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The wave functions, energy levels, and oscillator strengths of B 2+ions and B +ions are calculated by using a relativistic potential model, which is named the relativistic configuration interaction plus core polarization (RCICP) method.The presently calculated energy levels are in very good agreement with experimental energy levels tabulated in NIST Atomic Spectra Database, with difference no more than 0.05%.The presently calculated oscillator strengths agree very well with NIST and some available theoretical results. The difference is no more than 0.6%. By using these energy levels and oscillator strengths, the electric-dipole static polarizability of the 2s 1/2, 2p 1/2, 2p 3/2, and 3s 1/2state and static hyperpolarizability of the ground state 2s 1/2for B 2+ion, as well as electric-dipole static polarizability of the 2s 2 1S 0state and 2s2p 3P 0state for B +ion are determined, respectively. The polarizability of the 2p 1/2state and 2p 3/2state of B 2+ion are negative. The main reason is that the absorption energy of the 2p 1/2,3/2→ 2s 1/2resonance transition is negative. The contribution to the polarizability of the 2p 1/2state and 2p 3/2state are both negative. For the tensor polarizability of the 2p 3/2state, the main contribution from the 2p 3/2→ 2s 1/2transition and 2p 3/2→ 3d 5/2transition are 2.4963 a.u. and –0.2537 a.u., respectively, and the present RCICP result is 2.1683 a.u. The largest contribution to the hyperpolarizability of the ground state 2s 1/2originates from the term of
$ {\alpha }^{1}{\beta }_{0} $ . The electric-dipole static polarizability of the 2s 2 1S 0state and 2s2p 3P 0state of B +ion are 9.6220 a.u. and 7.7594 a.u., respectively. The presently calculated blackbody radiation (BBR) shift of the 2s2p 3P 0→ 2s 2 1S 0clock transition is 0.01605 Hz. This BBR shift is one or two orders of magnitude smaller than that for alkaline-earth-metal atom.-
Keywords:
- electric-dipole polarizability/
- hyperpolarizability/
- B2+ions/
- B+ions
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State j $ {\rho }_{l, j} $ 2s 1/2 0.72951 2p 1/2 0.67398 3/2 0.67164 3d 3/2 0.91441 5/2 0.91355 
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State j RCICP Expt.[33] Diff./% 2s 1/2 –1.3939235 –1.3939235 0 2p 1/2 –1.1735867 –1.1735867 0 3/2 –1.1734313 –1.1734313 0 3s 1/2 –0.5728008 –0.5728632 0.01 3p 1/2 –0.5146980 –0.5147730 0.01 3/2 –0.5146520 –0.5147274 0.01 3d 3/2 –0.5005686 –0.5005686 0 5/2 –0.5005553 –0.5005553 0 4s 1/2 –0.3108609 –0.3108905 0.01 4p 1/2 –0.2874707 –0.2875098 0.01 3/2 –0.2874514 –0.2874920 0.01 4d 3/2 –0.2815308 –0.2815324 0 5/2 –0.2815252 –0.2815268 0 4f 5/2 –0.2812848 –0.2812705 0.01 7/2 –0.2812820 –0.2812676 0.01 5s 1/2 –0.1948639 –0.1948793 0.01 5p 1/2 –0.1831864 –0.1832067 0.01 3/2 –0.1831765 –0.1831970 0.01 5d 3/2 –0.1801535 –0.1801552 0 5/2 –0.1801507 –0.1801523 0 5f 5/2 –0.1800204 –0.1800138 0 7/2 –0.1800190 –0.1800124 0 DownLoad:
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Transitions RCICP RMBPT[42] HR[43] NIST[41] Diff./% 2s1/2→2p1/2 0.121251 0.121101 0.121076 0.12099 0.22 2s1/2→2p3/2 0.242723 0.242501 0.242399 0.24215 0.24 2s1/2→3p1/2 0.051084 0.05108 0.01 2s1/2→3p3/2 0.102061 0.10240 0.33 2p1/2→3s1/2 0.046308 0.046288 0.04636 0.11 2p1/2→3d3/2 0.637937 0.63800 0.01 2p1/2→4s1/2 0.008193 0.008233 0.49 2p1/2→4d3/2 0.122573 0.12280 0.19 2p3/2→3s1/2 0.046346 0.046338 0.04636 0.03 2p3/2→3d3/2 0.063806 0.06381 0.01 2p3/2→3d5/2 0.574284 0.57430 0 2p3/2→4s1/2 0.008198 0.008236 0.46 2p3/2→4d3/2 0.012256 0.01228 0.20 2p3/2→4d5/2 0.110323 0.11050 0.16 3s1/2→3p1/2 0.203293 0.20310 0.10 3s1/2→3p3/2 0.406942 0.4068 0.04 3s1/2→4p1/2 0.048745 0.04850 0.51 3s1/2→4p3/2 0.097357 0.09700 0.37 DownLoad:
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2s1/2 2p1/2 2p3/2 3s1/2 Contr. $ {\alpha }_{}^{{\rm{S}}} $ FCPC[44] Contr. $ {\alpha }_{}^{{\rm{S}}} $ Contr. $ {\alpha }_{}^{{\rm{S}}} $ $ {\alpha }^{{\rm{T}}} $ Contr. $ {\alpha }_{}^{{\rm{S}}} $ 2p1/2 2.4975 2.4953[44] 2s1/2 –2.4975 2s1/2 –2.4963 2.4963 3p1/2 60.218 2p3/2 4.9926 4.9872[44] 3d3/2 1.4084 3d5/2 1.2684 –0.2537 3p3/2 120.35 Remains 0.3433 0.3453[44] Remains 0.4959 Remains 0.6371 –0.0743 Remains 2.3125 Core[30] 0.0195 0.0195[44] Core 0.0195 Core 0.0195 Core 0.0195 Total 7.8529 7.8473[44] Total –0.5737 Total –0.5713 2.1683 Total 182.90 CICP[45] 7.8460 –0.56938 182.94 SCC[46] 7.85 FCG[47] 7.8591 DownLoad:
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Contributions $ {\gamma }_{0}\left(2{\rm{s}}\right) $ $ {\gamma }_{0}^{{\rm{C}}}\left(2{\rm{s}}\right) $ $ \dfrac{1}{18}T({\rm{s}}, {{\rm{p}}}_{1/2}, {\rm{s}}, {{\rm{p}}}_{1/2}) $ 1.251(1) 1.250 $ -\dfrac{1}{18}T({\rm{s}}, {{\rm{p}}}_{1/2}, {\rm{s}}, {{\rm{p}}}_{3/2}) $ 2.501(1) 2.500 $ -\dfrac{1}{18}T({\rm{s}}, {{\rm{p}}}_{3/2}, {\rm{s}}, {{\rm{p}}}_{1/2}) $ 2.501(1) 2.500 $ \dfrac{1}{18}T({\rm{s}}, {{\rm{p}}}_{3/2}, {\rm{s}}, {{\rm{p}}}_{3/2}) $ 5.001(1) 5.000 $T({\rm{s} }, { {\rm{p} } }_{ {j}^{'} }, {\rm{s} }, { {\rm{p} } }_{ {j}^{''} })$ 11.255(5) 11.250 $\dfrac{1}{18}T({\rm{s} }, { {\rm{p} } }_{1/2}{, {\rm{d} } }_{3/2}, { {\rm{p} } }_{1/2})$ 9.588(8) 9.580 $\dfrac{1}{18\sqrt{10} }T({\rm{s} }, { {\rm{p} } }_{1/2}{, {\rm{d} } }_{3/2}, { {\rm{p} } }_{3/2})$ 1.917(2) 1.915 $\dfrac{1}{18\sqrt{10} }T({\rm{s} }, { {\rm{p} } }_{3/2}{, {\rm{d} } }_{3/2}, { {\rm{p} } }_{1/2})$ 1.917(2) 1.915 $\dfrac{1}{180}T({\rm{s} }, { {\rm{p} } }_{3/2}{, {\rm{d} } }_{3/2}, { {\rm{p} } }_{3/2})$ 0.383(1) 0.382 $\dfrac{1}{30}T({\rm{s} }, { {\rm{p} } }_{3/2}{, {\rm{d} } }_{5/2}, { {\rm{p} } }_{3/2})$ 20.692(16) 20.676 $T({\rm{s} }, { {\rm{p} } }_{ {j}^{'} }{, {\rm{d} } }_{j}, { {\rm{p} } }_{ {j}^{''} })$ 34.497(28) 34.469 $ {\alpha }^{1}{\beta }_{0} $ 134.364(586) 133.778 RCICP –1063.346(6.645) –1056.701 UCHF[50] –1160 CHF[49] –1120 DownLoad:
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State RCICP Expt.[51] Diff./% 2$ {{\rm{s}}}^{2}{{}_{}{}^{1}{\rm{S}}}_{0} $ –2.318347 –2.318347 0 2s2p$ {{}_{}{}^{3}{\rm{P}}}_{0} $ –2.148235 –2.148233 0 2s2p$ {{}_{}{}^{3}{\rm{P}}}_{1} $ –2.148205 –2.148205 0 2s2p$ {{}_{}{}^{3}{\rm{P}}}_{2} $ –2.148178 –2.148132 0 2s2p$ {{}_{}{}^{1}{\rm{P}}}_{1} $ –1.9832 –1.983927 0.03 2$ {{\rm{p}}}^{2}{{}_{}{}^{3}{\rm{P}}}_{0} $ –1.867621 –1.867673 0 2$ {{\rm{p}}}^{2}{{}_{}{}^{3}{\rm{P}}}_{1} $ –1.867634 –1.867634 0 2$ {{\rm{p}}}^{2}{{}_{}{}^{3}{\rm{P}}}_{2} $ –1.867565 –1.867573 0 2$ {{\rm{p}}}^{2}{{}_{}{}^{1}{\rm{D}}}_{2} $ –1.852917 –1.851947 0.05 2$ {{\rm{p}}}^{2}{{}_{}{}^{1}{\rm{S}}}_{0} $ –1.736452 –1.736679 0.01 2s3s $ {{}_{}{}^{3}{\rm{S}}}_{1} $ –1.727042 –1.727053 0 2s3s $ {{}_{}{}^{1}{\rm{S}}}_{0} $ –1.690800 –1.691293 0.03 2s3p $ {{}_{}{}^{3}{\rm{P}}}_{0} $ –1.662206 –1.662280 0 2s3p $ {{}_{}{}^{3}{\rm{P}}}_{1} $ –1.662167 –1.662277 0.01 2s3p $ {{}_{}{}^{3}{\rm{P}}}_{2} $ –1.662006 –1.662261 0.02 2s3p $ {{}_{}{}^{1}{\rm{P}}}_{1} $ –1.661601 –1.661765 0.01 2s3d $ {{}_{}{}^{3}{\rm{D}}}_{1} $ –1.631934 –1.631936 0 2s3d $ {{}_{}{}^{3}{\rm{D}}}_{2} $ –1.631720 –1.631936 0.01 2s3d $ {{}_{}{}^{1}{\rm{D}}}_{2} $ –1.613116 –1.613545 0.03 $ 2{\rm{s}}4{\rm{s}}{{}_{}{}^{3}{\rm{S}}}_{1} $ –1.560411 –1.560423 0 $ 2{\rm{s}}4{\rm{s}}{{}_{}{}^{1}{\rm{S}}}_{0} $ –1.552914 –1.553177 0.02 $ 2{\rm{s}}4{\rm{p}} $ $ {{}_{}{}^{1}{\rm{P}}}_{1} $ –1.540973 –1.541075 0.01 $ 2{\rm{s}}4{\rm{p}} $ $ {{}_{}{}^{3}{\rm{P}}}_{1} $ –1.5366 –1.5367 0.01 $ 2{\rm{s}}4{\rm{p}} $ $ {{}_{}{}^{3}{\rm{P}}}_{2} $ –1.536439 –1.536726 0.02 $ 2{\rm{s}}4{\rm{p}} $ $ {{}_{}{}^{3}{\rm{P}}}_{0} $ –1.536693 –1.536726 0 $ 2{\rm{s}}4{\rm{d}} $ $ {{}_{}{}^{3}{\rm{D}}}_{2} $ –1.524938 –1.525210 0.02 $ 2{\rm{s}}4{\rm{d}} $ $ {{}_{}{}^{3}{\rm{D}}}_{1} $ –1.525198 –1.525210 0 DownLoad:
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Transition RCICP CICP[45] BCICP[52] MCHF-BP[53] MCHF[54] NIST.[41] 2s2 1S0→2s2p1P1 1.00092 0.99907 1.002 1.001 0.9976(22) 0.9990 2s2 1S0→2s3p1P1 0.10829 0.10959 0.108 0.1087 0.1093(3) 0.1090 2s2 1S0→2s4p1P1 0.05331 0.0530 0.0514 2s2 1S0→2s5p1P1 0.02244 0.0230 0.0241 2s2p3P0→2p23P1 0.34113 0.34298 0.365 0.3430 0.3427(2) 0.3400 2s2p3P0→2s3s3S1 0.06437 0.06377 0.06397 0.0640 2s2p3P0→2s3d3D1 0.47657 0.47627 0.473 0.4759 0.4750 2s2p3P0→2s4s3S1 0.01170 0.0115 2s2p3P0→2s4d3D1 0.12480 0.125 0.1260 DownLoad:
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2s2 1S0 2s2p3P0 Contributions polarizability/a.u. Contributions polarizability/a.u. 2s2 1S0→2s2p1P1 8.9149 2s2p3P0→2p2p3P1 4.3326 2s2 1S0→2s3p1P1 0.2511 2s2p3P0→2s3d3D1 1.7878 Remains 0.4365 Remains 1.6195 Core 0.0195 Core 0.0195 RCICP 9.6220 RCICP 7.7594 CI[55] 9.5750 CI[55] 7.7790 CI+MBPT[55] 9.6130 CI+MBPT[55] 7.7690 CI+all-orders[55] 9.6240 CI+all-order[55] 7.7720 CCD+ST[56] 9.5660 CICP[45] 9.6441 CICP[45] 7.7798 PRCC[29] 9.4130 CCSDpT[57] 10.395(22) RRV[58] 9.6210 DownLoad:
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