Improved Wavelengths and Energy Levels of Doubly-Ionized Argon (Ar III).

New measurements of Ar III wavelengths between 508 Å and 4183 Å are combined with measurements from the literature to find improved values for the energy of most of the known levels in Ar III. Parameters derived from fitting the new level energies to an LS-coupling model are presented along with eigenvector compositions of the levels. On the basis of this analysis new designations are recommended for several levels.

1. Introduction

The energy levels of Ar III in Vol. 1 of Atomic Energy Levels [1] (1948) are based on de Bruin’s 1937 paper [2]. A complete list of publications pertaining to observed wavelengths and energy levels published prior to 1948 is contained in Ref. [1]. de Bruin reported only the three lowest singlet terms (3s2 3p4 1D and 1S, and 3s 3p5 1Po), and the work published since 1948 has been concerned primarily with identifying singlet terms at higher energy. Fawcett et al. [3], in 1968, identified three lines at 389 Å, 387 Å, and 382 Å as transitions to 3s2 3p4 1D2 from 3s2 3p3(2D) 4d 1P1, 1D2, and 1F3, respectively. In 1975 Marling [4] identified three singlet-singlet transitions between levels of 3s2 3p3 4p and 3s2 3p3(3d and 4s). Agentoft et al. [5] confirmed in 1984 an identification of the 3s0 3p6 1S0 by McGuire [6].

In 1987 Hansen and Persson [7] published a revised analysis of the Ar III spectrum that contained all possible levels of the 3s2 3p4, 3s 3p5, 3s0 3p6, 3s2 3p3 (4s, 4p, and 3d) configurations. However, they include no observational data in their paper, and their energy values were given to only one decimal place. A recent paper by Whaling et al. [8], primarily concerned with the Ar I and Ar II spectra, identified about 60 lines of Ar III in the near ultraviolet. In the present paper we present improved level energies in Ar III derived from the best wavelengths in the literature, from new wavelengths measured expressly for this work, and from some older but hitherto unpublished wavelengths. A calculation of the Ar III level system in terms of LS-coupling suggests that several levels should be renamed.

2. Spectra

Wavelengths longer than 2250 Å were measured on 13 spectra from the archives of the National Solar Observatory (NSO); all were recorded on the 1 m Fourier Transform Spectrometer (FTS). Wavelengths between 2800 Å and 1850 Å were measured on spectra from the vacuum FTS at Lund University, Lund, Sweden. All spectra measured on the FTS were excited in an Ar discharge in a metal hollow-cathode source operating 0.13 kPa to 0.53 kPa (1 Torr to 4 Torr) and 0.1 kW to 1.0 kW in a cathode cavity 3 mm in diameter and 25 mm long. Several different cathode metals were used, and spectra were also recorded with Ne replacing the Ar to aid in the identification of Ar lines in the crowded metal spectrum. Further details of the spectral source will be found in Ref. [8].

Wavelengths shorter than 1850 Å were measured on spectrograms recorded at the National Bureau of Standards (NBS), now NIST, in 1971. A pulsed-rf source was used with halides of Na, Li, Ge, and Si during the study [9] primarily aimed at producing the spectra of singly and doubly ionized chlorine (Cl II and III). Argon was used to assist the discharge. The spectra were recorded photographically using the 10.7 m normal incidence vacuum spectrograph. Lines of C, N, O, Si, Ge, and Cu [10] were used as reference wavelengths for the reduction of the spectrograms by polynomial interpolation.

For all FTS spectra the wavenumber scale was calibrated using internal Ar II wavenumber standards derived from heterodyne measurements of CO molecular bands [11] as described in Ref. [8]. All FTS spectra were measured with the DECOMP [12] analysis program developed at the NSO by J. W. Brault. This program fits a Voigt profile to the observed feature and records the line-center wavenumber, peak amplitude, FWHM, and other parameters of the Voigt profile. The observed line-center wavenumber in vacuum has been converted to an observed air-wavelength (for λ> 2000 Å) using the expression for the index of refraction developed by Peck and Reeder [13] and appears in the first column of Table 1.

Table 1

Classified Ar III lines used for determining the level energies given in Table 2. Observed wavelength in the first column is in air for 2000 Å < λ < 10 000 Å; otherwise in vacuum. Calculated vacuum wavenumber in the second column is followed by its standard uncertainty in parentheses. The third column displays the difference between the observed (O) and calculated (C) wavenumber; the value 0.000 means < 0.0005. The meanings of the designations KL, B, D, B2, and * are given at the end of the table

