Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of Helium
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Abstract
The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1, 12, and 1 states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates. -
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References
[1] Träbert E 2014 Phys. Scr. 89 114003 doi: 10.1088/0031-8949/89/11/114003[2] Zhao Y, Deng B, Xiong G, Hu Z M, Wei M X, Zhu T, Shang W L, Li J, Yang G H, Zhang J Y, and Yang J M 2011 Chin. Phys. Lett. 28 065201 doi: 10.1088/0256-307X/28/6/065201[3] Woodworth J R and Moos H W 1975 Phys. Rev. A 12 2455 doi: 10.1103/PhysRevA.12.2455[4] Johnson W R, Plante D R, and Sapirstein J 1995 Adv. At. Mol. Opt. Phys. 35 255 doi: 10.1016/S1049-250X0860165-2[5] Baklanov E V and Denisov A 1997 Quantum Electron. 27 465 doi: 10.1070/QE1997v027n05ABEH000964[6] Lach G and Pachucki K 2001 Phys. Rev. A 64 042510 doi: 10.1103/PhysRevA.64.042510[7] Drake G W F and Morton D C 2007 Astrophys. J. Suppl. Ser. 170 251 doi: 10.1086/512239[8] Rooij R V, Borbely J S, Simonet J, Hoogerland M D, Eikema K S E, Rozendaal R A, and Vassen W 2011 Science 333 196 doi: 10.1126/science.1205163[9] Głowacki L and Migdałek J 2014 Phys. Rev. A 89 042503 doi: 10.1103/PhysRevA.89.042503[10] Zheng X, Sun Y R, Chen J J, Jiang W, Pachucki K, and Hu S M 2017 Phys. Rev. Lett. 119 263002 doi: 10.1103/PhysRevLett.119.263002[11] Thomas K F, Ross J A, Henson B M, Shin D K, Baldwin K G H, Hodgman S S, and Truscott A G 2020 Phys. Rev. Lett. 125 013002 doi: 10.1103/PhysRevLett.125.013002[12] Lewis S A, Pichanick F M J, and Hughes V W 1970 Phys. Rev. A 2 86 doi: 10.1103/PhysRevA.2.86[13] Feinberg G and Sucher J 1971 Phys. Rev. Lett. 26 681 doi: 10.1103/PhysRevLett.26.681[14] Schad T A 2018 Astrophys. J. 865 31 doi: 10.3847/1538-4357/aad962[15] Zhang D H, Xie L Y, Jiang J, and Dong C Z 2019 Chin. Phys. Lett. 36 083401 doi: 10.1088/0256-307X/36/8/083401[16] Li F, Yang Y J, Chen J, Liu X J, Wei Z Y, and Wang B B 2020 Chin. Phys. Lett. 37 113201 doi: 10.1088/0256-307X/37/11/113201[17] Antognin A, Nez F, Schuhmann K, and Amaro F D 2013 Science 339 417 doi: 10.1126/science.1230016[18] Bezginov N, Valdez T, Horbatsch M, Marsman A, Vutha A C, and Hessels E A 2019 Science 365 1007 doi: 10.1126/science.aau7807[19] Hodgman S S, Dall R G, Byron L J, Baldwin K G, Buckman S J, and Truscott A G 2009 Phys. Rev. Lett. 103 053002 doi: 10.1103/PhysRevLett.103.053002[20] Pachucki K 2006 Phys. Rev. Lett. 97 013002 doi: 10.1103/PhysRevLett.97.013002[21] Patkóš V, Yerokhin V A, and Pachucki K 2021 Phys. Rev. A 103 042809 doi: 10.1103/PhysRevA.103.042809[22] Zhang Y H, Tang L Y, Zhang X Z, and Shi T Y 2016 Phys. Rev. A 93 052516 doi: 10.1103/PhysRevA.93.052516[23] Yang S J, Mei X S, Shi T Y, and Qiao H X 2017 Phys. Rev. A 95 062505 doi: 10.1103/PhysRevA.95.062505[24] Pachucki K and Yerokhin V A 2009 Phys. Rev. A 79 062516 doi: 10.1103/PhysRevA.79.062516[25] Pachucki K and Yerokhin V A 2010 Phys. Rev. Lett. 104 070403 doi: 10.1103/PhysRevLett.104.070403[26] Wan J J 2015 Chin. Phys. Lett. 32 023102 doi: 10.1088/0256-307X/32/2/023102[27] Morton D C, Moffatt P, and Drake G W F 2011 Can. J. Phys. 89 129 doi: 10.1139/P10-067[28] Mitroy J and Tang L Y 2013 Phys. Rev. A 88 052515 doi: 10.1103/PhysRevA.88.052515[29] Morton D C, Schulhoff E E, and Drake G W F 2015 J. Phys. B 48 235001 doi: 10.1088/0953-4075/48/23/235001[30] Głowacki L 