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The absorption spectrum of the (1, 0), (3, 1) and (4, 2) bands in the c3Σg+–a3Σu+ system of He2 eximer
Journal of Molecular Spectroscopy 260 (2010) 85–87
Contents lists available at ScienceDirect
Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
The absorption spectrum of the (1, 0), (3, 1) and (4, 2) bands in the c3Rg+–a3Ru+ system of He2 eximer Chuanliang Li, Lunhua Deng, Junli Zhang, Xiaohua Yang, Yangqin Chen *, Longsheng Ma State Key Laboratory of Precision Spectroscopy, and Department of Physics, East China Normal University, Shanghai 200062, China
a r t i c l e
i n f o
Article history: Received 19 October 2009 In revised form 1 December 2009 Available online 4 December 2009 Keywords: He2 Concentration modulation spectroscopy Molecular constants
a b s t r a c t The near-infrared absorption spectrum of He2 has been recorded in the range of 12 090–13 300 cm1 using the optical heterodyne concentration modulation spectroscopy. Fifty-nine He2 spectral lines were assigned to the (1, 0), (2, 0), (3, 1) and (4, 2) bands in the c3Rg+–a3Ru+ system and a non-linear leastsquares fitting was performed to get the improved molecular constants for the levels (t = 1, 3 and 4) in the upper electronic state. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction He2 was the first discovered eximer as early as 1913. It is the simplest but the most studied exemplary both in experiments and in theory. The He2 molecule plays a significant role in the fields of chemical bond formation [1–3], the mechanism of low-temperature discharge plasma [4,5] and the spectroscopic study of superfluid helium nano-droplets [6,7]. In the past century, the electronic spectrum of He2 was the subject of many studies and was investigated by a variety of spectroscopic techniques. So far, more than 60 electronic states of He2 have been identified, among which the c3Rg+, a3Ru+, C1Rg+ and A1Ru+ states were extensively studied. Numerous references about the spectral studies of He2 can be cited, while only those on the c3Rg+–a3Ru+ system will be briefly summarized here. The earliest literature on the c3Rg+–a3Ru+ system of He2 was reported by Dieke et al. [8], who made a detailed investigation on the (0, 0) and (1, 1) bands in this system. In 1965, Ginter [9] studied the emission spectra in the c3Rg+–a3Ru+ system using grating measurements, and nine bands (i.e., (0, 0), (1, 0), (2, 0), (1, 1), (2, 1), (3, 1), (2, 2), (3, 2) and (4, 2) bands) were studied, which resulted in a set of molecular constants. In the late 1970s, Vierima and his coworkers [10,11] investigated the fine structure of spin–spin and spin–rotation interactions of the a3Ru+ state by employing highly precise magnetic resonance radio-frequency spectroscopy, and thus, the fine structural parameters for the N = 1 and 3 rotational levels of the t = 0 level were obtained. Another fine structural study of the c3Rg+–a3Ru+ system was carried out by Bjerre et al. [12–14] using
* Corresponding author. Fax: +86 21 6223 2056. E-mail address: [email protected] (Y. Chen). 0022-2852/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2009.12.002
laser-radio double-resonance spectroscopy in 1990s. Focsa et al. [15] reinvestigated the (0, 0), (1, 1), (2, 2), (1, 0) and (2, 1) bands in the c3Rg+–a3Ru+ system by Fourier transform spectroscopy in 1998, and they performed a global fitting in combination with the data of Vierima et al. [10,11] and Bjerre et al. [13,14] to obtain precise molecular constants of the t = 0, 1 and 2 levels for both the c3Rg+ and a3Ru+ states. Recently, Vrinceanu and Sadeghpour [16] studied the low-temperature radiative transitions of the c3Rg+–a3Ru+ system using molecular dimmer potentials method, and they gave the rovibrational frequency and the radiative transition squared dipole matrix elements. In the previous spectral studies on He2, most of them were based on emission spectroscopy, while the absorption spectroscopy with high resolution and accuracy was rarely adopted. In the present work, we employed the optical heterodyne-concentration modulation spectroscopy (OH-CMS), a sensitive absorption technique, to reinvestigate the spectra in the c3Rg+–a3Ru+ system of He2. 