X-ray spectroscopy of laser-produced L-series lines

P. G. Burkhalter; D. A. Newman; J. P. Knauer

doi:10.1364/JOSAB.6.001964

X-ray spectroscopy of laser-produced L-series lines

P. G. Burkhalter, D. A. Newman, and J. P. Knauer

Journal of the Optical Society of America B
Vol. 6,
Issue 11,
pp. 1964-1971
(1989)
•https://doi.org/10.1364/JOSAB.6.001964

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P. G. Burkhalter, D. A. Newman, and J. P. Knauer, "X-ray spectroscopy of laser-produced L-series lines," J. Opt. Soc. Am. B 6, 1964-1971 (1989)

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Abstract

High-intensity, frequency-tripled light from a multibeam laser system (OMEGA) was focused on targets in order to generate plasmas of highly ionized atoms. X-ray data were collected with high-resolution spectrographs. Accurate wavelength measurements of 2p–3d, 3s, 4d, and 4s lines in L-series spectra of transition elements were made. Classification of observed lines was based on atomic structure calculations in which the radial integrals, calculated ab initio, were adjusted with semiempirically determined scaling factors. The results are presented as isoelectronic sequences of the observed and calculated wavelengths for the Li-, Be-, and B-like spectra from atomic numbers 22 (Ti) through 32 (Ge).

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Number	Wavelength (Å)		gf	Trans.	Class.

	Expt.	Calc.
(1)	16.380	16.379	0.67	2s2p–2s3d	³P₀–³D₁
(2)	16.422	16.419	1.5	2s2p–2s3d	³P₁–³D₂

		16.424	0.50	2s2p–2s3d	³P₁–³D₁
(3)	16.526	16.527	2.8	2s2p–2s3d	³P₂–³D₃
		16.535	0.50	2s2p–2s3d	³P₂–³D₂
(4)	16.614^a	16.613	0.33	2p²–2p3d	³P₁–³P₀
(5)	16.630	16.620	0.68	2p²–2p3d	³P₁–³P₁
(6)	16.697	16.693	1.3	2p²–2p3d	³P₀–³D₁
(7)	16.704	16.701	0.41	2p²–2p3d	³P₂–³P_l
(8)	16.710	16.709	1.6	2p²–2p3d	³P₂–³P₂

		16.714	1.6	2p²–2p3d	³P₁–³D₂
(9)	16.739	16.745	3.6	2p²–2p3d	³P₂–³D₃
(10)	16.780^a	16.783	0.31	2p²–2p3d	³P₁–³D₁
(11)	16.802	16.802	5.2	2p²–2p3d	¹D₂–¹F₃
(12)	16.833	16.838	0.93	2p²–2p3d	³P₁–¹D₂
(13)	16.944	16.942	0.59	2p²–2p3d	³P₂–³F₃
		16.955	0.39	2p²–2p3d	¹D₂–³P₂
		17.175	0.34	2p²–2p3d	¹D₂–¹D₂
(14)	17.064	17.057	1.9	2s2p–2s3d	¹P₁–¹D₂
(15)	17.180	17.192	1.3	2p²–2p3d	¹S₀–¹P₁

Number	Wavelength (Å)		gf	Trans.	Class.

	Expt.	Calc.
(1)	8.879^a	8.882	0.68	2s2p–2s3d	³P₀–³D₁
(2)	8.912	8.914	1.5	2s2p–2s3d	³P₁–³D₂

		8.918	0.48	2s2p–2s3d	³P₁–³D₁
(3)	8.973	8.969	0.50	2p²–2p3d	³P₂–¹F₃
		8.971	0.34	2p²–2p3d	³P₁–³P₀
		8.973	0.77	2p²–2p3d	³P₁–³P₁
(4)	9.024	9.014	0.88	2p²–2p3d	³P₁–¹D₂
		9.019	1.3	2p²–2p3d	³P₀–³D₁

		9.022	0.87	2p²–2p3d	³P₂–³P₂
		9.029	2.8	2s2p–2s3d	³P₂–³D₃
(5)	9.037^a	9.039	0.49	2s2p–2s3d	³P₂–³D₂

		9.041	2.8	2p²–2p3d	³P₂–³D₃
		9.064	0.33	2p²–2p3d	³P₂–¹D₂
(6)	9.129	9.130	4.7	2p²–2p3d	¹D₂–¹F₃
(7)	9.141^b	9.147	1.6	2p²–2p3d	³P₁–³P₂
(8)	9.189^b	9.185	1.1	2p²–2p3d	¹D₂–³P₂
(9)	9.201^c	9.201	1.4	2p²–2p3d	³P₂–³F₃

		9.205	0.36	2p²–2p3d	¹D₂–³D₃
(10)	9.228^c	9.221	1.9	2s2p–2s3d	¹P₁–¹D₂
(11)	9.267^c	9.276	1.3	2p²–2p3d	¹S₀–¹P₁

Number	Wavelength (Å)		gf	Trans.	Class.

