Tables of Atomic Transition Probabilities for Beryllium and Boron J. R. Fuhra… and W. L. Wiese National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA ͑Received 11 December 2009; accepted 11 December 2009; published online 12 March 2010͒ We have carried out a comprehensive critical compilation of the atomic transition probabilities for the spectra of beryllium and boron. We tabulated these data for a total of about 1400 allowed and forbidden transitions and covered all stages of ionization. The hydrogenlike ions are included with relations scaled to the data for neutral hydrogen. The tables are arranged in multiplets, and these are ordered in increasing excitation energies. © 2010 U.S. Secretary of Commerce on behalf of the United States. All rights reserved.. ͓doi:10.1063/1.3286088͔ Key words: allowed and forbidden transitions; atomic transition probabilities; oscillator strengths; f values; line strengths; beryllium; boron. CONTENTS 5. References............................... 79 List of symbols. .............................. 2 1. Introduction.............................. 2 List of Tables 1.1. Overview............................ 2 1. Comparison of dipole-length oscillator strength 1.2. Useful relations....................... 3 data ͑gf-values͒ for Be I.................... 4 2. Beryllium................................ 4 2. List of tabulated lines for allowed transitions 2.1. Be I................................. 4 of Be I.................................. 5 2.1.1. Be I allowed transitions........... 4 3.BeI: Allowed transitions.................... 6 2.1.2. Be I forbidden transitions. ......... 17 4.BeI: Forbidden transitions.................. 17 2.2. Be II................................ 18 5. Comparison of calculated multiplet oscillator 2.2.1. Be II allowed transitions........... 18 strength results ͑dipole-length values͒ for a 2.2.2. Be II forbidden transitions......... 24 few key transitions of Be II, where the selected 2.3. Be III................................ 25 sources overlap........................... 18 2.3.1. Be III allowed transitions.......... 25 6. List of tabulated lines for allowed transitions 2.3.2. Be III forbidden transitions......... 34 of Be II.................................. 18 2.4. Be IV............................... 36 7.BeII: Allowed transitions................... 19 2.4.1. Be IV allowed transitions.......... 36 8.BeII: Hyperfine structure, magnetic dipole 3. Boron................................... 37 transition................................ 24 3.1. B I................................. 37 9.BeII: Forbidden transitions.................. 25 3.1.1. B I allowed transitions............ 37 10. List of tabulated lines for allowed transitions 3.1.2. B I forbidden transitions........... 47 of Be III................................. 25 3.2. B II................................. 47 11.BeIII: Allowed transitions................... 26 3.2.1. B II allowed transitions............ 47 12. List of tabulated lines for forbidden transitions 3.2.2. B II forbidden transitions. ......... 61 of Be III................................. 34 3.3. B III................................ 63 13.BeIII: Forbidden transitions................. 35 3.3.1. B III allowed transitions. .......... 63 14. Comparison of experimental and theoretical 3.3.2. B III forbidden transitions.......... 68 lifetime data ͑in ns͒ for B I.................. 37 3.4. B IV................................ 68 15. List of tabulated lines for allowed transitions 3.4.1. B IV allowed transitions........... 68 of B I................................... 37 3.4.2. B IV forbidden transitions......... 77 16.BI: Allowed transitions.................... 39 3.5. B V................................. 79 17.BI: Isotopes, hyperfine structure, magnetic 3.5.1. B V allowed transitions........... 79 dipole transition........................... 47 4. Acknowledgments......................... 79 18.BI: Forbidden transitions................... 47 19. Oscillator strengths for B II. Comparison of a͒ calculated and measured oscillator strengths Electronic mail: [email protected] © 2010 U.S. Secretary of Commerce on behalf of the United States. All for three strong transitions and a weak rights reserved.. intercombination line. All experimental data 0047-2689/2010/39„1…/013101/80/$47.00013101-1 J. Phys. Chem. Ref. Data, Vol. 39, No. 1, 2010 013101-2 J. R. FUHR AND W. L. WIESE are based on lifetime measurements. The For E2 transitions: 4 2 ϫ −79 4 2 calculated data are dipole-length values and a0e =2.0129 10 m C , the Tachiev and Froese Fischer data contain, in For M1 transitions: ͑ ͒ ␮2 ͑ / ␲ ͒2 ϫ −47 2 −2 parentheses, the relative differences in % B = eh 4 me =8.6007 10 J T , between their dipole length and dipole velocity For M2 transitions: ␮2 2 ϫ −67 2 2 −2 results, an indicator of their accuracy.......... 