2. Experiment The experimental apparatus for OH-CMS is similar to optical heterodyne-velocity modulation spectroscopy [17] originated from our previous optical heterodyne and magnetic rotation enhanced velocity modulation spectroscopy [18]. A tunable Ti: sphere laser (Coherent Ring 899-29) was used as the excitation source. The laser beam was first phase-modulated by an electro-optical modulator at a radio frequency of 500 MHz, then passed through an audio frequency (23 kHz) glow discharge absorption cell and finally focused into a PIN detector (ET-2030A). The output of the detector was first demodulated by a double balance mixer at 500 MHz for
86
C. Li et al. / Journal of Molecular Spectroscopy 260 (2010) 85–87
the implement of optical heterodyne detection, then further demodulated by a lock-in amplifier at 2 23 kHz (concentration demodulation) with a time constant of 100 ms. The spectral data were acquired and processed by a personal computer. The wavelength of laser was roughly determined by the laser-attached wavemeter and further calibrated to the spectrum of I2 [19] with an absolute accuracy of about 0.005 cm1. He2 was generated by discharging the flowing helium gas (99.995% purity, 400 Pa) in the absorption cell with a discharge current of 400 mA (peak-to-peak). Unexpectedly, we found that the spectral intensity of He2 can be increased by a factor of 2–3 while filled with a trace of phosphorus vapor when we intended to search phosphorus molecule spectrum. It indicates that the collision of the excited P atoms is helpful to produce He2 in the discharge. The concentration of transient species is modulated by the magnitude of the discharging electric field [20,21]. The generation delay referring to the electric field and the lifetime determine the optimal demodulation phase at the lock-in. Therefore, the relative spectral phases of different species may be opposite. This can be verified by our experimental results. Fig. 1 shows that the spectral phase of He2 is opposite to those of Ar and P atoms when the reference phase is optimized. It is helpful for picking up the spectral lines of He2 from other transient species. By the way, argon is the impurity in helium gas.
3. Results and discussion
Ar
12318
alternately. Both the upper and lower states are Hund’s case (b) coupling. So the well-known effective Hamiltonian [14] is adopted in the analysis,
H ¼ Bt R2 Dt R4 þ Ht R6 þ Lt R8 þ et ð3S2z S2 Þ þ ct S N;
The spectrum of He2 was recorded in the range of 12 090– 13 300 cm1. A portion of observed spectra of the R branch in the (1, 0) band together with their assignments are shown in Fig. 2. The insert represents the observed spectral profile is the first derivative of the Gaussian profile due to optical phase modulation [22]. And the fitted line is also added to the insert for illustration. The signal-to-noise ratio of the strong (1, 0) band spectral lines is high up to 200 when the He2 signals are enhanced by a trace of phosphorus vapor. The observed 59 lines are listed in Table 1 and were assigned to the (1, 0), (2, 0), (3, 1) and (4, 2) bands in the c3Rg+–a3Ru+ system according to the previous atlas [9]. We only observed seven lines of the (2, 0) band in the range of our laser system’s covering, so these spectra were not used to fit the constants of the t = 2 level in the c3Rg+ state. The nucleus spin of 4He atom is zero, thus the even N levels in the a3Ru+ state as well as the odd N levels in the c3Rg+ state disappear, which results in the spectral lines’ missing
He2
Fig. 2. Portion of the observed spectrum of the R branch of the (1, 0) band in the c3Rg+–a3Ru+ system of He2 eximer. As shown in the inset, the observed line (black) is approximately the first derivative of the Gaussian due to optical phase modulation, and the fitted (red) is also plotted for illustration. (For interpretation of color mentioned in this figure legend the reader is referred to the web version of the article.)
Wavenumber (cm-1)
P
12319
Fig. 1. Typical spectrum of concentration modulation spectroscopy for selective measurement of He2 spectra while filled with a trace of phosphorus vapor. It shows that the relative spectral phase of He2 is opposite to those of Ar and P atoms.
