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Isotope shifts in the spectrum of the neutral titanium atom
Spectrochimica Acta Part B 152 (2019) 30–37
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Isotope shifts in the spectrum of the neutral titanium atom ⁎
T
Shinji Kobayashi , Nobuo Nishimiya, Masao Suzuki Department of Electronic and Information Technology, Tokyo Polytechnic University, Iiyama 1583, Atsugi City, Kanagawa 243-0297, Japan
A R T I C LE I N FO
A B S T R A C T
Keywords: Isotope Shift Saturated absorption spectroscopy
An investigation of 53 saturated absorption lines of titanium at wavelengths ranging from 695 to 1005 nm is performed. In addition, transitions 3d34s a5FJ → 3d34p y5FJ (J = 3, 4, 5) in the ultraviolet range are measured. The isotope lines of 46Ti, 48Ti, and 50Ti are clearly observed for 53 transitions. A facing target sputtering system containing a magnetic field is used as a sample cell of titanium in this experiment. The Zeeman effect in a hyperfine structure is calculated for the condition of an intermediate field approximation to determine the unperturbed line positions in the odd mass isotopes 47Ti and 49Ti. For all observed transitions, the King plot analysis is performed to determine the electronic factors of the field shift and specific mass shift.
1. Introduction The isotope shift (IS) in atomic spectra is caused by interactions between an electron and the nucleus. In particular, the isotope shift is caused by the influence of the difference in the mass of the nucleus and the difference in the volume of the nucleus between isotopes. The former is called the mass shift, and the latter is called the field shift (FS). An analysis of the IS can provide information about the electronic states and the physical properties of the nucleus. Titanium is a very interesting atom in the field of nuclear physics because the atomic number of Ti, which is 22, is close to the proton magic number Z = 20, and 50Ti has the neutron magic number N = 28 [1,2]. The high-resolution Doppler-limited spectroscopy of the electronic transitions of Ti has been studied by several researchers[3–10]. The isotopes of the mass numbers ranging from 46 to 50 are stable, and their respective percentages of abundance are 8.25%, 7.44%, 73.72%, 5.41%, and 5.18%. The spectra of 47Ti and 49Ti are complicated due to their nuclear spin values of 5/2 and 7/2, respectively. The positions of the isotopic lines, including the hyperfine components, overlap within the Doppler profiles. Therefore, Doppler-free spectroscopy is useful for obtaining the line positions of the isotopic spectra and hyperfine lines of the odd-mass isotopes. U. Johan et al. measured the hyperfine structure of high-lying metastable states of 3d-shell atoms using atomic beam magnetic resonance detected by laser induced resonance fluorescence (ABMR–LIRF)[11]. They reported the strong configuration interaction between 3d24s2 a3P and 3d34s b3P. The fine-structure analysis of the even parity metastable state was investigated by E. Stachowska [12]. The results obtained systematically show the mixing effect of the metastable states belonging
⁎
to the even parity configuration. However, the configuration interactions of the fine structure in the odd parity levels at relatively higher energy levels than the metastable state are known to be complicated [13,14]. In this paper, we report the saturated absorption spectra of Ti I in the near-infrared region and in the ultraviolet region. The even-mass isotope spectra in 46, 48, 50Ti were measured for 53 transitions. The intermediate field approximation analysis was used to determine the unperturbed line positions of the odd mass isotopes 47, 49Ti. Electronic factors Fik and MikSMS were also determined. In addition, a combination difference (CD) analysis was adopted for two transitions with common upper levels to compare the electronic factors between the levels belonging to even-parity configurations 3d24s2 and those belonging to 3d34s. Using the results of the CD analysis for the even-parity levels, the electronic factors that referred to the ground state 3d24s2 a3F2 were determined. In the odd-parity level, the configuration 3d24s4p interacted with the configuration 3d34p. The factors Fik and MikSMS are affected by this interaction. To consider the influence of the perturbation between the odd-parity configuration on the electronic factors, a configuration-interaction analysis is performed. 2. Experiments An experiment was performed using a facing target sputtering (FTS) chamber and a Ti:sapphire ring laser. The experimental system is the same as the system shown in our previous report [15]. The spectroscopic measurement was carried out in the near-infrared region (695 − 1005 nm). An ultraviolet (UV) beam in the 450 nm region was obtained using a second harmonic generator (M-Squared Lasers, ECD-
Corresponding author. E-mail addresses: [email protected] (S. Kobayashi), [email protected] (N. Nishimiya).
https://doi.org/10.1016/j.sab.2018.08.010 Received 22 November 2017; Received in revised form 15 August 2018; Accepted 22 August 2018 Available online 05 September 2018 0584-8547/ © 2018 Elsevier B.V. All rights reserved.
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
X). The FTS chamber was used to obtain a gaseous state of neutral titanium. The discharge current of 300–500 mA was applied with a voltage of 400–450 V. Argon gas was enclosed at a pressure of 4 Pa in the chamber for sputtering gas. The magnetic field was determined by the saturated absorption lines of 40Ar I to be 45.39 (2.9) mT [15]. The windows of the FTS were tilted close to Brewster’s angle to avoid the reflecting loss of the incident laser. The direction of polarization of the pump and probe beam were set to be parallel to the magnetic field (parallel field case). The power of the pump and probe beam were 150 − 380 μW and 90 − 240 μW, respectively. The intensity of the pump beam was modulated by an acousto-optic modulator (AOM) at 50 kHz. The double-pass method using the AOM [16,17] was adopted for the lock-in detection of the saturated absorption lines. For the UV case, a mechanical chopper was used for the intensity modulation. A wavelength meter (HighFinesse, WS6) and a 100-cm confocal Fabry–Pérot interferometer were used for the frequency measurement. To calibrate the frequency from the wavelength meter and the spacing of the fringe marker, two photon spectra of the Rb atom (5S1/2 − 5D5/ 87 85 Rb (2→4) : 385 284 2 Rb (3→5) : 385 285 142 367.0 (80) kHz and 566 366.3 (80) kHz) [18] were observed. The accuracy of the absolute frequency error was less than 30 MHz, and the relative error of our measuring system was estimated to be less than 5 MHz. These uncertainties include the the error related to the determination of the center of the lines and the frequency-measurement procedure mentioned above.
Fig. 1. Recorder trace of the saturated absorption lines in b3FJ → y3DJ−1 (J=2,3,4). These lines are split into the Zeeman lines of ΔJ = 1-type. (α′, α ) δr 2 MOD = Δr 2(α′, α )
′ Δνik(α ,α)Obs
where expressed as
m α′ − mα νik mα′⋅mα
where νik is the frequency of the transition i → k and me and mα are expressed in unit of (amu). The SMS is the correlations of the motion of multiple electrons, and can be expressed as
∑
×
i, j = X , Y , Z
is the electronic factor of the SMS. where The FS represents the effects of the difference of the nuclear charge distribution by the isotope, and is expressed as
(7)
In our calculations, a basis-wave function ∣I, MI; J, MJ〉 was used. The matrix elements of the Zeeman splitting of the hyperfine levels can be derived as follows (See the supplementary material for details). Diagonal:
(3)
G HFS I ′ ′, MI′ ′ ; J ′ ′, MJ′ ′ | H | I ′, MI′ ; J ′, MJ′ = μB (gJ MJ + gI MI ) BZ + AJ (MI MJ ) 1 BJ + (I (I + 1) − 3MI2 )(J (J + 1) − 3MJ2) 4 J (2J − 1) I (2I − 1)
where Fik is the electronic factor corresponding to the variation in ′ the electron charge distribution at the nucleus, and δr2(α ,α) is the change in the mean-square nuclear charge radii. These values for the isotope chain of Ti were reported by Y. P. Gangrsky et al. [1], as shown in ′ Table 1. The modified ISs ΔνikMOD and δr2(α ,α) are defined as
mα′⋅mα , m α′ − mα
BJ 2J (2J − 1) I (2I − 1) 2⎞ ⎛ Ji Jj + Jj Ji 2⎞ ⎛ Ii Î j ̂ + Ij Î i ̂ J ⎟. − δi, j I ̂ ⎟ ⎜3 − δi, j ⎜3 2 2 ⎠ ⎝ ⎠⎝
JZ + gI IZ ̂ ) BZ + AJ ⋅( I ⋅ J ) + = μB (gJ
MikSMS
Δνik(α′, α ) MOD = Δνik(α′, α ) Obs
can be obtained from the King
G HFS G + H A + H B H =H
(2)
ΔνikFS = Fik⋅δr 2(α′, α )
(6)
Owing to the nuclear spin, the lines of odd mass numbers are split into several components. These hyperfine lines are also split due to the magnetic field. The Hamiltonian of the Zeeman effect in hyperfine structures (HFSs) is given as follows [20]:
(1)
m α′ − mα mα′⋅mα
SMS
3.2. Hyperfine structure
The mass shift consists of the normal mass shift (NMS) and the specific mass shift (SMS). The NMS between the reference isotope α and the isotope α′ is given as
ΔνikSMS = MikSMS
νik + MikSMS . 1836.15
The electronic factor Fik and Mik plot analysis[19].
3.1. Isotope shift
(5)
is the observed IS. Therefore, the modified IS is
(α′, α ) ΔνikMOD = Fik⋅δr 2 MOD +
3. Fundamentals
ΔνikNMS = me
mα′⋅mα , m α′ − mα
(8) Off-diagonal:
HFS | I ′, MI′ ; J ′, MJ′ I ′ , MI′ ′ ; J ′ ′, MJ′ ′ | H ′
(4)
G
(9)
Table 1 Properties of the Ti isotopes. Isotope
Mass[21]
46
45.9526294 46.9517640 47.9479473 48.9478711 49.9447921
Ti Ti 48 Ti 49 Ti 50 Ti 47
(14) (11) (11) (11) (12)
'
Abundance[21]
δr2(α ,48) (fm2) [1]
I
8.25 (3) 7.44 (2) 73.72 (3) 5.41 (2) 5.18 (2)
0.110 (7) 0.030 (4)
0 5/2 0 7/2 0
-0.139 (9) -0.160 (7)
31
μI (nm)[22]
Q (fm2)[22]
-0.78846(6)
+29(1)
-1.10414(9)
+24(1)
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
Fig. 3. Estimation of Fik and MikSMS. The example shows an analysis for b3FJ → y3DJ−1 (J = 2, 3, 4).
