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应用基于B样条基组的相对论耦合簇理论方法, 计算了 212Fr原子的 nS ( n= 7—12), nP ( n= 7—12)和 nD ( n= 6—11)态的磁偶极超精细结构常数. 与精确实验值的比较说明这套理论方法能精确计算出磁偶极超精细结构常数, 其中7P态的磁偶极超精细常数的理论值与实验值之间的差异小于1%. 在忽略场移效应对Fr原子7P态超精细结构常数的影响下, 通过结合实验值进一步定出了 207−213,220−228Fr核磁偶极矩
$\mu $ , 这些值与已有的测量值具有非常好的一致性. 本文报道了12S, nP ( n= 9—12)和 nD ( n= 10—11)态的磁偶极超精细结构常数.-
关键词:
- 磁偶极超精细结构常数/
- B样条/
- 耦合簇理论方法/
- 磁偶极矩
As the heaviest atom in alkali-metal elements, Fr atom has been regarded as a candidate for the search of the permanent electric dipole moment of the electron and of parity-nonconservation effects. Accurate knowledge of Fr atomic properties is of great interest. In this work, we use a relativistic coupled-cluster method to calculate the magnetic dipole hyperfine structure constants for nS ( n= 7－12), nP ( n= 7－12) and nD ( n= 6－11) states of 212Fr. A finite B-spline basis set is used to expand the Dirac radial function, including completely the single and double excitation in correlation calculation. Our results are compared with available theoretical and experimental values. The comparison shows that our method can offer accurate calculation of magnetic dipole hyperfine structure constant. For 7P state the differences between our results and experimental values are within 1%. The magnetic dipole hyperfine structure constants for 12S, nP ( n= 9－12) and nD ( n= 10－11) states are reported for the first time, which are very useful as benchmarks for experimental measurements and calculations by other theoretical methods of these quantities. In the relativistic coupled-cluster theoretical framework, we study the electron correlation effect on hyperfine-structure constant Afor the S, P, and D states of Fr. We observe that the electron correlation effect is very important for hyperfine-structure constant properties. The D state has a considerable correlation effect. At the same time, we also investigate contribution trends of individual electron correlation effects involving direct, core-polarization and pair-correlation ones in S, P, and D Rydberg series. It is found that the dominant contributions for the S 1/2, P 1/2,3/2and nD 3/2( n= 7－11) states are to from the direct effect; however, the dominant contributions for the 6D 3/2, and nD 5/2( n= 6－11) states are due to the pair-correlation and the core-polarization, respectively. For D 5/2states, there is very strong cancellation among these individual correlation effects. The knowledge of these correlation trends is useful for studying the permanent electric dipole moment and parity-nonconservation effect of Fr in future. Moreover, the magnetic dipole moment$ {\mu}$ for each of isotopes 207−213,220−228Fr is determined by combining with experimental values for magnetic dipole hyperfine structure constant of 7P state. For each of isotope 207−213Fr, our magnetic dipole moment$ {\mu}$ is perfectly consistent with the experimental value, and our uncertainties are twice smaller than those in the experiments . For each of isotope 220−228Fr, our magnetic dipole moment$ {\mu}$ has a larger uncertainty, but is still in agreement with the experimental magnetic dipole moment$ {\mu}$ .[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] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] -