ð1Þ
where R is the rotational angular momentum, S is the total electronic spin-angular momentum, N is the total angular momentum except spin (N = L + R), L is the sum electronic orbital angular momentum, Bt is the rotational constant, Dt, Ht and Lt are the centrifugal distortion constants, and et is the spin–spin coupling constant, which is substituted by kt defined as
kt ¼ ð3=2Þet :
ð2Þ
The triplet fine structure splittings are too small to be resolved in comparison with the Doppler linewidth, so the spectra can be simplified as the singlet system in analysis. The PGOPHER program [23] was employed to fit the molecular constants. As mentioned above, the triplet splittings were not resolved in our experiment, so c, k and their high order correction terms in the upper state were fixed at those of Focsa et al. [15]. Additionally, the constants of the lower state and the Ht, Lt of the t = 1 level in the c3Rg+ state were all fixed at those of Focsa et al., since they were obtained by a global fitting in combination with the previous r.f. data. The improved constants of the t = 1, 3, 4 levels in the c3Rg+ state are listed in Table 2, and those of Ginter [9] and Focsa et al. [15] are also listed for comparison. Our results are basically in good agreement with those of literatures within 3r error. Additionally, the overall fitting errors are less than the experimental uncertainty proves the reliability of our results. Note that, the rotational level N = 22 in the t = 1 level of the c3Rg+ state is perturbed by one rotational level in the t = 5 level in the b3Gg state [15], therefore the spectral line R(21) in the (1, 0) band was excluded in the fitting. Furthermore, our results of the t = 3 and 4 levels in the c3Rg+ state show about one order magnitude improved in comparison with the Ref. [9], due to the high accuracy and high resolution spectroscopy being employed. In addition, helium gas, as one of the most important buffer gases in the plasma discharge, is often used in the velocity/concentration modulation spectroscopy. The spectrum of He2 often acts as disturbers, so our original motivation of the work was to obtain precise spectral atlas for the help of further studies.
87
C. Li et al. / Journal of Molecular Spectroscopy 260 (2010) 85–87 Table 1 Wavenumbers (in cm1) and assignments in the c3Rg+–a3Ru+ system of the He2. N
1 3 5 7 9 11 13 15 17 19 21 23 25 a b c
(1, 0)
(3, 1)
(2, 0)c
(4, 2)
R
P
R
P
R
P
12393.6454(11)a 12409.4197(7) 12416.6981(3) 12415.3521(3) 12405.2385(2) 12386.2019(34) 12358.0516(7) 12320.5904(3) 12273.5656(1) 12216.6766(0) 12149.9791(4234)b
12354.3249(9) 12317.8351(11) 12273.2370(12) 12220.6336(26) 12160.0898(11) 12091.6765(38)
13276.8970(23) 13284.9866(10)
13241.8869(10) 13203.4920(10) 13153.1356(7) 13090.8147(1) 13016.4581(10) 12929.9154(22) 12830.9358(32) 12719.1389(71) 12593.8887(72) 12454.3132(43) 12299.0090(29)
12715.9394(58) 12719.4942(12) 12708.4032(8) 12682.1522(33) 12639.9801(13) 12580.8159(11) 12503.0472(2)
12683.9185(63) 12645.0051(30) 12592.0956(6) 12525.0356(8) 12443.5217(7) 12347.0099(17) 12234.6221(2)
13263.5248(7) 13233.3368(9) 13189.6105(51) 13131.7416(1) 13058.9606(12) 12970.1699(27) 12863.8192(58) 12737.6641(8)
R
13221.6816
P
13231.4377 13117.4389 12992.0514 12854.7967 12704.9623 12540.9921
Values in parentheses are (vobs vcal) 104 cm1. Perturbation. The observed spectra of (2, 0) band were not used to fit the constants of t = 2 in the c3Rg+ state, since only seven lines were obtained.