Wavelength(Å)	Vacuum wavenumber and standard uncertainty (cm−1)	O–C(cm−1)	Classification
89 913.8 KL	1 112.176 (0.015)	0.001	3p4 3P2	3p4 3P1
7 751.06 B	12 897.787 (0.046)	0.12	3p4 3P1	3p4 1D2
7 135.80 B	14 010.009 (0.045)	−0.03	3p4 3P2	3p4 1D2
5 191.82 B	19 255.72 (0.24)	−0.01	3p4 1D2	3p4 1S0
4 182.9667	23 899.742 (0.001)	−0.000	4s′ 1D2o	4p′ 1P1
4 088.8900	24 449.603 (0.002)	0.002	3d′ 1P1o	4p″ 1D2
4 059.89 D	24 624.31 (0.11)	−0.05	3d′ 3P0o	4p″ 3S1
4 023.5864	24 846.439 (0.005)	−0.012	3d′ 3P1o	4p″ 3S1
3 960.4873	25 242.272 (0.003)	0.004	3d′ 3P2o	4p″ 3S1
3 907.84 D	25 582.28 (0.11)	0.06	3d′ 3P0o	4p″ 3D1
3 858.2923	25 910.853 (0.002)	0.002	3d′ 3P1o	4p″ 3D2
3 795.3435	26 340.600 (0.002)	−0.003	3d′ 3P2o	4p″ 3D3
3 637.8731	27 480.757 (0.001)	−0.000	4s′ 1D2o	4p′ 1F3
3 514.2005	28 447.837 (0.002)	0.002	4s 3S1o	4P3P1
3 511.6671	28 468.364 (0.002)	−0.002	4s′ 3D3o	4p′ 3D2
3 511.1485	28 472.568 (0.002)	−0.002	4s 3S1o	4p 3P2
3 509.3334	28 487.293 (0.002)	−0.000	4s 3S1o	4p 3P0
3 503.5892	28 533.995 (0.002)	0.001	4s′ 3D2o	4p′ 3D2
3 502.6829	28 541.376 (0.002)	0.003	4s′ 3D2o	4p′ 3D1
3 499.6693	28 565.955 (0.002)	0.001	4s′ 3D1o	4p′ 3D1
3 497.10 D	28 586.97 (0.13)	−0.03	3d″ 3D1o	4p″ 3D1
3 484.12 D	28 693.42 (0.13)	0.02	3d″ 3D1o	4p″ 3D2
3 480.5022	28 723.267 (0.002)	−0.003	4s′ 3D3o	4p′ 3D3
3 417.49 D	29 252.63 (0.12)	0.22	3d″ 3D2o	4p″ 3D2
3 413.53 D	29 286.55 (0.12)	0.25	3d″ 3D2o	4p″ 3D3
3 391.8445	29 474.023 (0.002)	−0.000	3d″ 3P2o	4p″ 3P2
3 358.5305	29 766.375 (0.002)	−0.002	4s′ 3D1o	4p′ 3F2
3 344.7566	29 888.948 (0.002)	0.001	4s′ 3D2o	4p′ 3F3
3 342.5373	29 908.793 (0.001)	−0.000	3d′ 1P1o	3p6 1 S0
3 336.1746	29 965.832 (0.002)	0.001	4s′ 3D3o	4p′ 3F4
3 327.34 D	30 045.38 (0.14)	0.01	3d″ 3D3o	4p″ 3D2
3 323.59 D	30 079.29 (0.14)	0.001	3d″ 3D3o	4p″ 3D3
3 311.2423	30 191.453 (0.003)	0.003	4s 5S2o	4p 5 P1
3 301.8546	30 277.290 (0.002)	0.003	4s 5S2o	4p 5 P2
3 285.8413	30 424.844 (0.002)	−0.003	4s 5S2o	4p 5 P3
3 251.7907	30 743.419 (0.001)	−0.000	4s″ 1P1o	4p″ 1 P1
3 187.90 D	31 359.53 (0.13)	0.01	3d″ 3D1o	4p″ 3P0
3 110.41 D	32 141.23 (0.12)	−0.45	3d″ 3D2o	4p″ 3P1
3 109.08 B2	32 153.51 (0.24)	1.02	3p4 3P1	3p4 1 S0
3 083.64 D	32 419.97 (0.12)	−0.18	3d″ 3D2o	4p″ 3P2
3 054.7736	32 726.134 (0.004)	−0.000	4s″ 3P1o	4p″ 3D2
3 023.9801	33 059.372 (0.006)	0.002	4s″ 3P2o	4p″ 3D3
3 010.02 D	33 212.71 (0.14)	−0.02	3d″ 3D3o	4p″ 3P2
3 002.6408	33 294.312 (0.002)	−0.000	4s″ 1P1o	4p″ 1 D2
2 884.2142	34 661.318 (0.002)	0.004	4s′ 3D3o	4p′ 3P2
2 878.7636	34 726.950 (0.002)	−0.003	4s′ 3D2o	4p′ 3P2
2 855.3126	35 012.152 (0.002)	−0.003	4s′ 3D2o	4p′ 3P1
2 853.3087	35 036.731 (0.003)	0.006	4s′ 3D1o	4p′ 3P1
2 842.9654	35 164.199 (0.005)	0.003	4s′ 3D1o	4p′ 3P0
2 824.6461	35 392.250 (0.026)	−0.001	4s″ 3P1o	4p″ 3P0
2 818.2261	35 472.870 (0.035)	*	4s″ 3P0o	4p″ 3P1
2 796.6340	35 746.695 (0.005)	0.004	3d″ 1F3o	4p′ 1 D2
2 783.6035	35 914.061 (0.019)	−0.000	4s″ 3P2o	4p″ 3P1
2 762.1650	36 192.796 (0.006)	−0.003	4s″ 3P2o	4p″ 3P2
2 753.9120	36 301.217 (0.005)	−0.003	4s′ 1D2o	4p′ 1D2
2 724.7878	36 689.240 (0.004)	−0.000	3d′ 3D3o	4p′ 3D3
2 685.5827	37 224.825 (0.009)	−0.012	4p′ 3P0	4d′ 3D1o
2 678.3543	37 325.260 (0.005)	0.010	3d′ 3D2o	4p′ 3D2
2 673.9635	37 386.560 (0.005)	−0.003	4p′ 3P1	4d′ 3D2o
2 654.5492	37 659.972 (0.004)	−0.002	4p′ 3P2	4d′ 3D3o
2 631.8635	37 984.573 (0.012)	−0.007	3d′ 3D1o	4p′ 3D1
2 617.26 D	38 196.25 (0.22)	0.25	3d′ 3D1o	4p″ 3P0
2 602.12 D	38 418.74 (0.22)	−0.02	3d′ 3D1o	4p″ 3P1
2 591.4982	38 576.192 (0.005)	−0.013	4p″ 3P2	4d″ 3P1o
2 584.8765	38 674.998 (0.011)	−0.003	4p″ 3P2	4d″ 3P2o
2 583.39 D	38 697.47 (0.22)	−0.23	3d′ 3D1o	4p″ 3P2