Fig. 2. Comparison of the observed spectra and those of the calculated Zeeman spectra of HFS in b3FJ → y3DJ−1 J = (2,3,4). The column charts represent the calculated Zeeman components in HFS.
diagonal element has nuclear magnetic-dipole coupling effects and electronic quadruple coupling effects. Under the condition of the parallel field case, the selection rules for the optical transition between the lower level ∣I'', MI''; J'', MJ''〉 and the upper ∣I', MI'; J', MJ'〉 are
A = ⎡ J [I (I + 1) − MI (MI ± 1)][J (J + 1) − MJ (MJ ∓ 1)] ⎢2 ⎣ 3 BJ (2MI ± 1)(2MJ ∓ 1) + 4 2J (2J − 1) I (2I − 1) × [I (I + 1) − MI (MI ± 1)] 2 [J (J + 1) − MJ (MJ ∓ 1)] 2 ] δ I ′ ′, I ′± 1 δ J ′ ′, J ′∓ 1
ΔJ = 0, ± 1, ΔMJ = 0, ΔI = 0, ΔMI = 0,
3 BJ 1 [I (I + 1) − MI (MI ± 1)] 2 + 4 2J (2J − 1) I (2I − 1)
where the transition MJ = 0 is forbidden in ΔJ = 0. Relative intensities of the Zeeman components in the HFS are calculated from
1
[I (I + 1) − (MI ± 1)(MI ± 1
1
1 2)] 2
I∼
1
× [J (J + 1) − MJ (MJ ∓ 1)] 2 [J (J + 1) − (MJ ∓ 1)(MJ ∓ 2)] 2
∑
(11)
|C (J ′ ′, I ′ ′, F ′ ′; MJ′ ′ , MI′ ′ , MF′ ′ ) |2 C (J ′, I ′, F ′; MJ′ , MI′ , MF′ ) 2
MI′ ′, MI′, MJ′ ′ MJ′
δ I ′ ′, I ′± 2 δ J ′ ′, J ′∓ 2.
× J ′ ′, MJ′ ′ μJ ′, MJ′ (10)
2
. (12)
The Zeeman effects are adopted in the diagonal elements. The off-
The coefficients C are obtained from an orthogonal matrix when 32
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
Table 2 Isotope shifts of 3d24s2 → 3d24s4p, 3d34s → 3d34p, and 3d34s → 3d24s4p transitions in Ti I observed in this work and in the earlier work. Transition
Wavenumber
Lower [5]
J
Upper [5]
3d 4s → 3d 4s4p b3F 4 y3G b3F 3 z3P a3D 1 v3D 2 3 3 b P 1 y3P 0 1 2 1 2 3 b F 2 y3F 4 3 2 1 z5D a5F 2 3 4 5 3 a G 5 y3G 4 3 b3P 1 w3D 0 a5P 1 z5S 2 3 a5F 5 z5F 2 4 1 3 2 2 3 3
−1
−1
)
J
(cm
5 2 1 2 3 2 1 1 2 0 1 3 4 3 2 0 1 2 3 4 5 4 3 2 1 2
5 3 4 2 3 2 1 2
15979.286 13853.9138 13814.4747 13766.8098 13665.8088 13744.3504 13730.0949 13664.2009 13660.4579 13624.4348 13580.3045 13695.4504 13611.5141 13587.4080 13575.6496 11905.8877 11884.0038 11864.0482 11851.1837 11852.1562 12529.7304 12457.8693 12390.8596 11707.2830 11665.7515 11121.1014 11074.4379 10997.2399 10372.4271 10362.6771 10332.5020 10318.2858 10300.4359 10276.3548 10218.3990 10214.1162
3 4 5 6 5 4 4 5 J 5 2 1 1 0 2 1 5 3 2 1
22041.7801 22045.6258 22053.0944 17492.609 17418.386 17416.839 17166.495 16663.004 (cm−1 ) 16412.667 14288.6308 14272.3901 14264.7074 14259.3602 14203.0191 14179.0966 13904.6070 13866.8822 13799.0901 13786.0472
3 3 4 2 3 4 2 4 1 3 2 4
29914.7292 25227.2211 25218.1939 25107.4107 25057.0870 25001.4550 18525.049 18524.998 18482.772 18423.819 18354.912 18308.260
Obs.-Ref. (cm
)
Isotope shift (MHz) 50-48
MikSMS
Fik
49-48
47-48
−792 (9) −635 (10)
812 (6) 624 (10)
−757 (10)
756 (10)
−730 (6)
745 (6)
Ref.
3
46-48
(GHz/fm2)
(10 GHz amu)
858 (6) 1669 (2) 1308 (3) 1308 (4) 1305 (5) 1564 (5) 1552 (5) 1542 (3) 1558 (4) 1534 (3) 1538 (3) 1266 (3) 1277 (4) 1264 (3) 1318 (3) 1530 (3) 1529 (3) 1530 (3) 1528 (4) 1530 (3) 539 (3) 548 (3) 572 (3) 601 (6) 641 (3) 1441 (4) 1440 (3) 1439 (3) 1574 (1) 1575 (2) 1576 (2) 1575 (2) 1574 (2) 1577 (2) 1575 (2) 1575 (3)
−0.08 (18) 0.16 (12) 0.15 (23) 0.09 (23) 0.10 (24) 0.20 (23) 0.15 (16) 0.12 (16) 0.19 (22) 0.12 (16) 0.14 (25) 0.15 (17) 0.13 (21) 0.09 (15) 0.09 (15) 0.11 (13) 0.06 (14) 0.15 (17) 0.15 (21) 0.19 (18) −0.05 (11) −0.03 (11) −0.10 (9) −0.16 (20) −0.01 (12) 0.04 (18) 0.07 (14) 0.07 (14) 0.12 (8) 0.16 (13) 0.12 (12) 0.14 (12) 0.17 (13) 0.14 (12) 0.14 (12) 0.18 (17)
−1.218 −2.050 −1.647 −1.657 −1.653 −1.925 −1.919 −1.902 −1.919 −1.901 −1.934 −1.604 −1.616 −1.606 −1.665 −1.870 −1.876 −1.865 −1.861 −1.859 −0.806 −0.812 −0.846 −0.875 −0.899 −1.767 −1.762 −1.761 −1.892 −1.889 −1.893 −1.890 −1.885 −1.892 −1.889 −1.884
−680 (5) −682 (5) −676 (6) −576.5 (24) −565.7 (41) −542.0 (23) −510.0 (27) −233.3 (20) 46-48 −199.5 (42) 1000 (5) 1018 (3) 1022 (5) 1041 (2) 991 (2) 1040 (5) −100 (1) 759 (2) 1066 (2) 780 (2)
−0.33 (19) −0.29 (18) −0.29 (13) −0.24 (11) −0.25 (13) −0.33 (7) −0.27 (6) −0.27 (11) (GHz/fm2) −0.22 (11) 0.08 (20) 0.07 (21) 0.13 (26) 0.10 (10) 0.05 (20) 0.09 (24) −0.16 (10) 0.07 (7) 0.10 (10) 0.17 (11)
0.349 (48) 0.357 (46) 0.350 (33) 0.320 (18) 0.309 (22) 0.270 (12) 0.248 (10) −0.048 (18) (103 GHz amu) −0.076 (18) −1.321 (22) −1.347 (25) −1.345 (26) −1.370 (13) −1.319 (25) −1.369 (24) −0.137 (16) −1.052 (10) −1.390 (10) −1.066 (12)
−851 (5) −1303.3 (18) −1305.2 (18) −1241.7 (20) −1305.2 (18) −1274 (9) −771.0 (60) −768.0 (60) −767.0 (60) −768.0 (60) −762.0 (120) −776.1 (48)
−0.48 −0.31 −0.28 −0.43 −0.28 −0.27 −0.47 −0.47 −0.47 −0.37 −0.56 −0.33
0.392 0.986 0.988 0.909 0.998 0.965 0.488 0.488 0.487 0.502 0.472 0.517
2
3d34s → 3d34p a5F 3 4 5 3 a H 6 5 4 b1G 4 a3H 4 Lower [5] J 1 b G 4 3 1 c P 0 1 1 2 2 1 a H 5 3 b F 4 3 2
y5F
y3H
y3H z1H Upper [5] z1H x3P
z1H y3D
3d24s2 → 3d24s4p a3F 2 x3G a3F 2 y3F 3 2 3 4 a3F 2 z5D 3 2 3 3 4
(2) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (3) (3) (1) (1) (1) (1) (1) (2) (1) (1) (2) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (2) (1)
−0.0088 −0.0073 −0.0032 −0.0113 −0.0156 −0.0141 −0.0111 −0.0121 −0.0082 −0.0135 0.0103 −0.0049 −0.0049 −0.0043 −0.0063 −0.0072 −0.0097 −0.0112 −0.0087 −0.0126 −0.0127 −0.0094 0.0010 −0.0114 −0.0025 −0.0021 −0.0020 0.0031 0.0021 0.0030 0.0007 0.0048 0.0048 0.0030 0.0032
(4) (12) (20)
0.0051 0.0008 0.0004
(cm−1 ) (6) (2) (2) (3) (1) (1) (1) (1) (1) (1)
−0.0092 −0.0049 −0.0056 −0.0058 −0.0069 −0.0104 −0.0040 −0.0107 −0.0098 −0.0121
−785 (7) −1549 (2) −1206 (5) −1210 (4) −1208 (5) −1448 (5) −1438 (5) −1430 (3) −1446 (4) −1419 (5) −1430 (3) −1175 (3) −1184 (4) −1170 (3) −1219 (3) −1416 (3) −1412 (3) −1418 (3) −1416 (4) −1420 (3) −493 (3) −503 (3) −521 (3) −544 (6) −590 (3) −1330 (4) −1331 (3) −1244 (3) −1457 (1) −1460 (2) −1458 (2) −1459 (2) −1459 (2) −1461 (2) −1459 (2) −1461 (3) 646 (5) 645 (5) 640 (6) 543.3 (20) 534.7 (37) 514.1 (24) 490.0 (48) 231.0 (24) 50-48 195.0 (48) −921 (5) −941 (3) −949 (5) −964 (2) −916 (2) −963 (3) 102 (1) −699 (2) −985 (2) −725 (2) 812 (11) 1216.8 (24) 1215.6 (19) 1172.2 (20) 1215.6 (19) 1183 (18) 729.0 (90) 735.0 (60) 734.0 (60) 729.0 (60) 735.0 (90) 734.4 (48)
293.5 (51) 288.3 (68) 284.6 (27) 260.0 (39) 132.5 (54) 49-48 111.5 (30) −475 (10) −486 (10)
−270.5 (55) −269.3 (71) −252.8 (28) −236.5 (39) −104.6 (71) 47-48 −90.2 (21) 482 (10) 486 (10)
−498 (5) −467 (10)
506 (5) 476 (10)
−365 (3) −512 (4) −383 (4)
366 (3) 515 (4) 375 (4)
640.4 (21) 638.5 (21) 619.8 (21) 638.5 (21) 624 (10)
−628.2 (24) −627.6 (22) −595.3 (21) −627.6 (22) -615 (16)
(30) (6) (6) (7) (6) (22) (39) (39) (39) (36) (61) (30)
(46) (15) (26) (23) (23) (25) (25) (15) (22) (15) (24) (16) (20) (15) (15) (15) (13) (16) (20) (18) (10) (11) (9) (20) (12) (17) (14) (14) (7) (13) (12) (12) (13) (12) (12) (17)
(72) (10) (10) (12) (10) (32) (61) (61) (61) (56) (97) (47)
[6](a)
[8] [8] [8] [8] [8] [8]
[6] [23] [23] [23] [23] [24] [7] [7] [7] [7] [7] [7]
(continued on next page) 33
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
Table 2 (continued) Transition Lower [5]
J 4 1 1 2 0 1 1 4 2 1 0 4
a3P
a3P a3P a1G a3P
a1G
3d 4s → 3d 4p 2 a3F 3 4 a3P 2 1 0 2 1 2 2
2
Upper [5]
z3P
z3S y3F z1G z3D
z1F
Wavenumber
Obs.-Ref.