	Expt.	Calc.
(1)	7.164^a	7.155	0.68	2s2p–2s3d	³P₀–³D₁

		7.183	1.5	2s2p–2s3d	³P₁–³D₂
		7.188	0.47	2s2p–2s3d	³P₁–³D₁
		7.218	0.34	2p²–2p3d	³P₁–³P₀
		7.219	0.54	2p²–2p3d	³P₂–¹F₃
		7.220	0.79	2p²–2p3d	³P₁–³P₁
		7.249	0.82	2p²–2p3d	³P₁–¹D₂
(2)	7.263	7.256	0.65	2p²–2p3d	³P₂–³P₂
		7.257	1.3	2p²–2p3d	³P₀–³D1
		7.271	2.6	2p²–2p3d	³P₂–³D₃
		7.288	0.45	2p²–2p3d	³P₂–¹D₂
(3)	7.293	7.303	2.8	2s2p–2s3d	³P₂–³D₃
		7.313	0.49	2s2p–2s3d	³P₂–³D₂
(4)	7.375^b	7.375	4.6	2p²–2p3d	¹D₂–¹F₃
(5)	7.383^b	7.388	1.6	2p²–2p3d	³P₁–³P₂
(6)	7.412^b	7.414	1.3	2p²–2p3d	¹D₂–³P₂
		7.428	1.7	2p²–2p3d	³P₂–³F₃
		7.430	0.37	2p²–2p3d	¹D₂–³D₃
(7)	7.440^b	7.437	1.9	2s2p–2s3d	¹P₁–¹D₂
		7.477	1.3	2p²–2p3d	¹S₀–¹P₁

Number	Wavelength (Å)		gf	Classification

	Expt.	Calc.
(1)	17.092	17.093	1.7	²D_3/2–(¹P)²F_5/2
(2)	17.108	17.112	2.0	²D_5/2–(¹P)²F_7/2
(3)	17.149	17.150	0.68	⁴P_3/2–(³P)⁴P_1/2

		17.153	0.85	⁴P_3/2–(³P)⁴P_3/2
(4)	17.215	17.210	1.1	⁴P_1/2–(³P)⁴D_1/2

		17.216	1.4	⁴P_1/2–(³P)⁴D_3/2
(5)	17.237	17.238	0.67	⁴P_5/2–(³P)⁴P_3/2

		17.242	2.0	⁴P_5/2–(³P)⁴P_5/2
(6)	17.272	17.268	4.2	⁴p_5/2–(³p)⁴D_7/2
(7)	17.287	17.286	0.46	⁴P_3/2–(³P)⁴D_3/2
(8)	17.300	17.301	1.9	⁴P_3/2–(³P)⁴P_5/2
(9)	17.346	17.353	0.49	²S_1/2–(¹P)²P_1/2
(10)	17.441	17.436	0.53	⁴P_5/2–(³P)⁴F_7/2
(11)	17.516	17.522	0.49	²P_1/2–(¹P)²P_3/2
(12)	17.590^a	17.577	0.80	²P_3/2–(¹P)²P_3/2

		17.617	1.1	²P_1/2–(¹P)²D_3/2
(13)	17.640^a	17.633	4.1	²D_5/2–(³P)²F_7/2

		17.649	2.9	²P_3/2–(¹P)²D_5/2
(14)	17.721	17.719	1.8	²D_3/2–(³P)²F_5/2
(15)	17.738	17.738	0.57	²D_5/2–(³P)²F_5/2
(16)	17.991	18.001	0.94	²S_1/2–(³P)²P_3/2

Number	Wavelength (Å)		gf	Classification

	Expt.	Calc.
(1)	11.742	11.731	1.9	²D_3/2–(¹P)²F_5/2
		11.739	0.70	⁴P_3/2–(³P)⁴P_1/2

		11.741	0.95	⁴P_3/2–(³P)⁴P_3/2
		11.746	0.55	⁴P_3/2–(³P)⁴D_5/2
		11.762	1.8	²D_5/2–(¹P)²F_7/2
(2)	11.789	11.789	1.1	⁴P_1/2–(³P)⁴D_1/2

		11.794	1.4	⁴P_1/2–(³P)⁴D_3/2
(3)	11.824^a	11.823	2.0	⁴P_5/2–(³P)⁴D_5/2
(4)	11.837	11.834	3.8	⁴P_5/2–(³P)⁴D_7/2

		11.848	0.52	²P_1/2–(¹P)²P_1/2
(5)	11.883	11.887	1.7	⁴P_3/2–(³P)⁴P_5/2

		11.890	0.65	²P_1/2–(¹P)²D_3/2
(6)	11.981	11.975	0.97	⁴P_5/2–(³P)⁴F_7/2
(7)	12.008	12.005	0.58	²S_1/2–(¹P)²P_3/2
(8)	12.046	12.040	4.2	²D_5/2–(³P)²F_7/2
(9)	12.081	12.072	3.0	²P_3/2–(¹P)²D_5/2

