Quantum-electrodynamic contributions to Spin–orbit splitting in the ground state of aluminumlike ions

Y.-K. Kim; J. Sugar; V. Kaufman; M. A. Ali

doi:10.1364/JOSAB.5.002225

Journal of the Optical Society of America B
Vol. 5,
Issue 10,
pp. 2225-2229
(1988)
•https://doi.org/10.1364/JOSAB.5.002225

Quantum-electrodynamic contributions to Spin–orbit splitting in the ground state of aluminumlike ions

Y.-K. Kim, J. Sugar, V. Kaufman, and M. A. Ali

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Y.-K. Kim, J. Sugar, V. Kaufman, and M. A. Ali, "Quantum-electrodynamic contributions to Spin–orbit splitting in the ground state of aluminumlike ions," J. Opt. Soc. Am. B 5, 2225-2229 (1988)

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Abstract

It is shown that the inclusion of quantum-electrodynamic corrections for the M-shell electrons substantially improves the agreement between multiconfiguration Dirac–Fock calculations and experimental values of the Spin–orbit splitting in the ground state (3s²3p ²P) of Al-like ions. Recommended values of the Spin–orbit splitting are presented for Co¹⁴⁺–Xe⁴¹⁺.

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Ion	Z	MCDF	Nonrelativistic Offset	Theory	Experiment	Ref.	Theory –Exp	MCDF –Exp	Huang
Al	13	697	582	115	112.061 ±0.010	19	3	585	697
Si⁺	14	684	−398	286	287.24 ±0.015	20	−1	397	683
P²⁺	15	860	−308	552	559.1 ± 1.0	21	−7	301	859
S³⁺	16	1191	−254	937	951.985 ± 0.009	22	−15	239	1189
Cl⁴⁺	17	1688	−217	1471	1 492 ± 2	23	−21	196	1685
Ar⁵⁺	18	2 373	−192	2181	2 210 ± 3	23	−29	163	2 368
K⁶⁺	19	3 274	−173	3101	3 134 ± 1	24	−33	140	3 267
Ca⁷⁺	20	4 424	−160	4 264	4 308.3 ± 1	24	−44	116	4 415
Sc⁸⁺	21	5 862	−150	5 712	5 761.1 ±4	24	−49	101	5 849
Ti⁹⁺	22	7 626	−142	7 484	7 543 ± 4	24	−59	83	7 610
V¹⁰⁺	23	9 760	−136	9 624	9 696 ± 5	24	−72	64	9 741
Cr¹¹⁺	24	12 313	−133	12180	12 261 ± 1	24	−81	52	12 288
Mn¹²⁺	25	15 335	−129	15 206	15 295 ± 1	24	−89	40	15 303
Fe¹³⁺	26	18 878	−127	18 751	18 852 ± 5	24	−101	26	18 839
Co¹⁴⁺	27	23 000	−125	22 875	22 970 ± 50	24	−95	30	22 951
Ni¹⁵⁺	28	27 760	−124	27 636	27 761 ± 3	25	−125	−1	27 702
Cu¹⁶⁺	29	33 223	−123	33100	33 239 ± 11	1	−139	−16	33152
Zn¹⁷⁺	30	39 455	−122	39 333	39 490 ± 16	1	−157	−35	39 371
Ga¹⁸⁺	31	46 529	−123	46 406	46 584 ± 20	1	−178	−55	46 429
Ge¹⁹⁺	32	54 517	−122	54 395	54 579 ± 30	1	−184	−62	54 398
As²⁰⁺	33	63 498	−123	63 375	63 565 ± 40	1	−190	−67	63 358
Se²¹⁺	34	73 554	−123	73 431	73 629 ± 30	1	−198	−75	73 390
Br²²⁺	35	84 772	−123	84 649	84 849 ± 30	1	−200	−77	84 580
Kr²³⁺	36	97 239	−125	97114	97 312 ± 30	1	−198	−73	97 017
Rb²⁴⁺	37	111 053	−124	110 929	111 140 ± 50	1^a	−211	−87	110 796
Sr²⁵⁺	38	126 310	−125	126 185	126 400 ± 50	1^a	−215	−90	126 013
Y²⁶⁺	39	143 113	−125	142 988	143 204 ± 40	1	−216	−91	142 773
Zr²⁷⁺	40	161 570	−126	161 444	161 680 ± 50	1	−236	−110	161182
Nb²⁸⁺	41	181 793	−127	181 666	181 920 ± 50	1	−254	−127	181 353
Mo²⁹⁺	42	203 901	−127	203 774	204 020 ± 50	1	−246	−119	203 398
Tc³⁰⁺	43	228 011	−127	227 884					227 443
Ru³¹⁺	44	254 256	−128	254 128					253 612
Rh³²⁺	45	282 765	−129	282 636					282 039
Pd³³⁺	46	313 676	−130	313 546					312 858
Ag³⁴⁺	47	347 134	−131	347 003	347 460 ± 60	26	−457	−326	346 215
Cd³⁵⁺	48	383 287	−132	383 155					382 254
In³⁶⁺	49	422 290	−132	422 158					421135
Sn³⁷⁺	50	464 304	−132	464 172					463 017
Sb³⁸⁺	51	509 499	−133	509 366					508 067
Te³⁹⁺	52	558 046	−134	557 912					556 458
I⁴⁰⁺	53	610 134	−134	610 000					608 371
Xe⁴¹⁺	54	665 947	−136	665 811					663 995