Isotope shift (MHz)
J
(cm−1 )
(cm−1 )
50-48
3 0 2 2 1 1 2 4 3 2 1 3
18207.065 17082.494 17001.316 16891.396 16484.507 16428.698 16614.993 12576.4939 11523.7135 11513.6184 11501.2359 10286.3487
−0.0061 −0.0054 −0.0025 −0.0021 0.0007
735.0 (90) 661.0 (35) 845.8 (54) 838.7 (102) 637.6 (42) 627.9 (52) 1171.8 (24) 984 (2) 558 (2) 554 (2) 544 (2) 825 (2)
1 2 3 3 2 1 2 1 1
25324.983 25275.886 25263.945 17041.363 16946.492 16881.203 16836.570 16825.397 16715.479
(3) (1) (1) (1) (1)
49-48
47-48
347.0 (55) 444.3 (57) 436.4 (96) 341.7 (60) 348.4 (51) 614.9 (57) 522 (10)
−335.3 (45) −430.8 (54) −419.1 (84) −315.7 (53) −310.1 (51) −594.9 (51) −501 (10)
860.4 747.8 878.3 883.2 739.6 876.6 739.6 890.5 883.1
−837.2 −710.8 −857.1 −850.6 −720.8 −846.3 −718.6 −855.1 −848.2
Fik
MikSMS
46-48
(GHz/fm2)
(103 GHz amu)
−774.0 (60) −697.0 (35) −897.5 (75) −885.7 (98) −661.4 (46) −662.8 (60) −1237.8 (45) −1044 (2) −586 (2) −584 (2) −572 (2) −866 (2)
−0.38 −0.25 −0.27 −0.30 −0.39 −0.42 −0.45 −0.35 −0.30 −0.28 −0.28 −0.46
(27) (10) (11) (17) (12) (12) (13) (23) (17) (16) (16) (35)
0.511 0.461 0.681 0.664 0.417 0.408 1.045 0.905 0.422 0.422 0.410 0.733
(41) (16) (22) (34) (21) (21) (22) (40) (27) (26) (26) (55)
[7] [8] [14] [14] [8] [8] [8]
−1745.0 −1487.4 −1780.4 −1776.0 −1506.5 −1769.1 −1497.5 −1785.7 −1774.1
−0.47 −0.57 −0.47 −0.55 −0.37 −0.55 −0.41 −0.60 −0.60
(9) (9) (8) (14) (10) (10) (9) (4) (4)
1.454 1.160 1.495 1.616 1.340 1.609 1.327 1.620 1.612
(14) (13) (12) (49) (11) (12) (10) (6) (4)
[23] [23] [23] [14] [14] [14] [14] [14] [14]
Ref.
3
y3D
y3D
(a) L. Gianfrani reported IS were Δν(50
48)
1631.4 1403.3 1667.2 1670.2 1400.8 1663.5 1400.8 1678.5 1667.8
= 858 MHz and Δν(46
48)
(28) (24) (24) (98) (96) (110) (96) (87) (45)
(25) (21) (27) (24) (90) (90) (90) (60) (62)
(27) (20) (21) (112) (60) (79) (60) (52) (48)
(26) (20) (20) (90) (45) (82) (45) (105) (63)
= − 785 MHz. The values in the table are changed.
effects and the interaction of the magnetic field. The unperturbed line positions of the odd mass isotopes were determined by the analysis of the HFS in the intermediate-field approximation. The hyperfine constants AJ and BJ for the even-parity level were determined using ABMR–LIRF[13]. In addition, those of the odd-parity levels were reported using high-resolution atomic-beam ultraviolet laser spectroscopy[23]. However, the constants AJ and BJ of 3d34s b3FJ (J = 2, 3, 4) for 49Ti have not been reported. In this case, the following relationships can be used to perform the calculations. 47
A B
Ti / A49Ti
47
Ti / B 49Ti
= (μI / I ) 47Ti /(μI / I ) 49Ti = 0.99973(8)
(13)
= (Q) 47Ti /(Q) 49Ti = 1.21(7)
(14)
Additionally, the gJ factors determined by our previous work were used[15]. As an example of a result of the Zeeman splitting analysis for HFS spectra, the observed lines of b3FJ → y3DJ−1(J = 2,3,4) and those calculated HFS lines are shown in Fig. 2. The calculations for each Zeeman component are represented by column charts in this figure. The calculated lines were fitted to the observed lines to determine the center of the lines of 47Ti and 49Ti. The King plot analysis using Eq. (6) for the transitions b3FJ → y3DJ−1 (J = 2, 3, 4) are shown in Fig. 3. The electronic factors of Fik and MikSMS can be determined from the King plot analysis. A least squares fitting using the square of the reciprocal of frequency error as a weight was performed. The saturated absorption lines related to 53 transitions in Ti I were observed. The observed values of the IS, including 47Ti and 49Ti, are shown in Table 2. With the exception of b3FJ → y3DJ−1(J = 2,3,4) and b3F3 → z3P2, the lines of 47Ti and 49Ti were determined by the peaks of the lines because these HFS-splitting lines were small. The assignment of the isotope lines was based on the fact that the spectral intensity is proportional to its natural abundance. In addition, for comparison, the previous reports of IS in Ti I performed by other researchers [6–8,14,23] are also listed in Table 2. The assignment of the levels used is reported by E. B. Saloman [5]. The lines of 3d24s2 → 3d24s4p, 3d24s2 → 3d34p, 3d34s → 3d34p, and 3d34s → 3d24s4p are compiled in the table. These transitions are from the metastable states belonging to the configurations 3d24s2 and 3d34s. The frequency of the lines of MJ = 0 in 48Ti are also shown in this Table. The centers of the Zeeman lines in the ΔJ = 0 type were determined by calculating the center of
Fig. 4. Schematic diagram of the CD analysis for transitions a3F2 → y3F2 and b3F2 → y3F2.
diagonalizing the energy matrix. 4. Results and discussion 4.1. Isotope line positions and king plot The traces of the saturated absorption lines in b3FJ → y3DJ−1 (J = 2,3,4) are shown in Fig. 1. The full width at half maximum (FWHM) of the lines were approximately 15 MHz. In the figure, the lines related to five stable isotopes 46Ti, 47Ti, 48Ti, 49Ti, and 50Ti can be seen clearly. The intensity of the lines depends on the natural abundance of the isotopes, as shown in Table 1. These lines were split into Zeeman components of ΔJ = ± 1 type in the parallel field case. Because the Zeeman components of the even-mass isotopes 46Ti,48Ti, and 50 Ti are only the components of MJ = 0, ⋯, ± J, the centers of those lines can be easily determined. The IS of the 46, 50Ti of the transition b3F3 → y3D2 was shifted approximately 300 MHz, which is wider than that of b3F2 → y3D1 and b3F4 → y3D3. The lines of the odd mass isotopes are complex due to the hyperfine 34
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S. Kobayashi et al.
Table 3 Results of the CD analysis in order to compare the electronic factors Fgi and MgiSMS between the ground state a3F2 and the levels belonging to the configurations 3d24s2 and 3d34s. Even-parity level
Mixing rate [5]
Configuration
Term
Energy (cm−1 )
First
3d24s2 3d24s2 3d24s2 3d24s2 3d24s2 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(2G)4s
a3F3 a3F4 a3P0 a3P1 a3P2 a5F1 a5F2 a5F3 a5F4 a5F5 b3F2 b3F3 b3F4 a3G5
170.1328 386.874 8436.618 8492.422 8602.3441 6556.883 6598.765 6661.006 6742.756 6842.962 11531.761 11639.8109 11776.812 15220.393
1.00 1.00 0.92 0.92 0.90 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98 0.98
Second
3
0.07 0.07 0.07
3
3d 4s P 3d34s3P 3d34s3P
Fgi
MgiSMS
(GHz/fm2)
(103 GHz amu)
−0.03 (12) −0.04 (40) 0.08 (19) 0.13 (15) 0.13 (15) −0.53 (77) −0.53 (53) −0.62 (56) −0.55 (69) −0.53 (76) −0.59 (22) −0.40 (21) −0.44 (39) −0.47 (68)(a)
−0.006 (20) 0.020 (62) −0.155 (26) −0.166 (20) −0.160 (18) 2.361 (98) 2.363 (74) 2.353 (77) 2.360 (96) 2.404 (107) 2.540 (27) 2.595 (25) 2.603 (50) 2.191 (106)(a)
(a) The changed electronic factors of b3F4 → y3G5 listed in Table 1 were used. Table 4 The electronic factors Fgk and MgkSMS of the odd parity states referred to the ground state a3F2. Odd parity Levels
Mixing rate[26]
Configurations
Terms
Energy (cm−1 )
First
3d2(3F)4s4p
z5F1 z5F2 z5F3 z5F4 z5F5 z5D0 z5D1 z5D2 z5D3 z5D4 z3D1 z3D2 z3D3 z3S1 z3P2 z3P0 y3D1 y3D2 y3D3 y3F2 y3F3 y3F4 y3G5 y5F3 y5F4 y5F5 x3G3
16817.160 16875.124 16961.442 17075.258 17215.390 18462.722 18482.774 18525.059 18593.947 18695.134 19937.855 20006.039 20126.062 24921.117 25493.733 25574.908 25317.814 25438.908 25643.701 25107.411 25227.222 25388.331 27750.135 28702.778 28788.380 28896.059 29914.737
0.96 0.95 0.97 0.98 0.99 0.95 0.95 0.94 0.95 0.95 0.85 0.86 0.85 0.91 0.52 0.51 0.51 0.37 0.36 0.48 0.46 0.42 0.49 0.98 0.97 0.97 0.76
3d2(3F)4s4p
3d2(3F)4s4p
3d2(3P)4s4p 3d2(1D)4s4p 3d3(4F)4p
3d2(3F)4s4p
3d2(2F)4s4p 3d3(4F)4p
3d2(1G)4s4p
Second
Third
0.07 0.08 0.07 0.07 0.36 0.34 0.36 0.32 0.34 0.24 0.22 0.25 0.24
3d24s4p3D 3d24s4p3D 3d24s4p3D 3d34p3S 3d24s4p5D 3d24s4p5D 3d24s4p3D 3d24s4p3D 3d24s4p3D 3d34p3F 3d34p3F 3d24s4p3F 3d34p3G
0.18
3d24s4p3G
0.13 0.12
3d24s4p3D 3d24s4p3S
0.21 0.20 0.23 0.22 0.23 0.09
3d24s4p3D 3d24s4p3D 3d24s4p3F 3d24s4p3F 3d34p3F 3d34p3G
Contribution
Fgk
MgkSMS
3d34p ζ
(GHz/fm2)
(103-GHz amu)
0.04 0.05 0.03 0.02 0.01 0.05 0.05 0.06 0.03 0.03 0.08 0.06 0.08 0.07 0.10 0.03 0.51 0.37 0.36 0.23 0.22 0.23 0.33 0.98 0.97 0.97 0.06
−0.39 −0.41 −0.41 −0.43 −0.41 −0.42 −0.47 −0.47 −0.40 −0.50 −0.20 −0.15 −0.17 −0.30 −0.18 −0.12 −0.46 −0.36 −0.43 −0.42 −0.34 −0.31 −0.52 −0.95 −0.84 −0.82 −0.48
0.474 0.470 0.471 0.464 0.512 0.491 0.487 0.488 0.496 0.482 0.255 0.256 0.264 0.252 0.522 0.295 1.458 1.176 1.509 0.888 0.976 0.987 1.385 2.702 2.714 2.754 0.392
(4) (5) (3) (2) (1) (5) (5) (6) (3) (3) (8) (6) (8) (2) (10) (3) (13) (10) (10) (5) (10) (10) (18) (2) (3) (3) (6)
(65) (76) (68) (81) (84) (90) (39) (39) (48) (51) (35) (31) (32) (29) (30) (25) (23) (25) (39) (24) (25) (18) (57)(a) (75) (87) (89) (30)
(86) (97) (89) (108) (114) (113) (61) (61) (76) (81) (51) (46) (45) (44) (45) (36) (28) (32) (67) (32) (31) (30) (96)(a) (125) (142) (140) (72)
(a) The changed electronic factors of b3F4 → y3G5 were used.