		12.084	0.85	²D_3/2–(³P)²F_5/2
(10)	12.102	12.095	0.32	²P_3/2–(¹P)²D_3/2

		12.119	0.95	²D_5/2–(³P)²F_5/2
(11)	12.203	12.195	1.3	²D_3/2–(³P)²D_5/2

		12.199	0.65	²P_1/2–(³P)²P_3/2

Number	Wavelength (Å)		gf	Classification

	Expt.	Calc.
(1)	9.201^a	9.190	1.0	⁴P_3/2–(³P)⁴P_3/2
		9.196	0.75	⁴P_3/2–(³P)⁴D_5/2
		9.196	2.0	²D_3/2–(¹P)²F_5/2
(2)	9.228^a	9.234	1.1	⁴P_1/2–(³P)⁴D_1/2
		9.238	1.4	⁴P_1/2–(³P)⁴D_3/2
		9.239	1.7	²D_5/2–(¹P)²F_7/2
(3)	9.254	9.259	0.53	²P_1/2–(¹P)²P_1/2

		9.260	0.61	⁴P_5/2–(³P)⁴P_3/2
(4)	9.267^a	9.265	1.9	⁴P_5/2–(³P)⁴D_5/2

		9.270	3.5	⁴P_5/2–(³P)⁴D_7/2
(5)	9.292	9.287	0.69	²P_1/2–(¹P)²D_3/2
(6)	9.375	9.375	0.47	⁴P_3/2–(³P)⁴F_5/2
(7)	9.424	9.423	4.3	²D_5/2–(³P)²F_7/2
(8)	9.462	9.458	3.1	²P_3/2–(¹P)²D_5/2

		9.461	0.78	²S_1/2–(¹P)²D_3/2
(9)	9.540	9.544	1.7	²D_3/2–(³P)²F_5/2
(10)	9.657	9.654	0.76	²P_1/2–(³P)²D_3/2
(11)	9.696	9.694	0.30	²P_3/2–(³P)²P_3/2
(12)	9.738	9.730	0.25	³P_3/2–(²P)²D_5/2

Number	Wavelength (Å)		gf	Classification

	Expt.	Calc.
(1)	7.375^a	7.379	1.0	⁴P_3/2–(³P)⁴P_3/2
(2)	7.384^a	7.392	2.1	²D_3/2–(¹P)²F_5/2
(3)	7.412^a	7.418	1.1	⁴P_1/2–(³P)⁴D_1/2
	7.440^a	7.440	0.56	⁴P_5/2–(³P)⁴P_3/2
(4)	7.446	7.445	1.7	⁴P_5/2–(³P)⁴D_5/2
		7.446	3.2	⁴P_5/2–(³P)⁴D_7/2
		7.448	1.5	²D_5/2–(¹P)²F_7/2
(5)	7.518	7.527	1.5	⁴P_3/2–(³P)⁴P_5/2
		7.554	0.16	²D_3/2–(³P)²D_5/2
(6)	7.576	7.575	4.3	²D_5/2–(³P)²F_7/2

		7.578	1.7	⁴P_5/2–(³P)⁴F_7/2
(7)	7.593	7.594	0.74	²P_3/2–(¹P)²P_3/2
(8)	7.612	7.608	3.2	²P_3/2–(¹P)²D_5/2
		7.617	1.3	²D_5/2–(³P)²D_5/2
		7.617	0.70	²S_1/2–(¹P)²D_3/2
(9)	7.671	7.674	1.8	²D_3/2–(³P)²F_5/2
(10)	7.776	7.778	0.30	²P_3/2–(³P)²P_3/2
(11)	7.797	7.801	0.27	²P_3/2–(³P)²D_5/2

Scale Factors	Radial Integral	Scaled Integrals (cm⁻¹)