Ion	Z	Recommended Value (cm⁻¹)^a	Ion	Z	Recommended Value (cm⁻¹)^a
Co¹⁴⁻	27	22 984	Ni¹⁵⁺	28	27 756
Cu¹⁶⁺	29	33 231	Zn¹⁷⁺	30	39 475
Ga¹⁸⁺	31	46 559	Ge¹⁹⁺	32	54 559
As²⁰⁺	33	63 550	Se²¹⁺	34	73 617
Br²²⁺	35	84 846	Kr²³⁺	36	97 322
Rb²⁴⁺	37	111 148	Sr²⁵⁺	38	126 415
Y²⁶⁺	39	143 229	Zr²⁷⁺	40	161696
Nb²⁸⁺	41	181 929	Mo²⁹⁺	42	204 048
Tc³⁰⁺	43	228 169	Ru³¹⁺	44	254 424
Rh³²⁺	45	282 943	Pd³³⁺	46	313 864
Ag³⁴⁺	47	347 332	Cd³⁵⁺	48	383 495
In³⁶⁺	49	422 509	Sn³⁷⁺	50	464 534
Sb³⁸⁺	51	509 739	Te³⁹⁺	52	558 296
I⁴⁰⁺	53	610 395	Ze⁴¹⁺	54	666 217