2 579.6397	38 753.501 (0.001)	−0.000	4s″ 1P1o	3p6 1S0
2 566.3790	38 953.733 (0.018)	−0.001	4p″ 3P1	4d″ 3P2o
2 506.6580	39 881.750 (0.003)	−0.010	4p′ 3P1	4d′ 3P2o
2 504.3879	39 917.877 (0.007)	0.012	4p′ 3P0	4d′ 3P1o
2 494.8516	40 070.460 (0.011)	*	4p′ 3P1	4d′ 3P0o
2 488.8577	40 166.952 (0.002)	0.002	4p′ 3P2	4d′ 3P2o
2 484.1046	40 243.804 (0.012)	0.001	3d″ 3D4o	4p′ 3F4
2 479.76 D	40 314.45 (0.24)	−0.14	4p′ 3P0	4d′ 3 S1
2 478.7619	40 330.548 (0.006)	−0.008	4p′ 3P2	4d′ 3P1o
2 476.5289	40 366.908 (0.003)	−0.005	4p′ 3D2	4d′ 3D2o
2 476.057D	40 374.590 (0.008)	0.001	4p′ 3D3	4d′ 3D3o
2 472.9445	40 425.406 (0.002)	0.002	4p′ 3D4	4d′ 3D4o
2 471.92 D	40 441.92 (0.24)	0.24	4p′ 3P1	4d′ 3D1o
2 468.6732	40 495.345 (0.004)	0.002	4p″ 3P2	4d″ 3D3o
2 454.63 D	40 727.12 (0.24)	−0.11	4p′ 3P2	4d′ 3D1o
2 443.6241	40 910.412 (0.003)	0.013	4p′ 3P2	5s′ 3D3o
2 441.2307	40 950.532 (0.051)	*	4p″ 3P1	4d″ 3D2o
2 427.4901	41 182.325 (0.005)	−0.013	4p″ 3D3	4d″ 3D3o
2 426.1764	41 204.609 (0.007)	−0.000	4p″ 3D2	4d″ 3D2o
2 425.4917	41 216.238 (0.002)	0.002	4p″ 3D2	4d″ 3D3o
2 424.2959	41 236.571 (0.002)	−0.002	4p 5P3	4d 5D3o
2 423.9600	41 242.282 (0.001)	*	4p 5P3	4d 5D4o
2 423.5239	41 249.702 (0.003)	*	4p′ 3D4	4d′ 3Do 5
2 419.9242	41 311.058 (0.003)	−0.000	4p″ 3D1	4d″ 3D2o
2 418.8421	41 329.538 (0.003)	*	4p′ 3D3	4d′ 3D4o
2 416.0030	41 378.092 (0.004)	0.010	4p 5P2	4d 5D1o
2 415.8638	41 380.487 (0.002)	−0.001	4p 5P2	4d 5D2o
2 415.6512	41 384.126 (0.002)	0.001	4p 5P2	4d 5D3o
2 413.2214	41 425.793 (0.003)	−0.000	4p′ 3D2	4d′ 3D3o
2 411.0017	41 463.929 (0.002)	−0.000	4p 5P1	4d 5D1o
2 410.8622	41 466.324 (0.003)	0.002	4p 5P1	4d 5D2o
2 410.3798	41 474.639 (0.009)	−0.014	4p′ 3D3	4d′ 3D3o
2 405.0036	41 567.328 (0.002)	0.004	4p′ 3D1	4d′ 3D2o
2 404.5772	41 574.709 (0.003)	−0.007	4p′ 3D2	4d′ 3D2o
2 399.1952	41 667.972 (0.003)	−0.014	4p′ 3D3	4d′ 3D4o
2 395.6539	41 729.542 (0.008)	0.005	4p′ 3D2	4d′ 3D3o
2 377.7480	42 043.776 (0.003)	−0.061	4s′ 1D2o	4p″ 1P1
2 358.9539	42 378.691 (0.005)	0.022	4p′ 3D3	4d′ 3D3o
2 347.5774	42 584.065 (0.004)	−0.001	4p″ 3P2	5s″ 3P2o
2 345.1967	42 627.291 (0.003)	−0.000	3d′ 3D3o	4p′ 3P2
2 338.1614	42 755.541 (0.010)	*	4p″ 3D1	4d″ 3P0o
2 335.2989	42 807.944 (0.003)	−0.000	4p″ 3D1	4d″ 3P1o
2 329.9196	42 906.749 (0.012)	0.022	4p″ 3D1	4d″ 3P2o
2 319.2632	43 103.910 (0.004)	−0.012	4p 3P2	4d 3D2o
2 319.0123	43 108.564 (0.005)	−0.002	4p 3P0	4d 3D1o
2 317.9324	43 128.641 (0.002)	0.002	4p 3P1	4d 3D2o
2 317.3757	43 139.005 (0.003)	*	4p 3P2	4d 3D3o
2 316.8911	43 148.020 (0.005)	0.006	4p 3P1	4d 3D1o
2 312.1238	43 236.984 (0.011)	*	3d″ 3P1o	4p′ 3P0
2 300.7825	43 450.094 (0.031)	*	4p 3P1	5s 3D1o
2 292.9752	43 598.024 (0.002)	−0.000	4p′ 3D3	4d′ 3D3o
2 292.2647	43 611.527 (0.031)	0.007	4s′ 3D3o	4p″ 3D3
2 291.3594	43 628.768 (0.004)	−0.004	4p″ 3D3	4d″ 3D3o
2 282.2226	43 803.417 (0.004)	−0.001	3d′ 3D2o	4p′ 3P1
2 281.1989	43 823.070 (0.008)	0.001	4p′ 3D1	4d′ 3D1o
2 279.0328	43 864.717 (0.005)	−0.000	4p′ 3D2	4d′ 3D2o
2 269.9537	44 040.146 (0.001)	*	3d″ 1D3o	4p″ 1D2
2 269.7517	44 044.065 (0.002)	−0.000	4s″ 1P1o	4p″ 1S0
2 265.1420	44 133.641 (0.008)	−0.000	3d″ 1D2o	4p′ 1P1
2 242.3207	44 582.817 (0.011)	0.001	3d′ 3D1o	4p′ 3P0
2 241.7248	44 594.668 (0.002)	−0.000	4s′ 1D2o	4p″ 1D2
2 192.0137	45 605.898 (0.003)	−0.001	4p′ 3D4	5s′ 3D3o
2 191.1210	45 624.475 (0.072)	*	4p″ 3D2	5s″ 3P1o
2 188.1716	45 685.966 (0.004)	−0.000	4p′ 3D3	5s′ 3D2o
2 186.6626	45 717.489 (0.003)	−0.000	4p″ 3D3	5s″ 3P2o
2 184.0268	45 772.659 (0.006)	*	4p′ 3D2	5s′ 3D1o
2 177.1971	45 916.235 (0.018)	−0.006	4p 5P3	5s 5D2o
2 170.2217	46 063.789 (0.018)	0.005	4p 5P2	5s 5D2o