Table 2 Molecular constants (cm1) of the t = 1, 3, 4 levels in the c3Rg+ state of He2.
t=1 Tta Bt Dt 104 Ht 108 Lt 1012 ct 105 cDt 108 kt 102 kDt 106
r a b
t=3
t=4
This work
Ref. [15]
Ref. [9]
This work
Ref. [9]
This work
Ref. [9]
12369.50264(89)b 6.556864(14) 5.80751(36) 4.49 3.68 8.0805 2.2828 3.6664342 6.5887 0.0020
12369.4987(25) 6.556820(63) 5.8067(49) 4.49(135) 3.68(120) 8.0805 2.2828 3.6664342 6.5887
12369.50(2) 6.556 (2) 5.76(2) 1.3(1)
14988.7411(21) 5.839938(76) 7.2707(70) 1.18(22) 184.0(22) 8.0805 2.2828 3.6664342 6.5887 0.0037
14988.80(2) 5.837(1) 6.98(5) 13(1)
16084.6134(24) 5.34436(21) 9.190(47) 19.7(36) 687(88) 8.0805 2.2828 3.6664342 6.5887 0.0034
16084.63(2) 5.340(1) 8.57(4) 54(2)
The energy of t = 0 level in the a3Ru+ state is set to 0. Numbers in parentheses denote one standard deviation in unit of the last quoted digit. If the numbers are missing, the values are fixed at those of Ref. [15].
4. Conclusion In summary, the (1, 0), (3, 1), (4, 2) and a portion of (2, 0) bands in the c3Rg+–a3Ru+ system of He2 were recorded in the region 12 090–13 300 cm1 by OH-CMS. Fifty-two spectral lines of the (1, 0), (3, 1) and (4, 2) bands were non-linear least-squares fitted, yielding about one order of magnitude improved constants of the t = 3 and 4 levels in the c3Rg+ state. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 10574045), the National Key Basic Research and Development Program of China (Grant Nos. 2006CB921604 and 2010CB922903), and the Basic Key Program of Shanghai Municipality (Grant No. 07JC14017). One of the authors (C.L.L.) is grateful to the support of the PhD Program Scholarship Fund of ECNU 2009, and another (L.H.D.) would like to thank the support of the National Science Foundation for Post-doctoral Scientist of China. References [1] H.L. Williams, T. Korona, R. Bukowski, B. Jeziorski, K. Szalewicz, Chem. Phys. Lett. 262 (1996) 431–436.
[2] Ronald A. Aziz, Alec R. Janzen, Phys. Rev. Lett. 74 (1995) 1586–1589. [3] T. Yasuike, K. Someda, J. Phys. B 37 (2004) 3149–3162. [4] Y.A. Tolmachev, Y.A. Piotrovskiï, O.V. Zhigalov, Opt. Spectrosc. 98 (2005) 202– 207. [5] R. Deloche, P. Monchicourt, M. Cheret, F. Lambert, Phys. Rev. A 13 (1976) 1140– 1176. [6] J. Jortner, J. Chem. Phys. 119 (2003) 11335–11341. [7] S. Yurgenson, C.C. Hu, J.A. Northby, Eur. Phys. J. D9 (1999) 153–157. [8] G.H. Dieke, S. Imanishi, T. Takamine, Z. Physik. 57 (1929) 305–325. [9] M.L. Ginter, J. Chem. Phys. 42 (1965) 561–568. [10] W. Lichten, M.V. McCusker, T.L. Vierima, J. Chem. Phys. 61 (1974) 2925–2926. [11] T.L. Vierima, J. Chem. Phys. 62 (1975) 2200–2212. [12] D.C. Lorents, S. Keiding, N. Bjerre, J. Chem. Phys. 90 (1989) 3096–3101. [13] M. Kristensen, N. Bjerre, J. Chem. Phys. 93 (1990) 983–990. [14] I. Hazell, A. Nørregaard, N. Bjerre, J. Mol. Spectrosc. 172 (1995) 135– 152. [15] C. Focsa, P.F. Bernath, R. Colin, J. Mol. Spectrosc. 191 (1998) 209–214. [16] D. Vrinceanu, H.R. Sadeghpour, Phys. Rev. A 65 (2002) 0627121– 0627128. [17] G.L. Chen, X.H. Yang, X. Ying, G. Liu, Y.X. Huang, Y.Q. Chen, Chin. Sci. Bull. 49 (2004) 2354–2359. [18] R. Wang, Y. Chen, P. Cai, J. Lu, Z. Bi, X. Yang, L. Ma, Chem. Phys. Lett. 307 (1999) 339–342. [19] S. Gerstenkorn, J. Chevillard, ORSAY, Laboratoire. Aimé. Cotton. CNRS II, 1982. [20] P.B. Davies, Chem. Soc. Rev. 24 (1995) 15–157. [21] C.S. Gudeman, R.J. Saykally, Ann. Rev. Phys. Chem. 35 (1984) 387–418. [22] G.C. Bjorklund, M.D. Levenson, W. Lenth, C. Ortiz, Appl. Phys. B 32 (1983) 145– 152. [23] C.M. Western, PGOPHER, A Program for Simulating Rotational Structure, University of Bristol. Available from:.
