency-dependent electric-dipole (E1) dynamic polarizability of an atomic state can reach zero. The wavelength corresponding to such a frequency is referred to as the “turn-out” wavelength. In this work, the “turn-out” wavelengths for the 3s 2 1S 0and 3s3p 3P 0clock states of Al +are calculated by using the configuration interaction plus many-body perturbation theory (CI+MBPT) method. The values of energy and E1 reduced matrix elements of low-lying states of Al +are calculated. By combining these E1 reduced matrix elements with the experimental energy values, the E1 dynamic polarizabilities of the 3s 2 1S 0and 3s3p 3P 0clock states are determined in the angular frequency range of (0, 0.42 a.u.). The “turn-out” wavelengths are found at the zero-crossing points of the frequency-dependent dynamic polarizability curves for both the 3s 2 1S 0and 3s3p 3P 0states. For the ground state 3s 2 1S 0, a single “turn-out” wavelength at 266.994(1) nm is observed. On the other hand, the excited state 3s3p 3P 0exhibits four distinct “turn-out” wavelengths, namely 184.56(1) nm, 174.433(1) nm, 121.52(2) nm, and 119.71(2) nm. The contributions of individual resonant transitions to the dynamic polarizabilities at the “turn-out” wavelengths are examined. It is observed that the resonant lines situated near a certain “turn-out” wavelength can provide dominant contributions to the polarizability, while the remaining resonant lines generally contribute minimally. When analyzing these data, we recommend accurately measuring these “turn-out” wavelengths to accurately determine the oscillator strengths or reduced matrix elements of the relevant transitions. This is crucial for minimizing the uncertainty of the blackbody radiation (BBR) frequency shift in Al +optical clock and suppressing the systematic uncertainty. Meanwhile, precisely measuring these “turn-out” wavelengths is also helpful for further exploring the atomic structure of Al +.
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Keywords:
- Al+/
- polarizability/
- “tune-out” wavelengths/
- CI+MBPT
[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] -
State CI CI+MBPT +Breit NIST Diff./% Refs. 3s21S0 376617 381043 380973 381308 –0.088 381332[19], 379582[26], 381287[27], 382024[28] 3s3p3P0 36256 37342 37344 37393.03 –0.13 37396[19], 37395[26], 37374[27], 37191[28] 3s3p3P1 36318 37407 37405 37453.91 –0.13 37457[19], 37452[26], 37457[28], 36705[29] 3p21P1 59538 59905 59893 59852.02 0.069 59768[19], 60111[26], 60723[27], 54410[28], 63000[30] 3s4s3S1 90008 91254 91233 91274.50 –0.045 91279[19], 91043[26], 91262[27], 91274[28] 