2 168.2822	46 105.004 (0.004)	−0.012	4p′ 3D3	4d′ 3P2o
2 148.3890	46 531.847 (0.032)	0.012	4s′ 3D2o	4p″ 3P1
2 135.3565	46 815.817 (0.005)	0.003	4p″ 3D1	5s″ 3P2o
2 133.8685	46 848.464 (0.003)	−0.001	4p′ 3D3	5s′ 3D3o
2 128.207D	46 973.080 (0.006)	−0.008	4p′ 3D1	5s′ 3D1o
2 125.1373	47 040.919 (0.004)	−0.000	4p′ 3D2	5s′ 3D2o
2 006.8504	49 813.208 (0.036)	*	3d″ 3P2o	4p″ 3S1
1 973.7936	50 663.849 (0.024)	0.009	4s 3D1o	4p′ 3P2
1 962.7446	50 949.051 (0.024)	0.014	4s 3D1o	4p′ 3P1
1 957.8466	51 076.519 (0.024)	0.006	4s 3D1o	4p′ 3P0
1 938.7892	51 578.584 (0.005)	*	3d′ 1D4o	4p′ 1F3
1 919.5200	52 096.342 (0.018)	0.016	3d 3D1o	4p 3P1
1 918.0681	52 135.798 (0.018)	−0.007	3d 3D1o	4p 3P0
1 915.5767	52 203.594 (0.016)	0.005	3d 3D2o	4p 3P1
1 914.6703	52 228.325 (0.016)	−0.013	3d 3D2o	4p 3P2
1 914.4119	52 235.365 (0.018)	−0.001	3d 3D3o	4p 3P2
1 878.0056	53 247.972 (0.072)	−0.006	3d″ 3D2o	4p″ 3D1
1 865.6622	53 600.271 (0.029)	*	3d″ 3D3o	4p″ 3D2
1 855.6497	53 889.499 (0.031)	−0.018	3d″ 3D4o	4p″ 3D3
1 843.0838	54 256.894 (0.090)	*	3d′ 3D3o	4p′ 3F2
1 839.3986	54 367.595 (0.059)	*	3d′ 3D4o	4p′ 3F3
1 836.3722	54 455.191 (0.039)	*	3d′ 3Do 5	4p′ 3F4
1 675.6232	59 679.270 (0.035)	0.018	3d 5D2o	4p 5P1
1 675.4773	59 684.485 (0.043)	−0.000	3d 5D1o	4p 5P1
1 673.4061	59 758.269 (0.043)	0.089	3d 5D3o	4p 5P2
1 673.2169	59 765.107 (0.035)	0.008	3d 5D2o	4p 5P2
1 673.0711	59 770.322 (0.043)	0.001	3d 5D1o	4p 5P2
1 669.6701	59 892.071 (0.061)	*	3d 5D4o	4p 5P3
1 669.2893	59 905.823 (0.043)	−0.089	3d 5D3o	4p 5P3
1 669.0970	59 912.661 (0.035)	−0.026	3d 5D2o	4p 5P3
1 617.7766	61 813.23 (0.29)	*	3d′ 1D0o	4p′ 1P1
1 614.7997	61 927.103 (0.058)	0.082	3d′ 3D4o	4p′ 3D3
1 611.0049	62 073.053 (0.071)	0.032	3d′ 3D3o	4p′ 3D2
1 586.6206	63 027.153 (0.058)	−0.113	3d′ 3D4o	4p′ 3F3
1 583.0377	63 169.668 (0.058)	0.022	3d′ 3D4o	4p′ 3F4
1 576.5915	63 428.006 (0.071)	−0.035	3d′ 3D3o	4p′ 3F3
1 572.3340	63 599.72 (0.10)	−0.000	3d′ 3D2o	4p′ 3F2
1 467.8533	68 126.780 (0.030)	−0.080	3d 3D1o	4p′ 3D1
1 465.7036	68 226.652 (0.028)	−0.034	3d 3D2o	4p′ 3D2
1 465.5506	68 233.692 (0.029)	0.049	3d 3D3o	4p′ 3D2
1 460.2487	68 481.555 (0.028)	−0.070	3d 3D2o	4p′ 3D3
1 460.0973	68 488.595 (0.029)	−0.009	3d 3D3o	4p′ 3D3
1 255.6374	79 640.83 (0.47)	*	3p5 1P1o	4p′ 1P1
887.4040	112 688.26 (0.13)	0.01	3p4 3P1	3p5 3 P2
883.1800	113 227.13 (0.23)	0.02	3p4 3P0	3p5 3 P1
879.6229	113 685.15 (0.13)	0.07	3p4 3P1	3p5 3 P1
878.7308	113 800.48 (0.13)	−0.13	3p4 3P2	3p5 3 P2
875.5354	114 215.82 (0.13)	*	3p4 3P1	3p5 3 P0
871.0995	114 797.37 (0.13)	−0.07	3p4 3P2	3p5 3P1o
695.5390	143 773.34 (0.32)	−0.05	3p4 3P1	3d 5D1o
643.2572	155 459.02 (0.43)	−0.21	3p4 3P0	3d 3D1o
641.8072	155 810.34 (0.09)	0.32	3p4 3P1	3d 3D2o
641.3658	155 917.60 (0.09)	0.34	3p4 3P1	3d 3D1o
637.2881	156 915.53 (0.08)	−0.63	3p4 3P2	3d 3D3o
636.8194	157 029.82 (0.08)	0.12	3p4 3P2	3d 3D1o
604.1590	165 519.51 (0.17)	0.17	3p4 1D2	3d″ 1D2o
578.3865	172 894.04 (0.11)	−0.72	3p4 1D2	3d′ 3D2o
577.1457	173 266.37 (0.32)	0.10	3p4 3P1	4s 5D2o
573.4666	174 378.59 (0.32)	−0.21	3p4 3P2	4s 5D2o
558.3231	179 107.53 (0.43)	0.23	3p4 3P0	4s 3D1o
556.8979	179 566.10 (0.08)	−0.05	3p4 3P1	4s 3D1o
553.4696	180 678.33 (0.08)	0.05	3p4 3P2	4s 3D1o
538.7890	185 601.23 (0.43)	0.18	3p4 3P0	3d′ 3D1o
537.4622	186 059.81 (0.09)	0.21	3p4 3P1	3d′ 3D1o
536.7451	186 307.93 (0.17)	−0.24	3p4 1D2	3d″ 1D3o
535.5881	186 711.74 (0.09)	1.09	3p4 3P1	3d′ 3D2o
529.9005	188 714.88 (0.08)	−0.21	3p4 3P2	3d′ 3D3o
511.5675	195 478.42 (0.09)	0.79	3p4 3P1	4s′ 3D1o
511.5018	195 503.00 (0.09)	0.27	3p4 3P1	4s′ 3D2o
508.4390	196 680.86 (0.08)	−0.43	3p4 3P2	4s′ 3D3o

