钫原子磁偶极超精细结构常数及其同位素的磁偶极矩的理论计算
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摘要
应用基于B样条基组的相对论耦合簇理论方法,计算了~(212)Fr原子的n S (n=7—12), n P (n=7—12)和n D (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~(207-213,220-228)Fr核磁偶极矩μ,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, n P (n=9—12)和n D (n=10—11)态的磁偶极超精细结构常数.
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 n S(n = 7-12), n P(n = 7-12) and n D(n = 6-11) states of ~(212)Fr. 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 7 P state the differences between our results and experimental values are within 1%. The magnetic dipole hyperfine structure constants for 12 S, n P(n = 9-12) and n D(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 A for 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_(1/2,3/2) and n D_(3/2)(n = 7-11)states are to from the direct effect; however, the dominant contributions for the 6 D_(3/2), and n D5/2(n = 6-11)states are due to the pair-correlation and the core-polarization, respectively. For D5/2 states, 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 μ for each of isotopes ~(207-213,220-228)Fr is determined by combining with experimental values for magnetic dipole hyperfine structure constant of 7 P state. For each of isotope ~(207-213)Fr, our magnetic dipole moment μ is perfectly consistent with the experimental value, and our uncertainties are twice smaller than those in the experiments. For each of isotope ~(220-228)Fr, our magnetic dipole moment μ has a larger uncertainty, but is still in agreement with the experimental magnetic dipole moment μ.
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 n S(n = 7-12), n P(n = 7-12) and n D(n = 6-11) states of ~(212)Fr. 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 7 P state the differences between our results and experimental values are within 1%. The magnetic dipole hyperfine structure constants for 12 S, n P(n = 9-12) and n D(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 A for 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_(1/2,3/2) and n D_(3/2)(n = 7-11)states are to from the direct effect; however, the dominant contributions for the 6 D_(3/2), and n D5/2(n = 6-11)states are due to the pair-correlation and the core-polarization, respectively. For D5/2 states, 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 μ for each of isotopes ~(207-213,220-228)Fr is determined by combining with experimental values for magnetic dipole hyperfine structure constant of 7 P state. For each of isotope ~(207-213)Fr, our magnetic dipole moment μ is perfectly consistent with the experimental value, and our uncertainties are twice smaller than those in the experiments. For each of isotope ~(220-228)Fr, our magnetic dipole moment μ has a larger uncertainty, but is still in agreement with the experimental magnetic dipole moment μ.
引文
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[25] Atutov S N, Calabrese R, Corradi L, Dainelli A, Mauro C D,Khanbekyan A, Mariotti E, Minguzzi P, Moi L, Sanguinetti S, Stancari G, Tomassetti L 2008 Proc. SPIE 7027 70270C
[26] Ekstrom C, Ingelman S, Wannberg G, Skarestad M 1978Physica Scripta 18 51
[27] Coc A, Thibault C, Touchard F, Duong H T, J uncar P,Liberman S, Pinard J, Lerme J, Vialle J L, Buttgenbach S,Mueller A C, Pesnelle A, the ISOLDE Collaboration 1985Phys. Lett. B 163 66