Contents lists available at ScienceDirect
Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
The absorption spectrum of the (1, 0), (3, 1) and (4, 2) bands in the c3Rg+–a3Ru+ system of He2 eximer Chuanliang Li, Lunhua Deng, Junli Zhang, Xiaohua Yang, Yangqin Chen *, Longsheng Ma State Key Laboratory of Precision Spectroscopy, and Department of Physics, East China Normal University, Shanghai 200062, China
a r t i c l e
i n f o
Article history: Received 19 October 2009 In revised form 1 December 2009 Available online 4 December 2009 Keywords: He2 Concentration modulation spectroscopy Molecular constants
a b s t r a c t The near-infrared absorption spectrum of He2 has been recorded in the range of 12 090–13 300 cm1 using the optical heterodyne concentration modulation spectroscopy. Fifty-nine He2 spectral lines were assigned to the (1, 0), (2, 0), (3, 1) and (4, 2) bands in the c3Rg+–a3Ru+ system and a non-linear leastsquares fitting was performed to get the improved molecular constants for the levels (t = 1, 3 and 4) in the upper electronic state. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction He2 was the first discovered eximer as early as 1913. It is the simplest but the most studied exemplary both in experiments and in theory. The He2 molecule plays a significant role in the fields of chemical bond formation [1–3], the mechanism of low-temperature discharge plasma [4,5] and the spectroscopic study of superfluid helium nano-droplets [6,7]. In the past century, the electronic spectrum of He2 was the subject of many studies and was investigated by a variety of spectroscopic techniques. So far, more than 60 electronic states of He2 have been identified, among which the c3Rg+, a3Ru+, C1Rg+ and A1Ru+ states were extensively studied. Numerous references about the spectral studies of He2 can be cited, while only those on the c3Rg+–a3Ru+ system will be briefly summarized here. The earliest literature on the c3Rg+–a3Ru+ system of He2 was reported by Dieke et al. [8], who made a detailed investigation on the (0, 0) and (1, 1) bands in this system. In 1965, Ginter [9] studied the emission spectra in the c3Rg+–a3Ru+ system using grating measurements, and nine bands (i.e., (0, 0), (1, 0), (2, 0), (1, 1), (2, 1), (3, 1), (2, 2), (3, 2) and (4, 2) bands) were studied, which resulted in a set of molecular constants. In the late 1970s, Vierima and his coworkers [10,11] investigated the fine structure of spin–spin and spin–rotation interactions of the a3Ru+ state by employing highly precise magnetic resonance radio-frequency spectroscopy, and thus, the fine structural parameters for the N = 1 and 3 rotational levels of the t = 0 level were obtained. Another fine structural study of the c3Rg+–a3Ru+ system was carried out by Bjerre et al. [12–14] using
* Corresponding author. Fax: +86 21 6223 2056. E-mail address: [email protected] (Y. Chen). 0022-2852/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2009.12.002
laser-radio double-resonance spectroscopy in 1990s. Focsa et al. [15] reinvestigated the (0, 0), (1, 1), (2, 2), (1, 0) and (2, 1) bands in the c3Rg+–a3Ru+ system by Fourier transform spectroscopy in 1998, and they performed a global fitting in combination with the data of Vierima et al. [10,11] and Bjerre et al. [13,14] to obtain precise molecular constants of the t = 0, 1 and 2 levels for both the c3Rg+ and a3Ru+ states. Recently, Vrinceanu and Sadeghpour [16] studied the low-temperature radiative transitions of the c3Rg+–a3Ru+ system using molecular dimmer potentials method, and they gave the rovibrational frequency and the radiative transition squared dipole matrix elements. In the previous spectral studies on He2, most of them were based on emission spectroscopy, while the absorption spectroscopy with high resolution and accuracy was rarely adopted. In the present work, we employed the optical heterodyne-concentration modulation spectroscopy (OH-CMS), a sensitive absorption technique, to reinvestigate the spectra in the c3Rg+–a3Ru+ system of He2. 