KL This magnetic-dipole wavelength is from D. Kelly and J. H. Lacy, Astrophys. J. Lett. 454, L161 (1995).

B These magnetic-dipole and electric-quadrupole wavelengths are from I. S. Bowen, Astrophys. J. 121, 306 (1955).

D These wavelengths are taken from T. L. de Bruin, Proc. Roy. Acad. Amsterdam 40, 340 (1937).

B2 This magnetic-dipole wavelength is from I. S. Bowen, Astrophys. J. 132, 1 (1960).

This is the the only transition connecting a level to the network; hence calculated and observed wavenumber are equal.

As a rough indication of the relative intensity of the Ar III lines as produced in the hollow cathode source, we list in column 2 of Table 1 the logarithm of the ratio (line amplitude)/(rms noise level) for lines measured on FTS spectra. The amplitude has not been corrected for the response of the spectrometer, and a comparison of two line amplitudes is meaningful only for neighboring lines. We are unable, of course, to include the intensity of lines in Table 1 not seen in our spectra, nor do we know the intensity of the far VUV lines measured at the NIST.

We have incorporated in our linelist a few additional wavelengths from the literature that establish important links between levels or that enable us to find values for levels that do not appear in our spectra. Five magnetic dipole lines measured by Bowen [14a,14b] in astronomical spectra, and a measurement in a planetary nebula by Kelly and Lacy [15], determine the spacing between several levels of the ground configuration; we have included their results in the least-squares fit of the levels to the lines on an equal footing with our own. de Bruin [2] has published values for several transitions that join the levels we have measured with levels in the 3d″ 3D, 3d′ 3S, 3d′ 3P, and 4d′ 3S terms. We have included de Bruin’s measurements in Table 1 (identified with the notation D) and used them to find the energy of these levels.

It is important to establish the uncertainty of the measured wavelengths because the uncertainties play an important role in the weighted least-squares analysis that we used to extract level energies from the measured transition energies. Of the several factors that limit the accuracy of interferometric wavenumber measurements, the important ones for the FTS spectra we used are the line-width produced in the hollow-cathode, and the noise continuum of broad-range FTS spectra. For a line well-separated from its nearest neighbor, we assign a standard uncertainty (i.e., 1 standard deviation estimate) to the measured line position of δWN = 0.5(FWHM)/(S/N), where the full width at half maximum FWHM, the peak amplitude S, and the RMS background noise level N, are parameters generated by the DECOMP line-fitting program. The factor 0.5 is a convenient approximation to the more precise, but difficult to evaluate, expression given by Brault [12]. For very strong lines (S/N ≥ 103) the expression above may underestimate δWN, as discussed in Ref. [8], and we therefore set a lower limit δWNmin = 0.001 cm−1. δWN varies from line to line and increases with wavenumber because of the increasing Doppler width; it is typically less than 0.010 cm−1.

For lines measured with the grating spectrometer the standard uncertainty in wavelength δWLVUV should be the same for all wavelengths, and we have set δWLVUV = ± 0.001 Å by analyzing the internal consistency of the network of 209 interconnected transitions used in the weighted least-squares analysis. Starting with a conservative estimate of δWLVUV = ± 0.004 Å, and giving each observed transition energy WNObs the weight w = (δWN)−2, we found that the residual Σ(w×(WNCalc − WNObs)2)/Σw was determined by internal consistency alone. Only when the wavelength uncertainty was reduced below 0.0009 Å did the residual show a significant increase, and we have set δWLVUV = ± 0.001 Å for all lines measured with the grating spectrometer.

For the wavelengths of the magnetic-dipole transitions taken from the literature we have adopted the uncertainty estimates of the original authors. The wavelengths measured by de Bruin [2] have been assigned a standard uncertainty of 0.02 Å, a value suggested by a comparison of his values with those measured on FTS spectra.

3. Line Identification

The hollow-cathode spectra contain Ar I, II, and III lines, plus lines from two or more stages of ionization of the cathode element. An Argon linelist was extracted from this mixture by finding lines common to spectra from two or more cathodes. Ar I and II lines, identified using the linelist published in Ref. [8], were removed and the remaining Ar lines were sufficiently sparse that the rough Ar III wavelengths compiled in Refs. [16] could be used to classify many of the remaining lines. In addition, we used transition energies computed from the Ar III level energies of Hansen and Persson [7] to identify singlet-singlet transitions not included in Refs. [16]. This initial list of classified Ar III transitions was further refined after we had obtained precise Ar III level energies and were able to calculate accurate transition energies and search our observed spectra with a small (±0.010 cm−1) search window.

4. Level Energies

Level energies were derived from our measured transition energies with the CLEVEL least-squares code of Palmer and Engleman [17] that solves a set of overdetermined linear equations (of the form E − E = WN) for the most probable energy values and their standard uncertainties, E ± δE. It is necessary to pay careful attention to the uncertainty assigned to each measurement.

The Ar III level energy values and their uncertainties, E ± δE produced by CLEVEL are listed in Table 2. For each input line, CLEVEL evaluates the calculated value of the transition energy from WN,Calc = E − E (see column 2 of Table 1) and the standard uncertainty of this calculated wavenumber which appears in parentheses following WNCalc. We list also the difference WNObs − WNCalc in column 3 of Table 1.

Table 2

Energy level values of Ar III and their standard uncertainties (in cm−1). The last column shows the number of transitions in Table 1 that involve this level