能级 ${A_{{\rm{DF}}}}$ ${A_{{\rm{CCSD}}}}$ $\varDelta /$% Ref.[38] 实验值 7S1/2 6001.76 9403.56 30.93 9124(94) 9064.2(2)[27] 9064.4(1.5)[39] 8S1/2 1538.03 2014.10 17.37 1986(19) 9S1/2 631.98 792.19 13.66 784(9) 10S1/2 321.24 396.86 11.95 419(9) 401(5)[29] 11S1/2 185.41 225.71 11.10 212(9) 225(3)[29] 12S1/2 116.42 141.25 10.80 
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能级 ${A_{{\rm{DF}}}}$ ${A_{{\rm{CCSD}}}}$ $\varDelta /$% Ref.[38] 实验值 7P1/2 642.48 1198.10 41.96 1181(9) 1189.1(4.6)[28] 1187.1(6.8)[39] 1192.0(2)[32] 8P1/2 228.04 372.04 33.66 371(5) 373.0(1)[39] 9P1/2 106.78 167.21 30.88 10P1/2 58.35 89.53 29.46 11P1/2 35.26 53.38 28.51 12P1/2 22.88 34.24 27.68 7P3/2 51.05 97.88 43.55 96(3) 97.2(1)[27] 97.2(1)[39] 8P3/2 18.67 32.51 37.82 32(3) 32.8(1)[39] 9P3/2 8.89 15.00 35.83 10P3/2 4.91 8.15 34.75 11P3/2 3.00 4.92 34.01 12P3/2 1.97 3.20 33.33 下载:
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能级 ${A_{{\rm{DF}}}}$ ${A_{{\rm{CCSD}}}}$ $\varDelta / $% Ref.[38] 实验值 6D3/2 33.25 92.91 61.27 79(5) 7D3/2 16.82 30.17 39.65 29(3) 8D3/2 8.65 13.81 32.20 13(1) 13.0(6)[29] 9D3/2 4.93 7.50 28.75 7(1) 7.1(7)[29] 10D3/2 3.06 4.52 26.64 11D3/2 2.03 2.93 24.97 6D5/2 13.14 –53.92 126.38 –54(5) 7D5/2 6.32 –13.64 150.21 –15(3) 8D5/2 3.20 –5.67 161.12 –6(1) –7.1(6)[29] 9D5/2 1.81 –2.96 166.96 –3.3(6) –3.6(4)[29] 10D5/2 1.12 –1.72 170.59 11D5/2 0.74 –1.10 173.16 下载:
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同位素 核自旋 7P1/2 7P3/2 ${\mu}$ ${A_{{\rm{expt}}.}}$[33] ${{\mu} _{1/2}}$ ${A_{{\rm{expt}}.}}$[33] ${{\mu} _{3/2}}$ ${{\mu} _{{\rm{present}}}}$ ${{\mu} _{{\rm{expt}}{\rm{.}}}}$[33] 207Fr 9/2 90.7(6) 3.85(3) 3.85(3) 3.89(9) 208Fr 7 874.8(3) 4.723(2) 72.4(5) 4.784(33) 4.753(33) 4.75(10) 209Fr 9/2 1127.9(2) 3.914(1) 93.3(5) 3.963(21) 3.939(22) 3.95(8) 210Fr 6 946.3(3) 4.379(1) 78.0(2) 4.418(11) 4.399(20) 4.40(9) 211Fr 9/2 1142.1(2) 3.964(1) 94.9(3) 4.031(13) 3.998(34) 4.00(8) 212Fr 5 1187(7) 4.577(26) 97.2(1) 4.588(5) 4.583(30) 4.62(9) 213Fr 9/2 1150(8) 3.991(28) 95.3(3) 4.047(13) 4.019(30) 4.02(8) 220Fr 1 –73.2(5) –0.691(5) –0.691(5) –0.67(1) 221Fr 5/2 808(12) 1.558(23) 65.5(6) 1.545(14) 1.552(25) 1.58(3) 222Fr 2 33(1) 0.623(19) 0.623(19) 0.63(1) 223Fr 3/2 83.3(9) 1.179(13) 1.179(13) 1.17(2) 224Fr 1 42.1(7) 0.397(7) 0.397(7) 0.40(1) 225Fr 3/2 77(3) 1.090(42) 1.090(42) 1.07(2) 226Fr 1 7(1) 0.066(9) 0.066(9) 0.071(2) 227Fr 1/2 316(2) 1.491(9) 1.491(9) 1.50(3) 228Fr 2 –41(2) –0.77(4) –0.77(4) –0.76(2) 下载:
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