2. Experiment The experimental apparatus for OH-CMS is similar to optical heterodyne-velocity modulation spectroscopy [17] originated from our previous optical heterodyne and magnetic rotation enhanced velocity modulation spectroscopy [18]. A tunable Ti: sphere laser (Coherent Ring 899-29) was used as the excitation source. The laser beam was first phase-modulated by an electro-optical modulator at a radio frequency of 500 MHz, then passed through an audio frequency (23 kHz) glow discharge absorption cell and finally focused into a PIN detector (ET-2030A). The output of the detector was first demodulated by a double balance mixer at 500 MHz for
86
C. Li et al. / Journal of Molecular Spectroscopy 260 (2010) 85–87
the implement of optical heterodyne detection, then further demodulated by a lock-in amplifier at 2 23 kHz (concentration demodulation) with a time constant of 100 ms. The spectral data were acquired and processed by a personal computer. The wavelength of laser was roughly determined by the laser-attached wavemeter and further calibrated to the spectrum of I2 [19] with an absolute accuracy of about 0.005 cm1. He2 was generated by discharging the flowing helium gas (99.995% purity, 400 Pa) in the absorption cell with a discharge current of 400 mA (peak-to-peak). Unexpectedly, we found that the spectral intensity of He2 can be increased by a factor of 2–3 while filled with a trace of phosphorus vapor when we intended to search phosphorus molecule spectrum. It indicates that the collision of the excited P atoms is helpful to produce He2 in the discharge. The concentration of transient species is modulated by the magnitude of the discharging electric field [20,21]. The generation delay referring to the electric field and the lifetime determine the optimal demodulation phase at the lock-in. Therefore, the relative spectral phases of different species may be opposite. This can be verified by our experimental results. Fig. 1 shows that the spectral phase of He2 is opposite to those of Ar and P atoms when the reference phase is optimized. It is helpful for picking up the spectral lines of He2 from other transient species. By the way, argon is the impurity in helium gas.
3. Results and discussion
Ar
12318
alternately. Both the upper and lower states are Hund’s case (b) coupling. So the well-known effective Hamiltonian [14] is adopted in the analysis,
H ¼ Bt R2 Dt R4 þ Ht R6 þ Lt R8 þ et ð3S2z S2 Þ þ ct S N;
The spectrum of He2 was recorded in the range of 12 090– 13 300 cm1. A portion of observed spectra of the R branch in the (1, 0) band together with their assignments are shown in Fig. 2. The insert represents the observed spectral profile is the first derivative of the Gaussian profile due to optical phase modulation [22]. And the fitted line is also added to the insert for illustration. The signal-to-noise ratio of the strong (1, 0) band spectral lines is high up to 200 when the He2 signals are enhanced by a trace of phosphorus vapor. The observed 59 lines are listed in Table 1 and were assigned to the (1, 0), (2, 0), (3, 1) and (4, 2) bands in the c3Rg+–a3Ru+ system according to the previous atlas [9]. We only observed seven lines of the (2, 0) band in the range of our laser system’s covering, so these spectra were not used to fit the constants of the t = 2 level in the c3Rg+ state. The nucleus spin of 4He atom is zero, thus the even N levels in the a3Ru+ state as well as the odd N levels in the c3Rg+ state disappear, which results in the spectral lines’ missing
He2
Fig. 2. Portion of the observed spectrum of the R branch of the (1, 0) band in the c3Rg+–a3Ru+ system of He2 eximer. As shown in the inset, the observed line (black) is approximately the first derivative of the Gaussian due to optical phase modulation, and the fitted (red) is also plotted for illustration. (For interpretation of color mentioned in this figure legend the reader is referred to the web version of the article.)