48 Ba0 =2.4085 10 J m T , 20. List of tabulated lines for allowed transitions where a0, e, me, and h are the Bohr radius, electron charge, ␮ of B II................................... 48 electron mass, and Planck constant, respectively, and B is 21.BII: Allowed transitions.................... 51 the Bohr magneton. 22. List of tabulated lines for forbidden transitions Note that for Ei and Ek, the customary unit for atomic of B II................................... 61 energy levels, used here, is related to the SI unit for energy 23.BII: Forbidden transitions.................. 62 ͑J͒ by 1 cm−1=1.986ϫ10−23 J. 24. Comparison of calculated multiplet oscillator Abbreviations appearing in the column labeled Type ͑for- strength data for B III...................... 63 bidden lines only͒: 25. List of tabulated lines for allowed transitions M1: Magnetic dipole transition, of B III.................................. 63 E2: Electric quadrupole transition, 26.BIII: Allowed transitions................... 64 M2: Magnetic quadrupole transition. 27.BIII: Forbidden transitions.................. 68 Special symbols used in the wavelength and energy level 28. List of tabulated lines for allowed transitions columns: of B IV.................................. 69 Numbers in italics indicate multiplet values, i.e., weighted 29.BIV: Allowed transitions. ................. 70 averages of line values. 30. Comparison of oscillator strength results for Notation for exponents: some electric quadrupole ͑E2͒ transitions of In all tables, we have shown the power of ten by the ex- B IV from the calculations of Cann and ponential notation. For example, 3.88e−03 stands for 3.88 Thakkar ͑Ref. 31͒ and Godefroid and ϫ10−3. Verhagen ͑Ref. 32͒........................ 77 31. List of tabulated lines for forbidden transitions 1. Introduction of B IV.................................. 77 32.BIV: Forbidden transitions.................. 78 1.1. Overview In 1966, the first edition of reference data for the atomic List of symbols transition probabilities of the light elements hydrogen through neon, of atomic numbers 1 to 10, was published by Symbols for indication of data accuracy: the U. S. National Bureau of Standards ͑NBS͒, now the Na- AAA ϭ uncertainty less than Ϯ0.3% tional Institute of Standards and Technology ͑NIST͒.1 Since AA ϭ uncertainty less than Ϯ1% then, large amounts of much higher quality data have be- A ϭ uncertainty less than Ϯ3% come available for these quantities, most of them from ad- B ϭ uncertainty less than Ϯ10% vanced quantum mechanical calculations. This progress was C ϭ uncertainty less than Ϯ25% achieved with the development of sophisticated atomic struc- D ϭ uncertainty less than Ϯ50% ture codes coupled with the advent of much more powerful E ϭ uncertainty greater than Ϯ50%, but within computers. Our new edition of reference data for the first ten factors of 3 elements covers the various spectra much more extensively, Symbols used for the table headings: and thus the data tables are greatly expanded and are pub- ␭ϭWavelength ͑Å͒ ϭ ͑ −1͒ lished in several parts. Ei lower energy level cm −1 A first part, containing all spectra of carbon, nitrogen and E ϭ upper energy level ͑cm ͒ 2 k oxygen, was published in 1996, and an update for C I and g ϭ statistical weight of the lower level i C II as well as N I and N II, containing still further improved g ϭ statistical weight of the upper level k data sets, was published in 2007.3 A second part, containing A ϭ atomic transition probability for spontane- ki the spectra of hydrogen and its isotopes deuterium and tri- ous emission, in 108 s−1 for all E1 ͑allowed: tium, as well as helium and lithium and their ions, is in press electric dipole͒ transitions, in s−1 for all M1, and is expected to be published in 2009.4 M2, and E2 transitions This third part covers all the spectra of beryllium and bo- f ϭ absorption oscillator strength ik ron. The tabulated data are the results of advanced, and S ϭ line strength in atomic units; formulas and partly very extensive, atomic structure calculations. In sev- values for these quantities in SI units are as eral of these, the results are computed in two ways, the follows: dipole-length and the dipole-velocity formalisms. Ideally, For E1 transitions: these two results should be identical, but normally they differ 2 2 ϫ −59 2 2 a0e =7.1883 10 m C , due to various approximations in the calculations of the wave J. Phys. Chem. Ref. Data, Vol. 39, No. 1, 2010 TRANSITION FOR BERYLLIUM AND BORON 013101-3 functions. The magnitude of the difference is thus utilized as gL =2JL +1. a key indicator for the quality of the result. The dipole-length ͑ approximation is considered to be the more accurate one and Similarly,