Configuration	Designation	J	Energy level value (cm−1)	Standard uncertainty(cm−1)	n
3s23p4	3p4 3P	2	0.000	0.000	10
		1	1 112.175	0.006	15
		0	1 570.229	0.150	4
3s23p4	3p4 1D	2	14 010.004	0.029	6
3s23p4	3p4 1S	0	33 265.724	0.153	2
3s3p5	3p5 3Po	2	113 800.459	0.092	2
		1	114 797.353	0.092	3
		0	115 328.002	0.130	1
3s3p5	3p5 1Po	1	144 022.323a	0.485	1
3s23p3(4So)3d	3d 5Do	0
		1	144 885.468	0.251	3
		2	144 890.681	0.254	3
		3	144 897.519	0.255	3
		4	144 911.271	0.259	1
3s23p3(4So)3d	3d 3Do	3	156 915.518	0.078	4
		2	156 922.558	0.078	5
		1	157 029.811	0.079	5
3s23p3(2Do)3d	3d′ 1So	0	161 849.923	0.323	1
3s23p3(2Do)3d	3d′ 3Fo	2	162 757.293	0.128	3
		3	163 076.157	0.105	2
		4	163 477.010	0.098	3
3s23p3(2Do)3d	3d′ 3Go	3	172 100.118	0.118	1
		4	172 136.569	0.098	1
		5	172 191.487	0.088	1
3s23p3(4So)4s	4s 5So	2	174 378.498	0.251	4
3s23p3(2Do)3d	3d′ 1Go	4	175 665.583	0.159	1
3s23p3(2Po)3d	3d″ 1Do	2	179 529.511	0.159	2
3s23p3(4So)4s	4s 3So	1	180 678.316	0.076	8
3s23p3(2Po)3d	3d″ 3Fo	4	186 402.875	0.081	2
		3	186 658.191	0.111	1
		2	186 904.041	0.109	2
3s23p3(2Do)3d	3d′ 3Do	1	187 172.018a	0.080	4
		2	187 823.950a	0.080	3
		3	188 714.874a	0.080	3
3s23p3(2Po)3d	3d″ 3Po	0
		1	188 517.851	0.080	2
		2	189 380.840	0.091	4
3s23p3(2Do)4s	4s′ 3Do	1	196 590.636	0.080	5
		2	196 615.215	0.080	7
		3	196 680.847	0.080	6
3s23p3(2Do)4s	4s′ 1Do	2	199 763.411	0.159	5
3s23p3(2Po)3d	3d″ 1Fo	3	200 317.932	0.159	3
3s23p3(4So)4p	4p 5P	1	204 569.951	0.251	5
		2	204 655.788	0.251	8
		3	204 803.342	0.251	7
3s23p3(2Do)3d	3d′ 3So	1	204 728.324	0.233	3
3s23p3(2Po)4s	4s″ 3Po	2	207 233.004	0.084	3
		1	207 532.328	0.084	2
		0	207 674.194	0.091	1
3s23p3(4So)4p	4p 3P	1	209 126.152	0.077	6
		2	209 150.883	0.077	5
		0	209 165.608	0.077	3
3s23p3(2Po)3d	3d″ 3Do	3	210 213.087	0.162	3
		2	211 005.831	0.146	4
		1	211 565.045	0.151	3
3s23p3(2Po)4s	4s″ 1Po	1	211 063.766	0.159	4
3s23p3(2Do)3d	3d′ 3Po	2	213 951.776	0.084	3
		1	214 347.609	0.084	2
		0	214 569.734	0.140	2
3s23p3(2Do)3d	3d′ 1Po	1	219 908.474	0.159	2
3s23p3(2Do)4p	4p′ 1P	1	223 663.153	0.159	4
3s23p3(2Do)4p	4p′ 3D	2	225 149.210	0.080	10
		1	225 156.591	0.080	6
		3	225 404.113	0.080	11
3s23p3(2Do)4p	4p′ 3F	2	226 357.012	0.080	6
		3	226 504.163	0.080	7
		4	226 646.678	0.080	7
3s23p3(2Do)4p	4p′ 1F	3	227 244.168	0.159	2
3s23p3(2Do)4p	4p′ 3P	2	231 342.165	0.080	9
		1	231 627.367	0.080	8
		0	231 754.835	0.080	7
3s23p3(2Do)4p	4p′ 1D	2	236 064.627	0.159	2
3s23p3(2Po)4p	4p″ 3S	1	239 194.048	0.084	8
3s23p3(2Po)4p	4p″ 3D	1	240 152.013	0.085	4
		2	240 258.462	0.084	9
		3	240 292.376	0.084	9
3s23p3(2Po)4p	4p″ 1P	1	241 807.185	0.159	2
3s23p3(2Po)4p	4p″ 3P	0	242 924.579	0.088	3
		1	243 147.064	0.085	7
		2	243 425.799	0.084	9
3s23p3(2Po)4p	4p″ 1D	2	244 358.078	0.159	2
3s23p3(4So)4d	4d 5Do	0
		1	246 033.879	0.251	2
		2	246 036.275	0.251	2
		3	246 039.914	0.251	2
		4	246 045.624	0.251	1
3p6	3p6 1S	0	249 817.267	0.159	2
3s23p3(4So)5s	5s 5So	2	250 719.577	0.252	2
3s23p3(4So)4d	4d 3Do	2	252 254.794	0.077	2
		1	252 274.172	0.077	2
		3	252 289.888	0.077	1
3s23p3(4So)5s	5s 3So	1	252 576.246	0.082	1
3s23p3(2Po)4p	4p″ 1S	0	255 107.831	0.159	1
3s23p3(2Do)4d	4d′ 3Fo	2	266 723.919	0.080	3
		3	266 878.753	0.080	2
		4	267 072.085	0.080	3
3s23p3(2Do)4d	4d′ 3Go	3	267 782.804	0.080	2
		4	267 833.701	0.080	1
		5	267 896.381	0.080	1
3s23p3(2Do)4d	4d′ 3Do	1	268 979.661	0.080	2
		3	269 002.137	0.080	2
		2	269 013.927	0.080	2
3s23p3(2Do)4d	4d′ 3Po	2	271 509.117	0.080	3
		1	271 672.713	0.080	2
		0	271 697.827	0.080	1
3s23p3(2Do)4d	4d′ 3So	1	272 069.287	0.249	3
3s23p3(2Do)5s	5s′ 3Do	1	272 129.671	0.080	1
		2	272 190.129	0.080	2
		3	272 252.577	0.080	3
3s23p3(2Po)4d	4d″ 3Fo	2	281 463.071	0.085	2
		3	281 474.701	0.084	2
		4
3s23p3(2Po)4d	4d″ 3Po	0	281 949.589	0.085	1
		1	282 001.992	0.084	2
		2	282 100.797	0.085	3
3s23p3(2Po)4d	4d″ 3Do	3	283 921.144	0.084	2
		2	284 097.597	0.099	1
		1
3s23p3(2Po)5s	5s″ 3Po	2	286 009.865	0.084	3
		1	285 882.937	0.110	1
		0

This level is not named for its major component. See Table 4 for percentage compositions.