Guo Jin et al.[23]. In addition, the significant ISs of the transitions related to y3D2 in a3FJ → y3DJ−1 and a3PJ → y3DJ were also reported by Wei-Guo Jin et al.[23] and Yu P. Gangrsky et al.[14]. Gangrsky et al. reported that these significant ISs are caused by the perturbation of the energy level of y3D2 and those of z3P2. Therefore, the significant IS of b3F3 → y3D2 was caused by the perturbation of y3D2 from z3P2. The IS of 46Ti and 50Ti of the transition b3F4 → y3G5 was reported by L. Gianfrani et al. [6] as Δν50, 48 = 858 MHz and Δν46, 48 = − 785 MHz. However, in the transitions 3d34s → 3d24s4p, the lines of 46Ti are higher than those of 50Ti in terms of frequency. Furthermore, the electronic factors calculated by their assignment showed deviations from those of all other transitions, as discussed in section 4.2.2. The IS of b3F4 → y3G5 must be changed to Δν50, 48 = − 785 MHz and Δν46, 48 = 858 MHz.
gravity of the lines of MJ = ± J. The sequence of the isotopic lines of the transitions between the levels belonging to 3d24s2 and 3d24s4p or 3d34p is 46Ti, 47Ti, 48Ti, 49Ti, and 50Ti, in order of frequency. In the transitions 3d34s → 3d24s4p, the sequence is reversed. However, the frequency order of the IS of transitions between the levels 3d34s and 3d34p were different in the individual transitions. For example, the sequence of the IS of a3HJ → y3HJ (J = 4, 5, 6) [8] was reversed to that of b3FJ → y3DJ−1 (J = 2, 3, 4). In the transitions b3FJ → y3FJ, b3FJ → y3DJ−1 (J = 2, 3, 4), a significant IS, which indicates that it has a J dependency caused by a perturbation from other levels, was observed at the transitions related to y3F2 and y3D2. The significant IS of the transition related to y3F2 was observed in the transitions a3FJ → y3FJ (J = 2, 3, 4) reported by Wei35
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between Fa3F2, y3F2 and Fb3F2, y3F2. Consequently, we can easily estimate the electronic factors based on the ground state a3F2. The results of the CD analysis for the comparison of the electronic factors of the evenparity levels are given in Table 3. The subscript gi denotes the transition between the ground state g and the even-parity level i. The first five row values of Fgi and MgiSMS should be zero if the provided levels are pure, and if the higher-order effects are neglected [11]. The other rows are the electronic factors for transitions between 3d24s2 and 3d34s. The difference in the factors of SMS between 3d24s2 and 3d34s is approximately 2.5 × 103 GHz amu, which is related to the difference in the number of d−electrons. 4.2.2. Odd parity state The IS analysis for the chromium atom was studied by B. Furmann et al. in 2005[25]. They reported the configuration interaction (CI) analysis for the isotopic effects in chromium. Similarly, the CI analysis can be adopted in the case of neutral titanium. Any electron state is expressed as a mixture of the levels belonging to different configurations
Ψ=
∑ ζn An , n
(16)
where An represents a configuration with the same parity, and ζn is the mixing rate of the configuration An. Obviously, ζn satisfies
∑ ζn = 1. n
(17)
Accordingly, the electronic factors of SMS and FS are described as linear combinations of the factors for pure configurations, as follows SMS Mgk =
∑ ζn MnSMS , n
Fgk =
4.2.1. Even parity state The electronic factors of the SMS and FS determined by the King plot analysis are not resolved into the individual levels. However, these relationships can be described as follows:
(15)
MiSMS
where and Fi represent the electronic factors of the i-th level. Therefore, the combination difference (CD) analysis is useful to estimate the factors of SMS and FS between the levels, which include even forbidden transitions. The schematic diagram of the CD analysis is shown in Fig. 4. The CD analysis was performed for the transitions a3FJ → y3FJ, J ± 1 (J = 2, 3, 4) and b3FJ → y3FJ (J = 2, 3, 4). The former transitions were reported by Wei-Guo Jin[23]. In addition, we reported the IS of the transition a3F4 → y3F4[24]. The latter, which is indicated by the thick arrow in the figure, is measured in this work. The synthetic transition is represented by the dashed arrows. For example, the factor of MikSMS for a3F2 and b3F2 is obtained using the CD analysis
M SMS 3
a F2, b3F2
=
(M SMS y3F2
= MaSMS 3 F
−
3 2, y F2
M SMS ) a3F2
−
− MbSMS 3 F
(M SMS y3F2
3 2, y F2
− M SMS 3 ) b F2
= M SMS − M SMS 3 3 . b F2
a F2
In addition, the factors of Fa3F2,
b3F2
(19)
In all the studied transitions in Ti I, although the degree of mixing of the lower levels is small, the electronic factors of the configuration 3d34s differ completely from those of the configuration 3d24s2. Hence, the difference in the electronic factors at lower levels cannot be ignored. In contrast, the odd-parity configurations 3d24s4p and 3d34p are complexly perturbed by each other. However, the perturbations from other odd-parity levels, such as 3d4s24p and 3d24s5p, are extremely small[26]. Therefore, the levels of 3d24s4p and 3d34p can be approximated as a case of just two configuration interactions. In order to cancel the difference in the electronic factors of the lower levels, the CD method was also adopted. The results are listed in Table 4. The subscript k represents the odd parity state belonging to 3d24s4p or 3d34p. The contributions of the 3d34p denoted by ζn are also tabulated. These values are reported by C. Roth[26]. The dependence of MgkSMS and Fgk on the configuration of 3d34p is shown in Fig. 5. These plots show almost linearity. These figures indicate the dependence of the electronic factors of FS and SMS on changes in the number of s− or d−electrons. However, the squared points in these figures have large discrepancies. These values were derived from the IS of b3F4 → y3G5, as reported by L. Gianfrani [6]. They assigned the IS to be Δν50, 48 = 858 MHz and Δν46, 48 = − 785 MHz, respectively. Using the King plot analysis, the Fik = − 2.30(59) GHz/fm2 and MikSMS = 0.327 (148) 103GHz⋅amu were obtained. The factors Fgk and MgkSMS, which refer to the ground state, were derived from the CD analysis using the values Fa3F2, b3F4 = − 0.44 (39) GHz/fm2 and Ma3F2, b3F4SMS = 2.592 (50) 103GHz⋅amu listed in Table 3. In this case, the factors of FS and SMS are −2.74 (120) GHz/fm2 and 2.930 (218) ×103GHz⋅amu, respectively. However, these values can be changed in the shaded area by making Δν50, 48 = − 785 MHz and Δν46, 48 = 858 MHz, as shown in Fig. 5.
4.2. Analysis of results
MikSMS = MkSMS − MiSMS , Fik = Fk − Fi ,
∑ ζn Fn. n
Fig. 5. The configuration interaction analysis for the electronic factors of the odd-parity states. The experimental plots were fallen off the shaded band except for the values indicated by the square.
(18)
are derived from the difference 36
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
5. Conclusion [12]
The saturated absorption line in Ti I was measured using a ring-type Ti:sapphire laser with wavelengths in the 9950 to 14380 cm−1 region. The electronic factors for the FS and for the SMS were newly determined using the King plot analysis in 53 transitions. The isotope lines of titanium can be easily estimated with accuracy as high as the Doppler width using the results of the configuration interaction.
[13]
[14]
[15]
References [16] [1] Yu.P. Gangrsky, K.P. Marinova, S.G. Zemlyanori, I.D. Moore, J. Billowes, P. Campbell, K.T. Flanagan, D.H. Forest, J.A.R. Griffith, J. Huikari, R. Moore, A. Nieminen, H. Thayer, G. Tungate, J. Aysto, Nuclear charge radii of neutron deficient titanium isotopes 44ti and 45ti, J. Phys. G 30 (2004) 1089. [2] E.W. Otten, Nuclear Radii and Moments of Unstable Isotopes, Vol. 8 Plenum, New York, 1989. [3] C. E. Moore, ”Atomic Energy Levels”, U. S. GPO, Washington D. C. I, nBS Circular 467. [4] P. Forsberg, The Spectrum and Term System of Neutral Titanium, Ti I, Phys. Scr. 44 (1991) 446–476. [5] E.B. Saloman, Energy levels and observed spectral lines of neutral and singly ionized titanium, Ti I and Ti II, J. Phys. Chem. Ref. Data 41 (2012) 013101. [6] L. Gianfrani, O. Monda, A. Sasso, M.I. Schisano, G.M. Tino, M. Inguscio, Visible and ultraviolet high resolution spectroscopy of Ti I and Ti II, Optics Comm. 83 (5) (1991) 300. [7] E.M. Azaroual, P. Luc, R. Vetter, Isotope shift measurements in titanium I, Z. Phys. D-Atoms, Molecules and Clusters 24 (1992) 161–164. [8] B. Furmann, D. Stefańska, A. Krzykowski, A. Jarosz, A. Kajoch, ’Isotope shift measurements in titanium I, Z. Phys. D 37 (1996) 289–294. [9] P. Luc, R. Vetter, C. Bauche-Arnoult, J. Bauche, Isotope shift and hyperfine structure measurements in titanium I, Z. Phys. D 31 (1994) 145–148. [10] F.C. Cruz, A. Mirage, J.V.B. Gomide, A. Scalabrin, D. Pereira, Wavenumber and isotopic shifts of the 3P0−3D1O transition of titanium, Optics Comm. 106 (1994) 59–64. [11] U. Johann, J. Dembczynski, W. Ertmer, Experimental evidence for far configuration
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mixing effects on off-diagonal hfs interaction between the (3d + 4s)N+2 configurations of free atoms, Z. Phys. A 303 (1) (1981) 7–12. E. Stachowska, Fine structure analysis of the even parity configuration system in Ti I, Z. Phys. D 42 (1997) 33–43. R. Aydin, E. Stachowska, U. Johann, J. Dembczynski, P. Unkel, W. Ertmer, Sternheimer free determination fo the 47Ti nuclear quadrupole momoent from hyperfine structure measurements, Z. Phys. D 15 (4) (1990) 281–291. Yu P Gangrsky, K.P. Marinova, ”. S G Zemlyanoi, J dependences of the isotope shifts in Ti I 3d24s2 a3P and 3d34p y3DO terms, J. Phys. B: At. Mol. Opt. Phys. 28 (1995) 957–964. S. Kobayashi, N. Nishimiya, M. Suzuki, Near-infrared spectroscopy for zeeman spectra of Ti I in plasma using a facing target sputtering system, J. Phys. Soc. Jpn. 86 (2017) 104303. E.A. Donley, T.P. Heavner, F. Levi, M.O. Tataw, S.R. Jefferts, Double-pass acoustooptic modulator system, Rev. Sci. Instrum. 76 (2005) 063112. Chih-Hao Chang, R.K. Heilmann, M.L. Schattengurg, P. Glenn, Design of doublepass shear mode acoust-optic modulator, Rev. Sci. Instrum. 79 (2008) 033104. F. Nez, F. Biraben, R. Felder, Y. Millerioux, ’optical frequency determination of the hyperfine components of the s1/2 − 5d3/2 two-photon transitions in rubidium, Optics Comm. 102 (1993) 432–438. W.H. King, Isotope Shifts in Atomic Spectra, Plenum, New York, 1984. C.H. Townes, A.L. Schawlow, Microwave Spectroscopy, McGRAW-HILL BOOK, 1955. J.R. Delaeter, J.K. Böhlke, P. De Bièvre, H. Hidaka, H.S. Peiser, K.J.R. Rosman, P.D.P. Taylor, Atomic Weights of the Elements:Review 2000, Pure Appl. Chem. 75 (6) (2003) 683–800. Gladys H. Fuller, Nuclear spines and moments, J. Phys. Chem. Ref. Data 5 (2009) 835. Wei-Guo Jin, Yoshikazu Nemoto, ”. Tatuya Minowa, Hyperfine sturcture and isotope shift in Ti I by UV laser spectroscopy, J. Phys. Soc. Jpn. 78 (9) (2009) 094301. N. Nishimiya, K. Watanabe, T. Yamaguchi, Y. Yasuda, M. Suzuki, Measurement of temperature and density of Ti a3FJ state in a facing target plasma by using saturated absorption spectroscopy, The 11th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas, Mons, Belgium, 2013. B. Furmann, A. Harosz, D. Stefańska, J. Dembczyński, E. Stachowska, Isotope shift in chromium, Spectrochim. Acta B 60 (2005) 33–40. C. Roth, Effective interactions for the configuration 3d34p + 3d24s4p + 3d4s24p in the first spectrum of titanium, Can. J. Chem. 60 (1982) 469–479.