Ion	Z	MCDF	Nonrelativistic Offset	Theory	Experiment	Ref.	Theory –Exp	MCDF –Exp	Huang
Al	13	697	582	115	112.061 ±0.010	19	3	585	697
Si⁺	14	684	−398	286	287.24 ±0.015	20	−1	397	683
P²⁺	15	860	−308	552	559.1 ± 1.0	21	−7	301	859
S³⁺	16	1191	−254	937	951.985 ± 0.009	22	−15	239	1189
Cl⁴⁺	17	1688	−217	1471	1 492 ± 2	23	−21	196	1685
Ar⁵⁺	18	2 373	−192	2181	2 210 ± 3	23	−29	163	2 368
K⁶⁺	19	3 274	−173	3101	3 134 ± 1	24	−33	140	3 267
Ca⁷⁺	20	4 424	−160	4 264	4 308.3 ± 1	24	−44	116	4 415
Sc⁸⁺	21	5 862	−150	5 712	5 761.1 ±4	24	−49	101	5 849
Ti⁹⁺	22	7 626	−142	7 484	7 543 ± 4	24	−59	83	7 610
V¹⁰⁺	23	9 760	−136	9 624	9 696 ± 5	24	−72	64	9 741
Cr¹¹⁺	24	12 313	−133	12180	12 261 ± 1	24	−81	52	12 288
Mn¹²⁺	25	15 335	−129	15 206	15 295 ± 1	24	−89	40	15 303
Fe¹³⁺	26	18 878	−127	18 751	18 852 ± 5	24	−101	26	18 839
Co¹⁴⁺	27	23 000	−125	22 875	22 970 ± 50	24	−95	30	22 951
Ni¹⁵⁺	28	27 760	−124	27 636	27 761 ± 3	25	−125	−1	27 702
Cu¹⁶⁺	29	33 223	−123	33100	33 239 ± 11	1	−139	−16	33152
Zn¹⁷⁺	30	39 455	−122	39 333	39 490 ± 16	1	−157	−35	39 371
Ga¹⁸⁺	31	46 529	−123	46 406	46 584 ± 20	1	−178	−55	46 429
Ge¹⁹⁺	32	54 517	−122	54 395	54 579 ± 30	1	−184	−62	54 398
As²⁰⁺	33	63 498	−123	63 375	63 565 ± 40	1	−190	−67	63 358
Se²¹⁺	34	73 554	−123	73 431	73 629 ± 30	1	−198	−75	73 390
Br²²⁺	35	84 772	−123	84 649	84 849 ± 30	1	−200	−77	84 580
Kr²³⁺	36	97 239	−125	97114	97 312 ± 30	1	−198	−73	97 017
Rb²⁴⁺	37	111 053	−124	110 929	111 140 ± 50	1^a	−211	−87	110 796
Sr²⁵⁺	38	126 310	−125	126 185	126 400 ± 50	1^a	−215	−90	126 013
Y²⁶⁺	39	143 113	−125	142 988	143 204 ± 40	1	−216	−91	142 773
Zr²⁷⁺	40	161 570	−126	161 444	161 680 ± 50	1	−236	−110	161182
Nb²⁸⁺	41	181 793	−127	181 666	181 920 ± 50	1	−254	−127	181 353
Mo²⁹⁺	42	203 901	−127	203 774	204 020 ± 50	1	−246	−119	203 398
Tc³⁰⁺	43	228 011	−127	227 884					227 443
Ru³¹⁺	44	254 256	−128	254 128					253 612
Rh³²⁺	45	282 765	−129	282 636					282 039
Pd³³⁺	46	313 676	−130	313 546					312 858
Ag³⁴⁺	47	347 134	−131	347 003	347 460 ± 60	26	−457	−326	346 215
Cd³⁵⁺	48	383 287	−132	383 155					382 254
In³⁶⁺	49	422 290	−132	422 158					421135
Sn³⁷⁺	50	464 304	−132	464 172					463 017
Sb³⁸⁺	51	509 499	−133	509 366					508 067
Te³⁹⁺	52	558 046	−134	557 912					556 458
I⁴⁰⁺	53	610 134	−134	610 000					608 371
Xe⁴¹⁺	54	665 947	−136	665 811					663 995

Ion	Z	Recommended Value (cm⁻¹)^a	Ion	Z	Recommended Value (cm⁻¹)^a
Co¹⁴⁻	27	22 984	Ni¹⁵⁺	28	27 756
Cu¹⁶⁺	29	33 231	Zn¹⁷⁺	30	39 475
Ga¹⁸⁺	31	46 559	Ge¹⁹⁺	32	54 559
As²⁰⁺	33	63 550	Se²¹⁺	34	73 617
Br²²⁺	35	84 846	Kr²³⁺	36	97 322
Rb²⁴⁺	37	111 148	Sr²⁵⁺	38	126 415
Y²⁶⁺	39	143 229	Zr²⁷⁺	40	161696
Nb²⁸⁺	41	181 929	Mo²⁹⁺	42	204 048
Tc³⁰⁺	43	228 169	Ru³¹⁺	44	254 424
Rh³²⁺	45	282 943	Pd³³⁺	46	313 864
Ag³⁴⁺	47	347 332	Cd³⁵⁺	48	383 495
In³⁶⁺	49	422 509	Sn³⁷⁺	50	464 534
Sb³⁸⁺	51	509 739	Te³⁹⁺	52	558 296
I⁴⁰⁺	53	610 395	Ze⁴¹⁺	54	666 217

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Journal of the Optical Society of America B