[28] Coc A, Thibault C, Touchard F, Duong H T, J uncar P,Liberman S, Pinard J, Carre M, Lerme J, Vialle J L,Biittgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1987 Nucl. Phys. A 468 1
[29] Arnold E, Borchers W, Duong H T, Juncar P, Lerme J,Lievens P, Neu W, Neugart R, Pellerin M, Pinard J, Vialle J L, Wendt K, the ISOLDE Collaboration 1990 J. Phys. B 233511
[30] Arnold E, Borchers W, Carre M, Duong H T, Juncar P,Lerme J, Liberman S, Neu W, Neugart R, Otten W, Pellerin M, Pinard J, Pesnelle A, Vialle J L, Wendt K, the ISOLDE Collaboration 1989 J. Phys. B 22 L391
[31] Bauche J, Duong H T, Juncar P, Liberman S, Pinard J, Coc A, Thibault C, Touchard F, Lerme J, Vialle J L,Biittgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1986 J. Phys. B 19 L593
[32] Grossman J S, Orozco L A, Simsarian J E, Sprouse G D,Zhao W Z 1999 Phys. Rev. Lett. 83 935
[33] Sansonetti J E 2007 J. Phys. Chem. Ref. Data 36 497
[34] Gomez E, Aubin S,Orozco L A, Sprouse G D, IskrenovaTchoukova E, Safronova M S 2008 Phys. Rev. Lett. 100 172502
[35] Dzuba V A, Flambaum V V, Sushkov O P 1984 J. Phys. B:At. Mol. Phys. 17 1953
[36] Owusu A, Dougherty R W, Gowri G, Das T P 1997 Phys.Rev. A 56 305
[37] Safronova M S, Johnson W R, Derevianko A 1999 Phys. Rev.A 60 4476
[38] Sahoo B K, Nandy D K, Das B P, Sakemi Y 2015 Phys. Rev.A 91 042507
[39] Duong H T, Juncar P, Liberman S, Mueller A C, Neugart R,Otten E W, Peuse B, Pinard J, Stoke H H, Thibault C,Touchard F, Vialle J L, Wendt K, the ISOLDE Collaboration1987 Europhys. Lett. 3 175
[40] Barber Z W, Stalnaker J E, Lemke N D, Poli N, Oates C W,Fortier T M, Diddams S A, Hollberg L, Hoyt C W,Taichenachev A V, Yudin V I 2008 Phys. Rev. Lett. 100103002
[41] Kien F L, Balykin V I, Hakuta K 2005 J. Phys. Soc. Jpn. 74910
[42] Ingvar L 1978 Int. J. Quantum Chem. 12 33
[43] Sinha D, Mukhopadhyay S, Mukherjee D 1986 Chem. Phys.Lett. 129 369
[44] Blundell S A, Johnson W R, Sapiratein J 1991 Phys. Rev. A43 3407
[45] Porsev S G, Beloy K, Derevianko A 2010 Phys. Rev. D 82036008
[46] Sahoo B K, Sur C, Beier T, Das B P, Chaudhuri R K,Mukherjee D 2007 Phys. Rev. A 75 042504
[47] Safronova M S, Safronova U I 2011 Phys. Rev. A 83 052508
[2] Fischer C F, Brage T, Jonsson P 1997 Computational Atomic Structure:An MCHF Approach(UK:Institute of Physics)pp1-67
[3] Jonsson P, Gaigalas G, Bieron J, Fishcher C F, Grant I 2013Computer Physics Communications. 184 2197
[4] Jonsson P, He X, Fishcher C F, Grant I 2007 Computer Physics Communications. 177 597
[5] Dzuba V A, Flambaum V V, Kozlov M G 1996 Phys. Rev. A54 3948
[6] Dzuba V A, Johnson W R 1998 Phys. Rev. A 57 2459
[7] Angstmann E J, Dzuba V A, Flambaum V V 2004 Phys. Rev.A 70 014102
[8] Dinh T H, Dzuba V A, Flambaum V V, Ginges J S M 2008Phys. Rev. A 78 054501
[9] Kozlov M G, Porsev S G, Johnson W R 2001 Phys. Rev. A 64052107
[10] Pal R, Safronova M S, Johnson W R, Derevianko A, Porsev S G 2007 Phys. Rev. A 75 042515
[11] Blundell S A, Johnson W R, Liu Z W, Sapirstein 1989 Phys.Rev. A 40 2233
[12] Eliav E, Vikas M J, Ishikawa Y, Kaldor U 2005 Chem. Phys.311 163
[13] Mani B K, Angom D 2011 Phys. Rev. A 83 012501
[14] Kallay M, Nataraj H S, Sahoo B K, Das B P, Visscher L 2011Phys. Rev. A 83 030503
[15] Nandy D K, Singh Y, Sahoo B K 2014 Phys. Rev. A 89 062509