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Spectrochimica Acta Part B journal homepage: www.elsevier.com/locate/sab
Isotope shifts in the spectrum of the neutral titanium atom ⁎
T
Shinji Kobayashi , Nobuo Nishimiya, Masao Suzuki Department of Electronic and Information Technology, Tokyo Polytechnic University, Iiyama 1583, Atsugi City, Kanagawa 243-0297, Japan
A R T I C LE I N FO
A B S T R A C T
Keywords: Isotope Shift Saturated absorption spectroscopy
An investigation of 53 saturated absorption lines of titanium at wavelengths ranging from 695 to 1005 nm is performed. In addition, transitions 3d34s a5FJ → 3d34p y5FJ (J = 3, 4, 5) in the ultraviolet range are measured. The isotope lines of 46Ti, 48Ti, and 50Ti are clearly observed for 53 transitions. A facing target sputtering system containing a magnetic field is used as a sample cell of titanium in this experiment. The Zeeman effect in a hyperfine structure is calculated for the condition of an intermediate field approximation to determine the unperturbed line positions in the odd mass isotopes 47Ti and 49Ti. For all observed transitions, the King plot analysis is performed to determine the electronic factors of the field shift and specific mass shift.
1. Introduction The isotope shift (IS) in atomic spectra is caused by interactions between an electron and the nucleus. In particular, the isotope shift is caused by the influence of the difference in the mass of the nucleus and the difference in the volume of the nucleus between isotopes. The former is called the mass shift, and the latter is called the field shift (FS). An analysis of the IS can provide information about the electronic states and the physical properties of the nucleus. Titanium is a very interesting atom in the field of nuclear physics because the atomic number of Ti, which is 22, is close to the proton magic number Z = 20, and 50Ti has the neutron magic number N = 28 [1,2]. The high-resolution Doppler-limited spectroscopy of the electronic transitions of Ti has been studied by several researchers[3–10]. The isotopes of the mass numbers ranging from 46 to 50 are stable, and their respective percentages of abundance are 8.25%, 7.44%, 73.72%, 5.41%, and 5.18%. The spectra of 47Ti and 49Ti are complicated due to their nuclear spin values of 5/2 and 7/2, respectively. The positions of the isotopic lines, including the hyperfine components, overlap within the Doppler profiles. Therefore, Doppler-free spectroscopy is useful for obtaining the line positions of the isotopic spectra and hyperfine lines of the odd-mass isotopes. U. Johan et al. measured the hyperfine structure of high-lying metastable states of 3d-shell atoms using atomic beam magnetic resonance detected by laser induced resonance fluorescence (ABMR–LIRF)[11]. They reported the strong configuration interaction between 3d24s2 a3P and 3d34s b3P. The fine-structure analysis of the even parity metastable state was investigated by E. Stachowska [12]. The results obtained systematically show the mixing effect of the metastable states belonging
⁎
to the even parity configuration. However, the configuration interactions of the fine structure in the odd parity levels at relatively higher energy levels than the metastable state are known to be complicated [13,14]. In this paper, we report the saturated absorption spectra of Ti I in the near-infrared region and in the ultraviolet region. The even-mass isotope spectra in 46, 48, 50Ti were measured for 53 transitions. The intermediate field approximation analysis was used to determine the unperturbed line positions of the odd mass isotopes 47, 49Ti. Electronic factors Fik and MikSMS were also determined. In addition, a combination difference (CD) analysis was adopted for two transitions with common upper levels to compare the electronic factors between the levels belonging to even-parity configurations 3d24s2 and those belonging to 3d34s. Using the results of the CD analysis for the even-parity levels, the electronic factors that referred to the ground state 3d24s2 a3F2 were determined. In the odd-parity level, the configuration 3d24s4p interacted with the configuration 3d34p. The factors Fik and MikSMS are affected by this interaction. To consider the influence of the perturbation between the odd-parity configuration on the electronic factors, a configuration-interaction analysis is performed. 2. Experiments An experiment was performed using a facing target sputtering (FTS) chamber and a Ti:sapphire ring laser. The experimental system is the same as the system shown in our previous report [15]. The spectroscopic measurement was carried out in the near-infrared region (695 − 1005 nm). An ultraviolet (UV) beam in the 450 nm region was obtained using a second harmonic generator (M-Squared Lasers, ECD-
Corresponding author. E-mail addresses: [email protected] (S. Kobayashi), [email protected] (N. Nishimiya).
https://doi.org/10.1016/j.sab.2018.08.010 Received 22 November 2017; Received in revised form 15 August 2018; Accepted 22 August 2018 Available online 05 September 2018 0584-8547/ © 2018 Elsevier B.V. All rights reserved.
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X). The FTS chamber was used to obtain a gaseous state of neutral titanium. The discharge current of 300–500 mA was applied with a voltage of 400–450 V. Argon gas was enclosed at a pressure of 4 Pa in the chamber for sputtering gas. The magnetic field was determined by the saturated absorption lines of 40Ar I to be 45.39 (2.9) mT [15]. The windows of the FTS were tilted close to Brewster’s angle to avoid the reflecting loss of the incident laser. The direction of polarization of the pump and probe beam were set to be parallel to the magnetic field (parallel field case). The power of the pump and probe beam were 150 − 380 μW and 90 − 240 μW, respectively. The intensity of the pump beam was modulated by an acousto-optic modulator (AOM) at 50 kHz. The double-pass method using the AOM [16,17] was adopted for the lock-in detection of the saturated absorption lines. For the UV case, a mechanical chopper was used for the intensity modulation. A wavelength meter (HighFinesse, WS6) and a 100-cm confocal Fabry–Pérot interferometer were used for the frequency measurement. To calibrate the frequency from the wavelength meter and the spacing of the fringe marker, two photon spectra of the Rb atom (5S1/2 − 5D5/ 87 85 Rb (2→4) : 385 284 2 Rb (3→5) : 385 285 142 367.0 (80) kHz and 566 366.3 (80) kHz) [18] were observed. The accuracy of the absolute frequency error was less than 30 MHz, and the relative error of our measuring system was estimated to be less than 5 MHz. These uncertainties include the the error related to the determination of the center of the lines and the frequency-measurement procedure mentioned above.
Fig. 1. Recorder trace of the saturated absorption lines in b3FJ → y3DJ−1 (J=2,3,4). These lines are split into the Zeeman lines of ΔJ = 1-type. (α′, α ) δr 2 MOD = Δr 2(α′, α )
′ Δνik(α ,α)Obs
where expressed as
m α′ − mα νik mα′⋅mα
where νik is the frequency of the transition i → k and me and mα are expressed in unit of (amu). The SMS is the correlations of the motion of multiple electrons, and can be expressed as
∑
×
i, j = X , Y , Z
is the electronic factor of the SMS. where The FS represents the effects of the difference of the nuclear charge distribution by the isotope, and is expressed as
(7)
In our calculations, a basis-wave function ∣I, MI; J, MJ〉 was used. The matrix elements of the Zeeman splitting of the hyperfine levels can be derived as follows (See the supplementary material for details). Diagonal:
(3)
G HFS I ′ ′, MI′ ′ ; J ′ ′, MJ′ ′ | H | I ′, MI′ ; J ′, MJ′ = μB (gJ MJ + gI MI ) BZ + AJ (MI MJ ) 1 BJ + (I (I + 1) − 3MI2 )(J (J + 1) − 3MJ2) 4 J (2J − 1) I (2I − 1)
where Fik is the electronic factor corresponding to the variation in ′ the electron charge distribution at the nucleus, and δr2(α ,α) is the change in the mean-square nuclear charge radii. These values for the isotope chain of Ti were reported by Y. P. Gangrsky et al. [1], as shown in ′ Table 1. The modified ISs ΔνikMOD and δr2(α ,α) are defined as
mα′⋅mα , m α′ − mα
BJ 2J (2J − 1) I (2I − 1) 2⎞ ⎛ Ji Jj + Jj Ji 2⎞ ⎛ Ii Î j ̂ + Ij Î i ̂ J ⎟. − δi, j I ̂ ⎟ ⎜3 − δi, j ⎜3 2 2 ⎠ ⎝ ⎠⎝
JZ + gI IZ ̂ ) BZ + AJ ⋅( I ⋅ J ) + = μB (gJ
MikSMS
Δνik(α′, α ) MOD = Δνik(α′, α ) Obs
can be obtained from the King
G HFS G + H A + H B H =H
(2)
ΔνikFS = Fik⋅δr 2(α′, α )
(6)
Owing to the nuclear spin, the lines of odd mass numbers are split into several components. These hyperfine lines are also split due to the magnetic field. The Hamiltonian of the Zeeman effect in hyperfine structures (HFSs) is given as follows [20]:
(1)
m α′ − mα mα′⋅mα
SMS
3.2. Hyperfine structure
The mass shift consists of the normal mass shift (NMS) and the specific mass shift (SMS). The NMS between the reference isotope α and the isotope α′ is given as
ΔνikSMS = MikSMS
νik + MikSMS . 1836.15
The electronic factor Fik and Mik plot analysis[19].