3p23P1 92660 94107 94097 94147.46 –0.053 94151[19], 93380[26], 93735[28] 3s3d3D1 94171 95490 95462 95551.44 –0.093 95527[19], 95253[26], 95695[28] 3s4p3P1 103975 105387 105366 105441.50 –0.071 3s4p1P1 105574 106880 106858 106920.56 –0.058 3p21S0 110488 111779 111779 111637.33 0.11 3s5s3S1 118590 120047 120022 120092.919 –0.059 3s4d3D1 119971 121422 121395 121484.252 –0.073 3s5p3P1 124142 125648 125624 125708.828 –0.068 3s5p1P1 124322 125814 125790 125869.015 –0.063 3s6s3S1 130638 132160 132134 132215.52 –0.061 3s5d3D1 131247 132761 132734 132822.95 –0.067 3s6p1P1 133307 134861 134835 134919.40 –0.062 3s6p3P1 133409 134954 134928 135015.70 –0.065 3s6d3D1 137210 138754 138727 138814.87 –0.064 3s7p1P1 138244 139828 139802 139918.98 –0.084 3s7p3P1 138422 139987 139960 140091.9 –0.094 3s8p1P1 140927 142519 142493 142961.20 –0.33 3s8p3P1 141127 142711 142685 143166.76 0.34 3s7d3D1 140741 142300 142274 142365.54 –0.065 3s9p1P1 143591 145260 145233 144941.10 0.20 3s9s3S1 142835 144377 144350 144644.14 –0.20 3s8d3D1 143118 144686 144658 144642.0 0.012 
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Method CI CI+MBPT Recommend Refs. Gauge Length Velocity Length Velocity 3s21S0-3s3p3P1 0.0092 0.0101 0.0098 0.0105 0.0098(13) 0.01513[26] 3s21S0-3s3p1P1 3.1830 3.1572 3.1156 3.1156 3.116(67) 3.112[19]
2.840[26]3s21S0-3s4p3P1 0.0018 0.0017 0.0022 0.0018 0.002(1) — 3s21S0-3s4p1P1 0.0844 0.0781 0.0460 0.0737 0.046(38) 0.045[19] 3s21S0-3s5p3P1 0.0037 0.0038 0.0051 0.0043 0.005(2) — 3s21S0-3s5p1P1 0.0474 0.0502 0.0662 0.0491 0.066(19) — 3s21S0-3s6p1P1 0.0595 0.0610 0.0704 0.0586 0.070(12) — 3s21S0-3s6p3P1 0.0013 0.0014 0.0023 0.0017 0.002(1) — 3s21S0-3s7p1P1 0.0575 0.0582 0.0638 0.0551 0.064(9) — 3s21S0-3s7p3P1 0.0015 0.0015 0.0022 0.0019 0.002(1) — 3s21S0-3s8p1P1 0.0493 0.0496 0.0505 0.0448 0.051(6) — 3s21S0-3s8p3P1 0.0199 0.0200 0.0250 0.0220 0.025(5) — 3s21S0-3s9p1P1 0.0759 0.0758 0.0784 0.0718 0.078(7) — 3s3p3P0-3s4s3S1 0.8936 0.8888 0.8979 0.8926 0.898(10) 0.900[19] 3s3p3P0-3p23P1 1.8870 1.8737 1.8394 1.8789 1.839(48) 1.836[19] 3s3p3P0-3s3d3D1 2.2623 2.2820 2.2350 2.2626 2.235(47) 2.236[19] 3s3p3P0-3s5s3S1 0.2671 0.2652 0.2690 0.2661 0.269(4) — 3s3p3P0-3s4d3D1 0.4651 0.4746 0.4456 0.4612 0.446(28) — 3s3p3P0-3s6s3S1 0.1492 0.1481 0.1505 0.1486 0.151(2) — 3s3p3P0-3s5d3D1 0.2058 0.2118 0.1921 0.2029 0.192(20) — 3s3p3P0-3s7s3S1 0.0421 0.0418 0.0414 0.0422 0.041(1) — 3s3p3P0-3s6d3D1 0.1199 0.1242 0.1097 0.1178 0.110(13) — 3s3p3P0-3s8s3S1 0.1012 0.1004 0.1027 0.1005 0.103(2) — 3s3p3P0-3s7d3D1 0.0802 0.0836 0.0722 0.0787 0.072(12) — 3s3p3P0-3s9s3S1 0.0990 0.0983 0.0991 0.0986 0.099(1) — 3s3p3P0-3s8d3D1 0.0642 0.0673 0.0571 0.0630 0.057(10) — 下载:
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Transition Contributions Ref. $ \alpha \left(0\right)( $3s21S0$ ) $ 3s21S0-3s3p3P1 0.003 — 3s21S0-3s3p1P1 23.73 23.661[19]
23.7294[27]3s21S0-3s4p3P1 6.5×10–6 — 3s21S0-3s4p1P1 0.0029 0.003[19] 3s21S0-3s5p3P1 3.0×10–5 — 3s21S0-3s5p1P1 0.0051 — 3s21S0-3snp3P1,n= 6—8 0.0006 — 3s21S0-3snp1P1,n= 6—9 0.0184 — Others 0.1135 — Core 0.265[19] 0.268[27] VC –0.019[19] — Total 24.1169 24.048[19]
24.1396[27]$ \alpha \left(0\right)( $3s21S0$ ) $ 3s3p3P0-3s4s3S1 2.1886 2.197[19]
2.1860[27]3s3p3P0-3p23P1 8.7226 8.687[19]
8.6830[27]3s3p3P0-3s3d3D1 12.5817 12.568[19]
12.6533[27]3s3p3P0-3s5s3S1 0.1281 — 3s3p3P0-3s4d3D1 0.3451 — 3s3p3P1-3sns3S1,n= 6—9 0.0656 — 3s3p3P1-3snd3D1,n= 5—8 0.0855 — Others 0.2117 — Core 0.256[19] 0.268[27] VC –0.010[19] — Total 24.5840 24.543[19] $ {{\Delta }}\alpha \left(0\right) $ 0.467 0.495[19]
0.482[27]
0.426Expt.[4]下载:
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3s21S0 3s3p3P0 $ {\lambda }_{0} $/nm 266.994(1) 184.56(7) 174.4(1) 121.5(1) 119.7(2) $ {\omega }_{0} $/a.u. 0.170653(2) 0.24688(7) 0.26171(15) 0.3750(3) 0.3806(6) $ {\alpha }_{0}\left({\lambda }_{0}\right)( $3s21S0$ ) $ 3s21S0-3s3p3P1 –39.3927 –0.0003 0.0003 –9.1×10–5 –8.7×10–5 3s21S0-3s3p1P1 39.0038 131.4864 287.4679 –26.6523 –25.0333 3s21S0-3s4p3P1 7.5×10–6 8.9×10–6 9.3×10–6 1.7×10–5 1.8×10–5 3s21S0-3s4p1P1 0.0033 0.0039 0.0041 0.0071 0.0074 3s21S0-3s5p3P1 3.3×10–5 3.7×10–5 3.8×10–5 5.3×10–5 5.4×10–5 3s21S0-3s5p1P1 0.0056 0.0062 0.0064 0.0089 0.0091 3s21S0-3snp3P1,n= 6—8 0.0007 0.0008 0.0008 0.0010 0.0010 3s21S0-3snp1P1,n= 6—9 0.0198 0.0216 0.0221 0.0281 0.0285 Others 0.1135 0.1135 0.1135 0.1135 0.1135 Core 0.265 0.265 0.265 0.265 0.265 VC –0.019 –0.019 –0.019 –0.019 –0.019 Total 0 131.8781 287.8605 –26.2478 –24.6278 $ {\alpha }_{0}\left({\lambda }_{0}\right)( $3s3p3P0$ ) $ 3s3p3P0-3s4s3S1 4.2349 –195.2541 –16.5755 –1.6425 –1.5594 3s3p3P0-3p23P1 15.4522 98.4756 –429.0192 –7.9128 7.4784 3s3p3P0-3s3d3D1 21.4976 95.2803 444.0076 –12.5559 –11.8356 3s3p3P0-3s5s3S1 0.1612 0.2245 0.2466 12.9773 –6.3146 3s3p3P0-3s4d3D1 0.4305 0.5901 0.6448 8.1466 26.1561 3s3p3P1-3sns3S1,n= 6—9 0.0765 0.0936 0.0987 0.2203 0.2388 3s3p3P1-3snd3D1,n= 5—8 0.1001 0.1234 0.1303 0.3005 0.3264 Others 0.2117 0.2117 0.2117 0.2117 0.2117 Core 0.265 0.265 0.265 0.265 0.265 VC –0.010 –0.010 –0.010 –0.010 –0.010 Total 42.4197 0 0 0 0 下载:
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[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]
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