2020 At. Data Nucl. Data Tables 133 101344 doi: 10.1016/j.adt.2020.101344[31] Smiciklas M and Shiner D 2010 Phys. Rev. Lett. 105 123001 doi: 10.1103/PhysRevLett.105.123001[32] Kato K, Skinner T D G, and Hessels E A 2018 Phys. Rev. Lett. 121 143002 doi: 10.1103/PhysRevLett.121.143002[33] Notermans R P and Vassen W 2014 Phys. Rev. Lett. 112 253002 doi: 10.1103/PhysRevLett.112.253002[34] Qing B, Chen S H, Gao X, and Li J M 2008 Chin. Phys. Lett. 25 2448 doi: 10.1088/0256-307X/25/7/032[35] Lin C D, Johnson W R, and Dalgarno A 1977 Phys. Rev. A 15 154 doi: 10.1103/PhysRevA.15.154[36] Indelicato P 1996 Phys. Rev. Lett. 77 3323 doi: 10.1103/PhysRevLett.77.3323[37] Drake G W F 1971 Phys. Rev. A 3 908 doi: 10.1103/PhysRevA.3.908[38] Jönsson P, He X, Froese F C, and Grant I P 2007 Comput. Phys. Commun. 177 597 doi: 10.1016/j.cpc.2007.06.002[39] Froese F C, Gaigalas G, Jönsson P, and Bieroń J 2019 Comput. Phys. Commun. 237 184 doi: 10.1016/j.cpc.2018.10.032[40] Jönsson P, Gaigalas G, Bieroń J, Fischer C F, and Grant I P 2013 Comput. Phys. Commun. 184 2197 doi: 10.1016/j.cpc.2013.02.016[41] Khatri I, Goyal A, Aggarwal S, Singh A K, and Man M 2016 Radiat. Phys. Chem. 123 46 doi: 10.1016/j.radphyschem.2016.02.017[42] Radžiūtė L, Gaidamauskas E, Gaigalas G, Li J G, Dong C Z, and Per J 2015 Chin. Phys. B 24 043103 doi: 10.1088/1674-1056/24/4/043103[43] Jönsson P and Bieroń J 2010 J. Phys. B 43 074023 doi: 10.1088/0953-4075/43/7/074023[44] Johnson W R, Savukov I M, Safronova U I, and Dalgarno A 2002 Astrophys. J. Suppl. Ser. 141 543 doi: 10.1086/340547[45] Aggarwal K M, Kato T, Keenan F P, and Murakami I 2011 Phys. Scr. 83 015302 doi: 10.1088/0031-8949/83/01/015302[46] Zhou F, Qu Y, Li J, and Wang J 2015 Phys. Rev. A 92 052505 doi: 10.1103/PhysRevA.92.052505[47] Li J, Jönsson P, Godefroid M, Dong C, and Gaigalas G 2012 Phys. Rev. A 86 052523 doi: 10.1103/PhysRevA.86.052523[48] Fano U 1965 Phys. Rev. 140 A67 doi: 10.1103/PhysRev.140.A67[49] Olsen J, Godefroid M R, Jonsson P, Malmqvist P, and Fischer C F 1995 Phys. Rev. E 52 4499 doi: 10.1103/PhysRevE.52.4499[50] Nahar S N, Eissner W, Chen G X, and Pradhan A K 2003 Astron. & Astrophys. 408 789 doi: 10.1051/0004-6361:20030945[51] Kelleher D E and Podobedova L I 2008 J. Phys. Chem. Ref. Data 37 267 doi: 10.1063/1.2735328[52] Kaur M, Dar D F, Sahoo B K, and Arora B 2021 At. Data Nucl. Data Tables 137 101381 doi: 10.1016/j.adt.2020.101381[53] Kramida A, Ralchenko Y, Reader J, and Team N A 2020 NIST Atomic Spectra Database ver. 5.8 Gaithersburg, MD: National Institute of Standards and Technology doi: 10.18434/T4W30F[54] Zhang T, Yan Z C, and Drake G W F 1996 Phys. Rev. Lett. 77 1715 doi: 10.1103/PhysRevLett.77.1715[55] Sims J S and Hagstrom S A 2014 J. Chem. Phys. 140 224312 doi: 10.1063/1.4881639[56] Jiao L G, Zan L R, Zhu L, Zhang Y Z, and Ho Y K 2019 Phys. Rev. A 100 022509 doi: 10.1103/PhysRevA.100.022509[57] Bai Z D, Zhong Z X, Yan Z C, and Shi T Y 2021 Chin. Phys. B 30 023101 doi: 10.1088/1674-1056/abc156[58] He X K, Liu J P, Zhang X, Shen Y, and Zou H X 2018 Chin. Phys. B 27 83102 doi: 10.1088/1674-1056/27/8/083102[59] Ynnerman A and Fischer C F 1995 Phys. Rev. A 51 2020 doi: 10.1103/PhysRevA.51.2020[60] Jönsson P and Fischer C F 1998 Phys. Rev. A 57 4967 doi: 10.1103/PhysRevA.57.4967[61] Chen M, Cheng K, and Johnson W 2001 Phys. Rev. A 64 042507 doi: 10.1103/PhysRevA.64.042507 -
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