3.1. Isotope shift
(5)
is the observed IS. Therefore, the modified IS is
(α′, α ) ΔνikMOD = Fik⋅δr 2 MOD +
3. Fundamentals
ΔνikNMS = me
mα′⋅mα , m α′ − mα
(8) Off-diagonal:
HFS | I ′, MI′ ; J ′, MJ′ I ′ , MI′ ′ ; J ′ ′, MJ′ ′ | H ′
(4)
G
(9)
Table 1 Properties of the Ti isotopes. Isotope
Mass[21]
46
45.9526294 46.9517640 47.9479473 48.9478711 49.9447921
Ti Ti 48 Ti 49 Ti 50 Ti 47
(14) (11) (11) (11) (12)
'
Abundance[21]
δr2(α ,48) (fm2) [1]
I
8.25 (3) 7.44 (2) 73.72 (3) 5.41 (2) 5.18 (2)
0.110 (7) 0.030 (4)
0 5/2 0 7/2 0
-0.139 (9) -0.160 (7)
31
μI (nm)[22]
Q (fm2)[22]
-0.78846(6)
+29(1)
-1.10414(9)
+24(1)
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
Fig. 3. Estimation of Fik and MikSMS. The example shows an analysis for b3FJ → y3DJ−1 (J = 2, 3, 4).
Fig. 2. Comparison of the observed spectra and those of the calculated Zeeman spectra of HFS in b3FJ → y3DJ−1 J = (2,3,4). The column charts represent the calculated Zeeman components in HFS.
diagonal element has nuclear magnetic-dipole coupling effects and electronic quadruple coupling effects. Under the condition of the parallel field case, the selection rules for the optical transition between the lower level ∣I'', MI''; J'', MJ''〉 and the upper ∣I', MI'; J', MJ'〉 are
A = ⎡ J [I (I + 1) − MI (MI ± 1)][J (J + 1) − MJ (MJ ∓ 1)] ⎢2 ⎣ 3 BJ (2MI ± 1)(2MJ ∓ 1) + 4 2J (2J − 1) I (2I − 1) × [I (I + 1) − MI (MI ± 1)] 2 [J (J + 1) − MJ (MJ ∓ 1)] 2 ] δ I ′ ′, I ′± 1 δ J ′ ′, J ′∓ 1
ΔJ = 0, ± 1, ΔMJ = 0, ΔI = 0, ΔMI = 0,
3 BJ 1 [I (I + 1) − MI (MI ± 1)] 2 + 4 2J (2J − 1) I (2I − 1)
where the transition MJ = 0 is forbidden in ΔJ = 0. Relative intensities of the Zeeman components in the HFS are calculated from
1
[I (I + 1) − (MI ± 1)(MI ± 1
1
1 2)] 2
I∼
1
× [J (J + 1) − MJ (MJ ∓ 1)] 2 [J (J + 1) − (MJ ∓ 1)(MJ ∓ 2)] 2
∑
(11)
|C (J ′ ′, I ′ ′, F ′ ′; MJ′ ′ , MI′ ′ , MF′ ′ ) |2 C (J ′, I ′, F ′; MJ′ , MI′ , MF′ ) 2
MI′ ′, MI′, MJ′ ′ MJ′
δ I ′ ′, I ′± 2 δ J ′ ′, J ′∓ 2.
× J ′ ′, MJ′ ′ μJ ′, MJ′ (10)
2
. (12)
The Zeeman effects are adopted in the diagonal elements. The off-
The coefficients C are obtained from an orthogonal matrix when 32
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
Table 2 Isotope shifts of 3d24s2 → 3d24s4p, 3d34s → 3d34p, and 3d34s → 3d24s4p transitions in Ti I observed in this work and in the earlier work. Transition
Wavenumber
Lower [5]
J
Upper [5]
3d 4s → 3d 4s4p b3F 4 y3G b3F 3 z3P a3D 1 v3D 2 3 3 b P 1 y3P 0 1 2 1 2 3 b F 2 y3F 4 3 2 1 z5D a5F 2 3 4 5 3 a G 5 y3G 4 3 b3P 1 w3D 0 a5P 1 z5S 2 3 a5F 5 z5F 2 4 1 3 2 2 3 3
−1
−1
)
J
(cm
5 2 1 2 3 2 1 1 2 0 1 3 4 3 2 0 1 2 3 4 5 4 3 2 1 2
5 3 4 2 3 2 1 2
15979.286 13853.9138 13814.4747 13766.8098 13665.8088 13744.3504 13730.0949 13664.2009 13660.4579 13624.4348 13580.3045 13695.4504 13611.5141 13587.4080 13575.6496 11905.8877 11884.0038 11864.0482 11851.1837 11852.1562 12529.7304 12457.8693 12390.8596 11707.2830 11665.7515 11121.1014 11074.4379 10997.2399 10372.4271 10362.6771 10332.5020 10318.2858 10300.4359 10276.3548 10218.3990 10214.1162
3 4 5 6 5 4 4 5 J 5 2 1 1 0 2 1 5 3 2 1
22041.7801 22045.6258 22053.0944 17492.609 17418.386 17416.839 17166.495 16663.004 (cm−1 ) 16412.667 14288.6308 14272.3901 14264.7074 14259.3602 14203.0191 14179.0966 13904.6070 13866.8822 13799.0901 13786.0472
3 3 4 2 3 4 2 4 1 3 2 4
29914.7292 25227.2211 25218.1939 25107.4107 25057.0870 25001.4550 18525.049 18524.998 18482.772 18423.819 18354.912 18308.260
Obs.-Ref. (cm
)
Isotope shift (MHz) 50-48
MikSMS
Fik
49-48
47-48
−792 (9) −635 (10)
812 (6) 624 (10)
−757 (10)
756 (10)
−730 (6)
745 (6)
Ref.
3
46-48
(GHz/fm2)
(10 GHz amu)
858 (6) 1669 (2) 1308 (3) 1308 (4) 1305 (5) 1564 (5) 1552 (5) 1542 (3) 1558 (4) 1534 (3) 1538 (3) 1266 (3) 1277 (4) 1264 (3) 1318 (3) 1530 (3) 1529 (3) 1530 (3) 1528 (4) 1530 (3) 539 (3) 548 (3) 572 (3) 601 (6) 641 (3) 1441 (4) 1440 (3) 1439 (3) 1574 (1) 1575 (2) 1576 (2) 1575 (2) 1574 (2) 1577 (2) 1575 (2) 1575 (3)
−0.08 (18) 0.16 (12) 0.15 (23) 0.09 (23) 0.10 (24) 0.20 (23) 0.15 (16) 0.12 (16) 0.19 (22) 0.12 (16) 0.14 (25) 0.15 (17) 0.13 (21) 0.09 (15) 0.09 (15) 0.11 (13) 0.06 (14) 0.15 (17) 0.15 (21) 0.19 (18) −0.05 (11) −0.03 (11) −0.10 (9) −0.16 (20) −0.01 (12) 0.04 (18) 0.07 (14) 0.07 (14) 0.12 (8) 0.16 (13) 0.12 (12) 0.14 (12) 0.17 (13) 0.14 (12) 0.14 (12) 0.18 (17)
−1.218 −2.050 −1.647 −1.657 −1.653 −1.925 −1.919 −1.902 −1.919 −1.901 −1.934 −1.604 −1.616 −1.606 −1.665 −1.870 −1.876 −1.865 −1.861 −1.859 −0.806 −0.812 −0.846 −0.875 −0.899 −1.767 −1.762 −1.761 −1.892 −1.889 −1.893 −1.890 −1.885 −1.892 −1.889 −1.884
−680 (5) −682 (5) −676 (6) −576.5 (24) −565.7 (41) −542.0 (23) −510.0 (27) −233.3 (20) 46-48 −199.5 (42) 1000 (5) 1018 (3) 1022 (5) 1041 (2) 991 (2) 1040 (5) −100 (1) 759 (2) 1066 (2) 780 (2)
−0.33 (19) −0.29 (18) −0.29 (13) −0.24 (11) −0.25 (13) −0.33 (7) −0.27 (6) −0.27 (11) (GHz/fm2) −0.22 (11) 0.08 (20) 0.07 (21) 0.13 (26) 0.10 (10) 0.05 (20) 0.09 (24) −0.16 (10) 0.07 (7) 0.10 (10) 0.17 (11)
0.349 (48) 0.357 (46) 0.350 (33) 0.320 (18) 0.309 (22) 0.270 (12) 0.248 (10) −0.048 (18) (103 GHz amu) −0.076 (18) −1.321 (22) −1.347 (25) −1.345 (26) −1.370 (13) −1.319 (25) −1.369 (24) −0.137 (16) −1.052 (10) −1.390 (10) −1.066 (12)
−851 (5) −1303.3 (18) −1305.2 (18) −1241.7 (20) −1305.2 (18) −1274 (9) −771.0 (60) −768.0 (60) −767.0 (60) −768.0 (60) −762.0 (120) −776.1 (48)
−0.48 −0.31 −0.28 −0.43 −0.28 −0.27 −0.47 −0.47 −0.47 −0.37 −0.56 −0.33
0.392 0.986 0.988 0.909 0.998 0.965 0.488 0.488 0.487 0.502 0.472 0.517
2
3d34s → 3d34p a5F 3 4 5 3 a H 6 5 4 b1G 4 a3H 4 Lower [5] J 1 b G 4 3 1 c P 0 1 1 2 2 1 a H 5 3 b F 4 3 2
y5F
y3H
y3H z1H Upper [5] z1H x3P
z1H y3D
3d24s2 → 3d24s4p a3F 2 x3G a3F 2 y3F 3 2 3 4 a3F 2 z5D 3 2 3 3 4
(2) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (3) (3) (1) (1) (1) (1) (1) (2) (1) (1) (2) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (2) (1)
−0.0088 −0.0073 −0.0032 −0.0113 −0.0156 −0.0141 −0.0111 −0.0121 −0.0082 −0.0135 0.0103 −0.0049 −0.0049 −0.0043 −0.0063 −0.0072 −0.0097 −0.0112 −0.0087 −0.0126 −0.0127 −0.0094 0.0010 −0.0114 −0.0025 −0.0021 −0.0020 0.0031 0.0021 0.0030 0.0007 0.0048 0.0048 0.0030 0.0032
(4) (12) (20)
0.0051 0.0008 0.0004
(cm−1 ) (6) (2) (2) (3) (1) (1) (1) (1) (1) (1)
−0.0092 −0.0049 −0.0056 −0.0058 −0.0069 −0.0104 −0.0040 −0.0107 −0.0098 −0.0121
−785 (7) −1549 (2) −1206 (5) −1210 (4) −1208 (5) −1448 (5) −1438 (5) −1430 (3) −1446 (4) −1419 (5) −1430 (3) −1175 (3) −1184 (4) −1170 (3) −1219 (3) −1416 (3) −1412 (3) −1418 (3) −1416 (4) −1420 (3) −493 (3) −503 (3) −521 (3) −544 (6) −590 (3) −1330 (4) −1331 (3) −1244 (3) −1457 (1) −1460 (2) −1458 (2) −1459 (2) −1459 (2) −1461 (2) −1459 (2) −1461 (3) 646 (5) 645 (5) 640 (6) 543.3 (20) 534.7 (37) 514.1 (24) 490.0 (48) 231.0 (24) 50-48 195.0 (48) −921 (5) −941 (3) −949 (5) −964 (2) −916 (2) −963 (3) 102 (1) −699 (2) −985 (2) −725 (2) 812 (11) 1216.8 (24) 1215.6 (19) 1172.2 (20) 1215.6 (19) 1183 (18) 729.0 (90) 735.0 (60) 734.0 (60) 729.0 (60) 735.0 (90) 734.4 (48)
293.5 (51) 288.3 (68) 284.6 (27) 260.0 (39) 132.5 (54) 49-48 111.5 (30) −475 (10) −486 (10)
−270.5 (55) −269.3 (71) −252.8 (28) −236.5 (39) −104.6 (71) 47-48 −90.2 (21) 482 (10) 486 (10)
−498 (5) −467 (10)
506 (5) 476 (10)
−365 (3) −512 (4) −383 (4)
366 (3) 515 (4) 375 (4)
640.4 (21) 638.5 (21) 619.8 (21) 638.5 (21) 624 (10)
−628.2 (24) −627.6 (22) −595.3 (21) −627.6 (22) -615 (16)
(30) (6) (6) (7) (6) (22) (39) (39) (39) (36) (61) (30)
(46) (15) (26) (23) (23) (25) (25) (15) (22) (15) (24) (16) (20) (15) (15) (15) (13) (16) (20) (18) (10) (11) (9) (20) (12) (17) (14) (14) (7) (13) (12) (12) (13) (12) (12) (17)
(72) (10) (10) (12) (10) (32) (61) (61) (61) (56) (97) (47)
[6](a)
[8] [8] [8] [8] [8] [8]
[6] [23] [23] [23] [23] [24] [7] [7] [7] [7] [7] [7]
(continued on next page) 33
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
Table 2 (continued) Transition Lower [5]
J 4 1 1 2 0 1 1 4 2 1 0 4
a3P
a3P a3P a1G a3P
a1G
3d 4s → 3d 4p 2 a3F 3 4 a3P 2 1 0 2 1 2 2
2
Upper [5]
z3P
z3S y3F z1G z3D
z1F
Wavenumber
Obs.-Ref.