Note that the standard uncertainty of the calculated wavenumber (from the appropriate element of the covariant matrix) is often very much smaller than the standard uncertainty of either level involved in the transition with respect to various other levels, including the ground level. These small uncertainties go with transitions between high levels of the same multiplicity and core configuration, and the difference in level energies depends only on the relative energy of the two levels and is independent of VUV transitions to the ground term. Any other transition between two such levels should likewise have a small standard uncertainty, and for this reason we have listed the level energies in Table 2 with more decimal places than appears to be justified by the standard uncertainty of the absolute energy of a level. For a calculated transition energy between dissimilar levels that are tied together only by transitions down to the ground term and back up again (e.g., between a quintet level and a triplet level), the standard uncertainty is much larger. For dissimilar levels the standard uncertainty should be estimated by combining in quadrature the uncertainty listed in Table 2 for the absolute energy of the initial and final level of the transition.

5. Theory

The ground state of doubly-ionized argon has the electron configuration 1s2 2s2 2p6 3s2 3p4, which gives rise to 3P, 1D, and 1S terms. All of the observed excited configurations (except 3s 3p5 and 3p6) result from the excitation of a 3p electron into a higher orbital to form 3p3 nl configurations. The parent configuration, 3p3, of Ar IV forms the terms 4So, 2Do, and 2Po. The arrangement of levels in all of the 3p3 nl configurations given herein (except 3p3 3d) is dominated by the separation of the parent terms.

In Table 3 we give the parameter set derived from a least-squares fit of the levels of the 3s 3p5, 3s2 3p3 (3d and 4d) configurations with the HFR Cowan code [18]. Also included are the HFR (relativistic approximations to the Hartree-Fock) values obtained and the ratio of the fitted value to that of the HFR value. Table 4 gives the eigenvector composition in the LS-coupling scheme of all of the levels of these three configurations including those for which we were unable to obtain experimental values. It is evident from the table that the 3p3 4d configuration is only very slightly perturbed by the 3s 3p5 and 3p3 3d configurations; the coupling appears to be very close to LS. There is very strong parental mixing among the three 3D terms of the 3p3 3d configuration, as was seen by Hansen and Persson [7]. Because of the difference between their parametric fit and ours, we have labeled the 3D terms near 156 900 and 187 800 cm−1 as having the 4S and 2D parents, respectively, while they did the reverse.

Table 3

Parameter values for the 3s3p5 + 3s23p33d + 3s23p34d energy fit in Ar III

Parameter	Fitted value and standard uncertaintya(cm−1)	HFR valueb(cm−1)	Ratio HFR/fitted value
Eav(sp5)	152 728 ± 469
ζ 3p	1 010	1 010	1.00
G1(3s3p)	80 158 ± 1162	94 485	0.85
Eav(p33d)	180 316 ± 159
F2(3p3p)	57 576 ± 479	69 716	0.83
ζ 3p	1 047	1 047	1.00
ζ 3d	26	26	1.00
F2(3p3d)	45 580 ± 529	54 962	0.83
G1(3p3d)	53 118 ± 658	68 640	0.77
X2(3p3d)c	4 595 ± 652
G3(3p3d)	33 838 ± 663	41 139	0.82
Eav(p34d)	268 455 ± 154
F2(3p3p)	58 419 ± 428	72 001	0.81
ζ 3p	1 111	1 111	1.00
ζ 4d	7	7	1.00
F2(3p4d)	8 067 ± 2020	11 700	0.69
G1(3p4d)	5 983 ± 608	8 964	0.67
G3(3p4d)	4 035 ± 410	6 046	0.67
R1(3p3p,3s3d)	64 267 ± 343	78 908	0.81
R1(3p3p,3s4d)	20 735 ± 1965	27 625	0.75
R0(3p3d,3p4d)	0	0	1.00
R2(3p3d,3p4d)	12 405 ± 1036	16 813	0.74
R1(3p3d,4d3p)	17 113 ± 1429	23 194	0.74
R3(3p3d,4d3p)	10 823 ± 904	14 669	0.74
Standard deviation of the fit = 363 cm−1

Where no standard uncertainty is given, the parameter was held fixed at the value given.

This value from the Cowan program is a relativistic approximation of the Hartree-Fock value.

No ab initio value is available for X2.

Table 4

Percent composition of the 3s3p5, 3s23p33d, and 3s23p34d levels derived from a least-squares fit of the parameters to the levels of these three configurations