[16] Borschevsky A, Eliav E, Vilkas M J, Ishikawa Y, Kaldor U2007 Phys. Rev. A 75 042514
[17] Eliav E, Kaldor U, Ishikawa Y 1996 Phys. Rev. A 53 3050
[18] Chaudhuri R K, Chattopadhyay S, Mahapatra U S 2013 J.Phys. Chem. A 117 12616
[19] Tang Y B, Lou B Q, Shi T Y 2017 Phys. Rev. A 96 022513
[20] Tang Y B, Gao N N, Lou B Q, Shi T Y 2018 Phys. Rev. A 98062511
[21] Byrnes T M R, Dzuba V A, Flambaum F F, Murray D W1999 Phys. Rev. A 59 3082
[22] Mukherjee D, Sahoo B K, Nataraj H S, Das B P 2009 J.Phys. Chem. A 113 12549
[23] Sakemi Y, Harada K, Hayamizu T, Itoh M, Kawamura H,Liu S, Nataraj H S, Oikawa A, Saito M, Sato T 2011 J. Phys.Conf. Ser. 302 012051
[24] Sahoo B K, Aoki T, Das B P, Sakemi Y 2016 Phys. Rev. A 93032520
[25] Atutov S N, Calabrese R, Corradi L, Dainelli A, Mauro C D,Khanbekyan A, Mariotti E, Minguzzi P, Moi L, Sanguinetti S, Stancari G, Tomassetti L 2008 Proc. SPIE 7027 70270C
[26] Ekstrom C, Ingelman S, Wannberg G, Skarestad M 1978Physica Scripta 18 51
[27] Coc A, Thibault C, Touchard F, Duong H T, J uncar P,Liberman S, Pinard J, Lerme J, Vialle J L, Buttgenbach S,Mueller A C, Pesnelle A, the ISOLDE Collaboration 1985Phys. Lett. B 163 66
[28] Coc A, Thibault C, Touchard F, Duong H T, J uncar P,Liberman S, Pinard J, Carre M, Lerme J, Vialle J L,Biittgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1987 Nucl. Phys. A 468 1
[29] Arnold E, Borchers W, Duong H T, Juncar P, Lerme J,Lievens P, Neu W, Neugart R, Pellerin M, Pinard J, Vialle J L, Wendt K, the ISOLDE Collaboration 1990 J. Phys. B 233511
[30] Arnold E, Borchers W, Carre M, Duong H T, Juncar P,Lerme J, Liberman S, Neu W, Neugart R, Otten W, Pellerin M, Pinard J, Pesnelle A, Vialle J L, Wendt K, the ISOLDE Collaboration 1989 J. Phys. B 22 L391
[31] Bauche J, Duong H T, Juncar P, Liberman S, Pinard J, Coc A, Thibault C, Touchard F, Lerme J, Vialle J L,Biittgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1986 J. Phys. B 19 L593
[32] Grossman J S, Orozco L A, Simsarian J E, Sprouse G D,Zhao W Z 1999 Phys. Rev. Lett. 83 935
[33] Sansonetti J E 2007 J. Phys. Chem. Ref. Data 36 497
[34] Gomez E, Aubin S,Orozco L A, Sprouse G D, IskrenovaTchoukova E, Safronova M S 2008 Phys. Rev. Lett. 100 172502
[35] Dzuba V A, Flambaum V V, Sushkov O P 1984 J. Phys. B:At. Mol. Phys. 17 1953
[36] Owusu A, Dougherty R W, Gowri G, Das T P 1997 Phys.Rev. A 56 305
[37] Safronova M S, Johnson W R, Derevianko A 1999 Phys. Rev.A 60 4476
[38] Sahoo B K, Nandy D K, Das B P, Sakemi Y 2015 Phys. Rev.A 91 042507
[39] Duong H T, Juncar P, Liberman S, Mueller A C, Neugart R,Otten E W, Peuse B, Pinard J, Stoke H H, Thibault C,Touchard F, Vialle J L, Wendt K, the ISOLDE Collaboration1987 Europhys. Lett. 3 175
[40] Barber Z W, Stalnaker J E, Lemke N D, Poli N, Oates C W,Fortier T M, Diddams S A, Hollberg L, Hoyt C W,Taichenachev A V, Yudin V I 2008 Phys. Rev. Lett. 100103002
[41] Kien F L, Balykin V I, Hakuta K 2005 J. Phys. Soc. Jpn. 74910
[42] Ingvar L 1978 Int. J. Quantum Chem. 12 33
[43] Sinha D, Mukhopadhyay S, Mukherjee D 1986 Chem. Phys.Lett. 129 369
[44] Blundell S A, Johnson W R, Sapiratein J 1991 Phys. Rev. A43 3407
[45] Porsev S G, Beloy K, Derevianko A 2010 Phys. Rev. D 82036008
[46] Sahoo B K, Sur C, Beier T, Das B P, Chaudhuri R K,Mukherjee D 2007 Phys. Rev. A 75 042504
[47] Safronova M S, Safronova U I 2011 Phys. Rev. A 83 052508