		Ti xx	Fe xxiv	Cu xxvii	Ge xxx
1.0	$\frac{1 s^{2} 2 s}{E (average)}$	0.0	0.0	0.0	0.0
1.0	$\frac{1 s^{2} 2 p}{E (average)}$	0.0	0.0	0.0	0.0
0.97	Zeta 2p	40 245.590	83 637.863	134 465.00	206 007.25
0.998935	$\frac{1 s^{2} 3 s}{E (average)}$	6 100 564.0	8 789 462.9	11 129 035.0	13 746 345.0
0.998807	$\frac{1 s^{2} 3 p}{E (average)}$	6 568 317.4	9 402 710.0	11 877 313.0	14 658 491.0
1.0	Zeta 3p	12 271.200	25 523.399	41 058.998	62 943.001
0.999166	$\frac{1 s^{2} 3 d}{E (average)}$	6 247 425.3	8 987 377.0	11 375 604.0	14 052 970.0
0.77	Zeta 3d	1 784.7060	3 711.9391	5 960.5699	9 109.8700
0.999256	$\frac{1 s^{2} 4 d}{E (average)}$	8 384 728.5	12 065 717.0	15 272 629.0	18 865 654.0
0.90	Zeta 4d	879.8400	1 830.6000	2 940.3000	4 495.5001

Number	Class.	Ti XX		Fe XXIV		Cu XXVII		Ge XXX

		Expt.	Calc.	Expt.	Calc.	Expt.	Calc.	Expt.	Calc.
(1)	$\frac{2 s - 4 p}{{}^{2}{S_{1 / 2}} - {}^{2}{P_{3 / 2}}}$	11.448	11.453	7.990	7.987	6.320	6.319		5.118
(2)	²S_1/2–²P_1/2		11.463		7.998		6.329		5.128
(3)	$\frac{2 p - 4 d}{{}^{2}{P_{1 / 2}} - {}^{2}{D_{3 / 2}}}$	11.872	11.871	8.230	8.233	6.490	6.492		5.245
(4)	²P_3/2–²D_5/2	11.957	11.954	8.316	8.316	6.575	6.575	5.316	5.328
(5)	$\frac{2 s - 3 p}{{}^{2}{S_{1 / 2}} - {}^{2}{P_{3 / 2}}}$	15.214	15.210	10.616	10.621	8.402	8.405	6.800	6.807
(6)	²S_1/2–²P_1/2	15.257	15.253	10.658	10.664	8.445	8.449	6.842	6.851
(7)	$\frac{2 p - 3 d}{{}^{2}{P_{1 / 2}} - {}^{2}{D_{3 / 2}}}$	15.914	15.911	11.028	11.031	8.693	8.695	7.015	7.020
(8)	²P_3/2–²D_5/2	16.058	16.054	11.175	11.174	8.837	8.838	7.164^b	7.164
(9)	²P_3/2–²D_3/2	16.071	16.065		11.186	8.848	8.850		7.176
(10)	$\frac{2 p - 3 s}{{}^{2}{P_{1 / 2}} - {}^{2}{S_{3 / 2}}}$	16.285	16.284	11.263	11.270	8.879^a	8.878	7.164^b	7.167
(11)	²P_3/2–²S_1/2	16.444	16.446	11.439	11.432	9.037^a	9.040	7.342^c	7.330

Number	Class.	Ti XX		Fe XXIV		Cu XXVII		Ge XXX

		Expt.	Calc.	Expt.	Calc.	Expt.	Calc.	Expt.	Calc.
(1)	$\frac{2 s - 4 p}{{}^{2}{S_{1 / 2}} - {}^{2}{P_{3 / 2}}}$	11.448	11.453	7.990	7.987	6.320	6.319		5.118
(2)	²S_1/2–²P_1/2		11.463		7.998		6.329		5.128
(3)	$\frac{2 p - 4 d}{{}^{2}{P_{1 / 2}} - {}^{2}{D_{3 / 2}}}$	11.872	11.871	8.230	8.233	6.490	6.492		5.245
(4)	²P_3/2–²D_5/2	11.957	11.954	8.316	8.316	6.575	6.575	5.316	5.328
(5)	$\frac{2 s - 3 p}{{}^{2}{S_{1 / 2}} - {}^{2}{P_{3 / 2}}}$	15.214	15.210	10.616	10.621	8.402	8.405	6.800	6.807
(6)	²S_1/2–²P_1/2	15.257	15.253	10.658	10.664	8.445	8.449	6.842	6.851
(7)	$\frac{2 p - 3 d}{{}^{2}{P_{1 / 2}} - {}^{2}{D_{3 / 2}}}$	15.914	15.911	11.028	11.031	8.693	8.695	7.015	7.020
(8)	²P_3/2–²D_5/2	16.058	16.054	11.175	11.174	8.837	8.838	7.164^b	7.164
(9)	²P_3/2–²D_3/2	16.071	16.065		11.186	8.848	8.850		7.176
(10)	$\frac{2 p - 3 s}{{}^{2}{P_{1 / 2}} - {}^{2}{S_{3 / 2}}}$	16.285	16.284	11.263	11.270	8.879^a	8.878	7.164^b	7.167
(11)	²P_3/2–²S_1/2	16.444	16.446	11.439	11.432	9.037^a	9.040	7.342^c	7.330

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