Energy level value (cm−1)	Percent composition
J=0
115 328.002	76 sp5(2S)3P	18 p33d(2D)3P	6 p33d(2P)3P
144 785.7b	100 p33d(4S)5D
161 849.923a	100 p33d(2D)1S
188 045.2b	77 p33d(2P)3P	23 p33d(2D)3P
214 569.734	59 p33d(2D)3P	23 sp5(2S)3P	16 p33d(2P)3P
245 894.8b	100 p34d(4S)5D
266 922.3b	100 p34d(2D)1S
271 697.827	97 p34d(2D)3P
281 949.589	99 p34d(2P)3P
J=1
114 797.353	76 sp5(2S)3P	17 p33d(2D)3P	7 p33d(2P)3P
144 022.323c	43 sp5(2S)1P	50 p33d(2D)1P	6 p33d(2P)1P
144 885.468	100 p33d(4S)5D
157 029.811	48 p33d(4S)3D	47 p33d(2D)3D	4 p33d(2P)3D
187 172.018c	36 p33d(2D)3D	50 p33d(2P)3D	15 p33d(4S)3D
188 517.851	78 p33d(2P)3P	22 p33d(2D)3P
204 728.324a	99 p33d(2D)3S
211 565.045	44 p33d(2P)3D	33 p33d(4S)3D	15 p33d(2D)3D
214 347.609	59 p33d(2D)3P	22 sp5(2S)3P	15 p33d(2P)3P
219 908.474	48 p33d(2D)1P	37 sp5(2S)1P	11 p33d(2P)1P
240 056.2b	75 p33d(2P)1P	15 sp5(2S)1P	9 p34d(2P)1P
246 033.879	100 p34d(4S)5D
252 274.172	88 p34d(4S)3D	5 p34d(2D)3D
268 979.661	94 p34d(2D)3D	3 p34d(4S)3D
271 199.1b	92 p34d(2D)1P	4 sp5(2S)1P
271 672.713	98 p34d(2D)3S
272 069.287	95 p34d(2D)3P
282 001.992	99 p34d(2P)3P
283 657.2b	97 p34d(2P)3D
292 098.8b	90 p34d(2P)1P	8 p33d(2P)1P
J=2
113 800.459	76 sp5(2S)3P	17 p33d(2D)3P	7 p33d(2P)3P
144 890.681	100 p33d(4S)5D
156 922.558	48 p33d(4S)3D	47 p33d(2D)3D	4 p33d(2P)3D
162 757.293	84 p33d(2D)3F	15 p33d(2P)3F
179 529.511	75 p33d(2P)1D	25 p33d(2D)1D
186 904.041	84 p33d(2P)3F	15 p33d(2D)3F
187 823.950c	35 p33d(2D)3D	49 p33d(2P)3D	15 p33d(4S)3D
189 380.840	79 p33d(2P)3P	21 p33d(2D)3P
211 005.831	44 p33d(2P)3D	33 p33d(4S)3D	15 p33d(2D)3D
213 951.776	60 p33d(2D)3P	22 sp5(2S)3P	14 p33d(2P)3P
217 177.3b	72 p33d(2D)1D	24 p33d(2P)1D	3 p34d(2D)1D
246 036.275	100 p34d(4S)5D
252 254.794	88 p34d(4S)3D	5 p34d(2D)3D
266 723.919	97 p34d(2D)3F
269 013.927	94 p34d(2D)3D	4 p34d(4S)3D
271 509.117	96 p34d(2D)3P
272 793.5b	86 p34d(2D)1D	10 p34d(2P)1D
281 463.071	97 p34d(2P)3F
282 100.797	98 p34d(2P)3P
283 347.7b	44 p34d(2P)1D	51 p34d(2P)3D	3 p34d(2D)1D
284 097.597	46 p34d(2P)3D	44 p34d(2P)1D	7 p34d(2D)1D
J=3
144 897.519	100 p33d(4S)5D
156 915.518	48 p33d(4S)3D	48 p33d(2D)3D	4 p33d(2P)3D
163 076.157	85 p33d(2D)3F	14 p33d(2P)3F
172 100.118	100 p33d(2D)3G
186 658.191	85 p33d(2P)3F	14 p33d(2D)3F
188 714.874c	35 p33d(2D)3D	49 p33d(2P)3D	15 p33d(4S)3D
200 317.932	63 p33d(2P)1F	37 p33d(2D)1F
210 213.087	44 p33d(2P)3D	33 p33d(4S)3D	15 p33d(2D)3D
225 295.2b	57 p33d(2D)1F	35 p33d(2P)1F	7 p34d(2D)1F
246 039.914	100 p34d(4S)5D
252 289.888	89 p34d(4S)3D	5 p34d(2D)3D
266 878.753	97 p34d(2D)3F
267 782.804	98 p34d(2D)3G
269 002.137	95 p34d(2D)3D	4 p34d(4S)3D
275 804.9b	87 p34d(2D)1F	7 p34d(2P)1F	4 p33d(2D)1F
281 474.701	97 p34d(2P)3F
283 921.144	97 p34d(2P)3D
286 173.7b	91 p34d(2P)1F	5 p34d(2D)1F
J=4
144 911.271	100 p33d(4S)5D
163 477.010	87 p33d(2D)3F	13 p33d(2P)3F
172 136.569	100 p33d(2D)3G
175 665.583	100 p33d(2D)1G
186 402.875	86 p33d(2P)3F	13 p33d(2D)3F
246 045.624	100 p34d(4S)5D
267 072.085	96 p34d(2D)3F	3 p34d(2D)3G
267 833.701	96 p34d(2D)3G	3 p34d(2D)3F
267 961.2b	99 p34d(2D)1G
281 629.2b	99 p34d(2P)3F
J=5
172 191.487	100 p33d(2D)3G
267 896.381	100 p34d(2D)3G

This known level was not used in the least-squares fit.

The value of this level has not been determined experimentally. The value given is from the least-squares fit.

This level is not named for its major eigenvector component.

It should be noted that Hansen and Persson [7] did a parametric fit to the 3s 3p5 + 3s2 3p3 (3d + 4s) configurations. On the basis of that fit, they named the terms at about 189 000 cm−1 and 214 000 cm−1 as 3d″ 3P and 3d′ 3P, respectively, in agreement with our designation for these terms. However, they found such strong mixing of the 3p3 (2D) 3d 3P and the 3p3 (2P) 4s 3P eigenvectors in the term at 214 000 cm−1 that it may be misleading to label this term with any specific core designation. Thus, the term at 214 000 cm−1, although labeled 3d′ 3P implying a 2D core, takes part in 17 known optical transitions, and, in all 17 cases, the transition partner has a well-established 2P core; no transition to a level with a 2D core has been reported.

It was shown that in Cl II [9] the lowest odd 1P1 level had only 33 % of 3s 3p5 1P and 57 % of 3p3(2D) 3d 1P1 and that level was given the latter designation. As shown in Table 4, the level at 144 022 cm−1 has only 43 % of 3s 3p5 1P and 50 % of 3s2 3p3(2D) 3d 1P. However, because the next higher 1P level at 219 908 cm−1 also has a larger eigenvector percentage of 1P from the (2D) 3d configuration, we have designated the lower level as 3s 3p5 1P.

Hansen and Persson [7] have given calculations for the 3p4 and the 3p3 4p configurations. With only minor exceptions, they find almost no interaction between levels of different parentage in the 3p3 4p configuration. They find, however, relatively large configuration interaction affecting the 1S0 levels of the 3p4, 3p3 4p, and 3p6 configurations.

6. Ionization Energy

In their paper on ionization energies of singly ionized rare earths, Sugar and Reader [19] showed that it is possible to use the difference in effective quantum numbers of unperturbed adjacent members of an ns series to calculate an ionization energy. Using published values of the ionization energies and 3p 4s and 3p 5s levels of Ca III and Sc III, we arrive at an average of δn = 1.0312. With this value and the experimentally determined value of δT = E(5s 5S2) − E(4s 5S2) = 76 341.079 cm−1 in Ar III, the equation where Z = 3, was solved for n(4s). The corresponding value of T(4s) = Z2R/[n(4s)]2 when added to the level value of 4s 5S2, gives the ionization energy as 328 550 cm−1. Although the values of δn for both Ca III and Sc III are in near agreement and would therefore lead to a relatively small value for the uncertainty of the calculated ionization energy, we feel that with such a small sampling of possible values of n it is necessary to place a standard uncertainty of approximately ± 100 cm−1 on the ionization energy. The value of 328 550 ± 100 cm−1 compares very well with the value of 328 600 cm−1 obtained by Edlén [20] using a semi-empirical isoionic method.