Isotope shift (MHz)
J
(cm−1 )
(cm−1 )
50-48
3 0 2 2 1 1 2 4 3 2 1 3
18207.065 17082.494 17001.316 16891.396 16484.507 16428.698 16614.993 12576.4939 11523.7135 11513.6184 11501.2359 10286.3487
−0.0061 −0.0054 −0.0025 −0.0021 0.0007
735.0 (90) 661.0 (35) 845.8 (54) 838.7 (102) 637.6 (42) 627.9 (52) 1171.8 (24) 984 (2) 558 (2) 554 (2) 544 (2) 825 (2)
1 2 3 3 2 1 2 1 1
25324.983 25275.886 25263.945 17041.363 16946.492 16881.203 16836.570 16825.397 16715.479
(3) (1) (1) (1) (1)
49-48
47-48
347.0 (55) 444.3 (57) 436.4 (96) 341.7 (60) 348.4 (51) 614.9 (57) 522 (10)
−335.3 (45) −430.8 (54) −419.1 (84) −315.7 (53) −310.1 (51) −594.9 (51) −501 (10)
860.4 747.8 878.3 883.2 739.6 876.6 739.6 890.5 883.1
−837.2 −710.8 −857.1 −850.6 −720.8 −846.3 −718.6 −855.1 −848.2
Fik
MikSMS
46-48
(GHz/fm2)
(103 GHz amu)
−774.0 (60) −697.0 (35) −897.5 (75) −885.7 (98) −661.4 (46) −662.8 (60) −1237.8 (45) −1044 (2) −586 (2) −584 (2) −572 (2) −866 (2)
−0.38 −0.25 −0.27 −0.30 −0.39 −0.42 −0.45 −0.35 −0.30 −0.28 −0.28 −0.46
(27) (10) (11) (17) (12) (12) (13) (23) (17) (16) (16) (35)
0.511 0.461 0.681 0.664 0.417 0.408 1.045 0.905 0.422 0.422 0.410 0.733
(41) (16) (22) (34) (21) (21) (22) (40) (27) (26) (26) (55)
[7] [8] [14] [14] [8] [8] [8]
−1745.0 −1487.4 −1780.4 −1776.0 −1506.5 −1769.1 −1497.5 −1785.7 −1774.1
−0.47 −0.57 −0.47 −0.55 −0.37 −0.55 −0.41 −0.60 −0.60
(9) (9) (8) (14) (10) (10) (9) (4) (4)
1.454 1.160 1.495 1.616 1.340 1.609 1.327 1.620 1.612
(14) (13) (12) (49) (11) (12) (10) (6) (4)
[23] [23] [23] [14] [14] [14] [14] [14] [14]
Ref.
3
y3D
y3D
(a) L. Gianfrani reported IS were Δν(50
48)
1631.4 1403.3 1667.2 1670.2 1400.8 1663.5 1400.8 1678.5 1667.8
= 858 MHz and Δν(46
48)
(28) (24) (24) (98) (96) (110) (96) (87) (45)
(25) (21) (27) (24) (90) (90) (90) (60) (62)
(27) (20) (21) (112) (60) (79) (60) (52) (48)
(26) (20) (20) (90) (45) (82) (45) (105) (63)
= − 785 MHz. The values in the table are changed.
effects and the interaction of the magnetic field. The unperturbed line positions of the odd mass isotopes were determined by the analysis of the HFS in the intermediate-field approximation. The hyperfine constants AJ and BJ for the even-parity level were determined using ABMR–LIRF[13]. In addition, those of the odd-parity levels were reported using high-resolution atomic-beam ultraviolet laser spectroscopy[23]. However, the constants AJ and BJ of 3d34s b3FJ (J = 2, 3, 4) for 49Ti have not been reported. In this case, the following relationships can be used to perform the calculations. 47
A B
Ti / A49Ti
47
Ti / B 49Ti
= (μI / I ) 47Ti /(μI / I ) 49Ti = 0.99973(8)
(13)
= (Q) 47Ti /(Q) 49Ti = 1.21(7)
(14)
Additionally, the gJ factors determined by our previous work were used[15]. As an example of a result of the Zeeman splitting analysis for HFS spectra, the observed lines of b3FJ → y3DJ−1(J = 2,3,4) and those calculated HFS lines are shown in Fig. 2. The calculations for each Zeeman component are represented by column charts in this figure. The calculated lines were fitted to the observed lines to determine the center of the lines of 47Ti and 49Ti. The King plot analysis using Eq. (6) for the transitions b3FJ → y3DJ−1 (J = 2, 3, 4) are shown in Fig. 3. The electronic factors of Fik and MikSMS can be determined from the King plot analysis. A least squares fitting using the square of the reciprocal of frequency error as a weight was performed. The saturated absorption lines related to 53 transitions in Ti I were observed. The observed values of the IS, including 47Ti and 49Ti, are shown in Table 2. With the exception of b3FJ → y3DJ−1(J = 2,3,4) and b3F3 → z3P2, the lines of 47Ti and 49Ti were determined by the peaks of the lines because these HFS-splitting lines were small. The assignment of the isotope lines was based on the fact that the spectral intensity is proportional to its natural abundance. In addition, for comparison, the previous reports of IS in Ti I performed by other researchers [6–8,14,23] are also listed in Table 2. The assignment of the levels used is reported by E. B. Saloman [5]. The lines of 3d24s2 → 3d24s4p, 3d24s2 → 3d34p, 3d34s → 3d34p, and 3d34s → 3d24s4p are compiled in the table. These transitions are from the metastable states belonging to the configurations 3d24s2 and 3d34s. The frequency of the lines of MJ = 0 in 48Ti are also shown in this Table. The centers of the Zeeman lines in the ΔJ = 0 type were determined by calculating the center of
Fig. 4. Schematic diagram of the CD analysis for transitions a3F2 → y3F2 and b3F2 → y3F2.
diagonalizing the energy matrix. 4. Results and discussion 4.1. Isotope line positions and king plot The traces of the saturated absorption lines in b3FJ → y3DJ−1 (J = 2,3,4) are shown in Fig. 1. The full width at half maximum (FWHM) of the lines were approximately 15 MHz. In the figure, the lines related to five stable isotopes 46Ti, 47Ti, 48Ti, 49Ti, and 50Ti can be seen clearly. The intensity of the lines depends on the natural abundance of the isotopes, as shown in Table 1. These lines were split into Zeeman components of ΔJ = ± 1 type in the parallel field case. Because the Zeeman components of the even-mass isotopes 46Ti,48Ti, and 50 Ti are only the components of MJ = 0, ⋯, ± J, the centers of those lines can be easily determined. The IS of the 46, 50Ti of the transition b3F3 → y3D2 was shifted approximately 300 MHz, which is wider than that of b3F2 → y3D1 and b3F4 → y3D3. The lines of the odd mass isotopes are complex due to the hyperfine 34
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
Table 3 Results of the CD analysis in order to compare the electronic factors Fgi and MgiSMS between the ground state a3F2 and the levels belonging to the configurations 3d24s2 and 3d34s. Even-parity level
Mixing rate [5]
Configuration
Term
Energy (cm−1 )
First
3d24s2 3d24s2 3d24s2 3d24s2 3d24s2 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(4F)4s 3d3(2G)4s
a3F3 a3F4 a3P0 a3P1 a3P2 a5F1 a5F2 a5F3 a5F4 a5F5 b3F2 b3F3 b3F4 a3G5
170.1328 386.874 8436.618 8492.422 8602.3441 6556.883 6598.765 6661.006 6742.756 6842.962 11531.761 11639.8109 11776.812 15220.393
1.00 1.00 0.92 0.92 0.90 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.98 0.98
Second
3
0.07 0.07 0.07
3
3d 4s P 3d34s3P 3d34s3P
Fgi
MgiSMS
(GHz/fm2)
(103 GHz amu)
−0.03 (12) −0.04 (40) 0.08 (19) 0.13 (15) 0.13 (15) −0.53 (77) −0.53 (53) −0.62 (56) −0.55 (69) −0.53 (76) −0.59 (22) −0.40 (21) −0.44 (39) −0.47 (68)(a)
−0.006 (20) 0.020 (62) −0.155 (26) −0.166 (20) −0.160 (18) 2.361 (98) 2.363 (74) 2.353 (77) 2.360 (96) 2.404 (107) 2.540 (27) 2.595 (25) 2.603 (50) 2.191 (106)(a)
(a) The changed electronic factors of b3F4 → y3G5 listed in Table 1 were used. Table 4 The electronic factors Fgk and MgkSMS of the odd parity states referred to the ground state a3F2. Odd parity Levels
Mixing rate[26]
Configurations
Terms
Energy (cm−1 )
First
3d2(3F)4s4p
z5F1 z5F2 z5F3 z5F4 z5F5 z5D0 z5D1 z5D2 z5D3 z5D4 z3D1 z3D2 z3D3 z3S1 z3P2 z3P0 y3D1 y3D2 y3D3 y3F2 y3F3 y3F4 y3G5 y5F3 y5F4 y5F5 x3G3
16817.160 16875.124 16961.442 17075.258 17215.390 18462.722 18482.774 18525.059 18593.947 18695.134 19937.855 20006.039 20126.062 24921.117 25493.733 25574.908 25317.814 25438.908 25643.701 25107.411 25227.222 25388.331 27750.135 28702.778 28788.380 28896.059 29914.737
0.96 0.95 0.97 0.98 0.99 0.95 0.95 0.94 0.95 0.95 0.85 0.86 0.85 0.91 0.52 0.51 0.51 0.37 0.36 0.48 0.46 0.42 0.49 0.98 0.97 0.97 0.76
3d2(3F)4s4p
3d2(3F)4s4p
3d2(3P)4s4p 3d2(1D)4s4p 3d3(4F)4p
3d2(3F)4s4p
3d2(2F)4s4p 3d3(4F)4p
3d2(1G)4s4p
Second
Third
0.07 0.08 0.07 0.07 0.36 0.34 0.36 0.32 0.34 0.24 0.22 0.25 0.24
3d24s4p3D 3d24s4p3D 3d24s4p3D 3d34p3S 3d24s4p5D 3d24s4p5D 3d24s4p3D 3d24s4p3D 3d24s4p3D 3d34p3F 3d34p3F 3d24s4p3F 3d34p3G
0.18
3d24s4p3G
0.13 0.12
3d24s4p3D 3d24s4p3S
0.21 0.20 0.23 0.22 0.23 0.09
3d24s4p3D 3d24s4p3D 3d24s4p3F 3d24s4p3F 3d34p3F 3d34p3G
Contribution
Fgk
MgkSMS
3d34p ζ
(GHz/fm2)
(103-GHz amu)
0.04 0.05 0.03 0.02 0.01 0.05 0.05 0.06 0.03 0.03 0.08 0.06 0.08 0.07 0.10 0.03 0.51 0.37 0.36 0.23 0.22 0.23 0.33 0.98 0.97 0.97 0.06
−0.39 −0.41 −0.41 −0.43 −0.41 −0.42 −0.47 −0.47 −0.40 −0.50 −0.20 −0.15 −0.17 −0.30 −0.18 −0.12 −0.46 −0.36 −0.43 −0.42 −0.34 −0.31 −0.52 −0.95 −0.84 −0.82 −0.48
0.474 0.470 0.471 0.464 0.512 0.491 0.487 0.488 0.496 0.482 0.255 0.256 0.264 0.252 0.522 0.295 1.458 1.176 1.509 0.888 0.976 0.987 1.385 2.702 2.714 2.754 0.392
(4) (5) (3) (2) (1) (5) (5) (6) (3) (3) (8) (6) (8) (2) (10) (3) (13) (10) (10) (5) (10) (10) (18) (2) (3) (3) (6)
(65) (76) (68) (81) (84) (90) (39) (39) (48) (51) (35) (31) (32) (29) (30) (25) (23) (25) (39) (24) (25) (18) (57)(a) (75) (87) (89) (30)
(86) (97) (89) (108) (114) (113) (61) (61) (76) (81) (51) (46) (45) (44) (45) (36) (28) (32) (67) (32) (31) (30) (96)(a) (125) (142) (140) (72)
(a) The changed electronic factors of b3F4 → y3G5 were used.
Guo Jin et al.[23]. In addition, the significant ISs of the transitions related to y3D2 in a3FJ → y3DJ−1 and a3PJ → y3DJ were also reported by Wei-Guo Jin et al.[23] and Yu P. Gangrsky et al.[14]. Gangrsky et al. reported that these significant ISs are caused by the perturbation of the energy level of y3D2 and those of z3P2. Therefore, the significant IS of b3F3 → y3D2 was caused by the perturbation of y3D2 from z3P2. The IS of 46Ti and 50Ti of the transition b3F4 → y3G5 was reported by L. Gianfrani et al. [6] as Δν50, 48 = 858 MHz and Δν46, 48 = − 785 MHz. However, in the transitions 3d34s → 3d24s4p, the lines of 46Ti are higher than those of 50Ti in terms of frequency. Furthermore, the electronic factors calculated by their assignment showed deviations from those of all other transitions, as discussed in section 4.2.2. The IS of b3F4 → y3G5 must be changed to Δν50, 48 = − 785 MHz and Δν46, 48 = 858 MHz.
gravity of the lines of MJ = ± J. The sequence of the isotopic lines of the transitions between the levels belonging to 3d24s2 and 3d24s4p or 3d34p is 46Ti, 47Ti, 48Ti, 49Ti, and 50Ti, in order of frequency. In the transitions 3d34s → 3d24s4p, the sequence is reversed. However, the frequency order of the IS of transitions between the levels 3d34s and 3d34p were different in the individual transitions. For example, the sequence of the IS of a3HJ → y3HJ (J = 4, 5, 6) [8] was reversed to that of b3FJ → y3DJ−1 (J = 2, 3, 4). In the transitions b3FJ → y3FJ, b3FJ → y3DJ−1 (J = 2, 3, 4), a significant IS, which indicates that it has a J dependency caused by a perturbation from other levels, was observed at the transitions related to y3F2 and y3D2. The significant IS of the transition related to y3F2 was observed in the transitions a3FJ → y3FJ (J = 2, 3, 4) reported by Wei35
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
between Fa3F2, y3F2 and Fb3F2, y3F2. Consequently, we can easily estimate the electronic factors based on the ground state a3F2. The results of the CD analysis for the comparison of the electronic factors of the evenparity levels are given in Table 3. The subscript gi denotes the transition between the ground state g and the even-parity level i. The first five row values of Fgi and MgiSMS should be zero if the provided levels are pure, and if the higher-order effects are neglected [11]. The other rows are the electronic factors for transitions between 3d24s2 and 3d34s. The difference in the factors of SMS between 3d24s2 and 3d34s is approximately 2.5 × 103 GHz amu, which is related to the difference in the number of d−electrons. 4.2.2. Odd parity state The IS analysis for the chromium atom was studied by B. Furmann et al. in 2005[25]. They reported the configuration interaction (CI) analysis for the isotopic effects in chromium. Similarly, the CI analysis can be adopted in the case of neutral titanium. Any electron state is expressed as a mixture of the levels belonging to different configurations
Ψ=
∑ ζn An , n
(16)
where An represents a configuration with the same parity, and ζn is the mixing rate of the configuration An. Obviously, ζn satisfies
∑ ζn = 1. n
(17)
Accordingly, the electronic factors of SMS and FS are described as linear combinations of the factors for pure configurations, as follows SMS Mgk =
∑ ζn MnSMS , n
Fgk =
4.2.1. Even parity state The electronic factors of the SMS and FS determined by the King plot analysis are not resolved into the individual levels. However, these relationships can be described as follows:
(15)
MiSMS
where and Fi represent the electronic factors of the i-th level. Therefore, the combination difference (CD) analysis is useful to estimate the factors of SMS and FS between the levels, which include even forbidden transitions. The schematic diagram of the CD analysis is shown in Fig. 4. The CD analysis was performed for the transitions a3FJ → y3FJ, J ± 1 (J = 2, 3, 4) and b3FJ → y3FJ (J = 2, 3, 4). The former transitions were reported by Wei-Guo Jin[23]. In addition, we reported the IS of the transition a3F4 → y3F4[24]. The latter, which is indicated by the thick arrow in the figure, is measured in this work. The synthetic transition is represented by the dashed arrows. For example, the factor of MikSMS for a3F2 and b3F2 is obtained using the CD analysis
M SMS 3
a F2, b3F2
=
(M SMS y3F2
= MaSMS 3 F
−
3 2, y F2
M SMS ) a3F2
−
− MbSMS 3 F
(M SMS y3F2
3 2, y F2
− M SMS 3 ) b F2
= M SMS − M SMS 3 3 . b F2
a F2
In addition, the factors of Fa3F2,
b3F2
(19)
In all the studied transitions in Ti I, although the degree of mixing of the lower levels is small, the electronic factors of the configuration 3d34s differ completely from those of the configuration 3d24s2. Hence, the difference in the electronic factors at lower levels cannot be ignored. In contrast, the odd-parity configurations 3d24s4p and 3d34p are complexly perturbed by each other. However, the perturbations from other odd-parity levels, such as 3d4s24p and 3d24s5p, are extremely small[26]. Therefore, the levels of 3d24s4p and 3d34p can be approximated as a case of just two configuration interactions. In order to cancel the difference in the electronic factors of the lower levels, the CD method was also adopted. The results are listed in Table 4. The subscript k represents the odd parity state belonging to 3d24s4p or 3d34p. The contributions of the 3d34p denoted by ζn are also tabulated. These values are reported by C. Roth[26]. The dependence of MgkSMS and Fgk on the configuration of 3d34p is shown in Fig. 5. These plots show almost linearity. These figures indicate the dependence of the electronic factors of FS and SMS on changes in the number of s− or d−electrons. However, the squared points in these figures have large discrepancies. These values were derived from the IS of b3F4 → y3G5, as reported by L. Gianfrani [6]. They assigned the IS to be Δν50, 48 = 858 MHz and Δν46, 48 = − 785 MHz, respectively. Using the King plot analysis, the Fik = − 2.30(59) GHz/fm2 and MikSMS = 0.327 (148) 103GHz⋅amu were obtained. The factors Fgk and MgkSMS, which refer to the ground state, were derived from the CD analysis using the values Fa3F2, b3F4 = − 0.44 (39) GHz/fm2 and Ma3F2, b3F4SMS = 2.592 (50) 103GHz⋅amu listed in Table 3. In this case, the factors of FS and SMS are −2.74 (120) GHz/fm2 and 2.930 (218) ×103GHz⋅amu, respectively. However, these values can be changed in the shaded area by making Δν50, 48 = − 785 MHz and Δν46, 48 = 858 MHz, as shown in Fig. 5.
4.2. Analysis of results
MikSMS = MkSMS − MiSMS , Fik = Fk − Fi ,
∑ ζn Fn. n
Fig. 5. The configuration interaction analysis for the electronic factors of the odd-parity states. The experimental plots were fallen off the shaded band except for the values indicated by the square.
(18)
are derived from the difference 36
Spectrochimica Acta Part B 152 (2019) 30–37
S. Kobayashi et al.
5. Conclusion [12]
The saturated absorption line in Ti I was measured using a ring-type Ti:sapphire laser with wavelengths in the 9950 to 14380 cm−1 region. The electronic factors for the FS and for the SMS were newly determined using the King plot analysis in 53 transitions. The isotope lines of titanium can be easily estimated with accuracy as high as the Doppler width using the results of the configuration interaction.
[13]
[14]
[15]
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