Wavenumber (cm-1)
P
12319
Fig. 1. Typical spectrum of concentration modulation spectroscopy for selective measurement of He2 spectra while filled with a trace of phosphorus vapor. It shows that the relative spectral phase of He2 is opposite to those of Ar and P atoms.
ð1Þ
where R is the rotational angular momentum, S is the total electronic spin-angular momentum, N is the total angular momentum except spin (N = L + R), L is the sum electronic orbital angular momentum, Bt is the rotational constant, Dt, Ht and Lt are the centrifugal distortion constants, and et is the spin–spin coupling constant, which is substituted by kt defined as
kt ¼ ð3=2Þet :
ð2Þ
The triplet fine structure splittings are too small to be resolved in comparison with the Doppler linewidth, so the spectra can be simplified as the singlet system in analysis. The PGOPHER program [23] was employed to fit the molecular constants. As mentioned above, the triplet splittings were not resolved in our experiment, so c, k and their high order correction terms in the upper state were fixed at those of Focsa et al. [15]. Additionally, the constants of the lower state and the Ht, Lt of the t = 1 level in the c3Rg+ state were all fixed at those of Focsa et al., since they were obtained by a global fitting in combination with the previous r.f. data. The improved constants of the t = 1, 3, 4 levels in the c3Rg+ state are listed in Table 2, and those of Ginter [9] and Focsa et al. [15] are also listed for comparison. Our results are basically in good agreement with those of literatures within 3r error. Additionally, the overall fitting errors are less than the experimental uncertainty proves the reliability of our results. Note that, the rotational level N = 22 in the t = 1 level of the c3Rg+ state is perturbed by one rotational level in the t = 5 level in the b3Gg state [15], therefore the spectral line R(21) in the (1, 0) band was excluded in the fitting. Furthermore, our results of the t = 3 and 4 levels in the c3Rg+ state show about one order magnitude improved in comparison with the Ref. [9], due to the high accuracy and high resolution spectroscopy being employed. In addition, helium gas, as one of the most important buffer gases in the plasma discharge, is often used in the velocity/concentration modulation spectroscopy. The spectrum of He2 often acts as disturbers, so our original motivation of the work was to obtain precise spectral atlas for the help of further studies.
87
C. Li et al. / Journal of Molecular Spectroscopy 260 (2010) 85–87 Table 1 Wavenumbers (in cm1) and assignments in the c3Rg+–a3Ru+ system of the He2. N
1 3 5 7 9 11 13 15 17 19 21 23 25 a b c
(1, 0)
(3, 1)
(2, 0)c
(4, 2)
R
P
R
P
R
P
12393.6454(11)a 12409.4197(7) 12416.6981(3) 12415.3521(3) 12405.2385(2) 12386.2019(34) 12358.0516(7) 12320.5904(3) 12273.5656(1) 12216.6766(0) 12149.9791(4234)b
12354.3249(9) 12317.8351(11) 12273.2370(12) 12220.6336(26) 12160.0898(11) 12091.6765(38)
13276.8970(23) 13284.9866(10)
13241.8869(10) 13203.4920(10) 13153.1356(7) 13090.8147(1) 13016.4581(10) 12929.9154(22) 12830.9358(32) 12719.1389(71) 12593.8887(72) 12454.3132(43) 12299.0090(29)
12715.9394(58) 12719.4942(12) 12708.4032(8) 12682.1522(33) 12639.9801(13) 12580.8159(11) 12503.0472(2)
12683.9185(63) 12645.0051(30) 12592.0956(6) 12525.0356(8) 12443.5217(7) 12347.0099(17) 12234.6221(2)
13263.5248(7) 13233.3368(9) 13189.6105(51) 13131.7416(1) 13058.9606(12) 12970.1699(27) 12863.8192(58) 12737.6641(8)
R
13221.6816
P
13231.4377 13117.4389 12992.0514 12854.7967 12704.9623 12540.9921
Values in parentheses are (vobs vcal) 104 cm1. Perturbation. The observed spectra of (2, 0) band were not used to fit the constants of t = 2 in the c3Rg+ state, since only seven lines were obtained.
Table 2 Molecular constants (cm1) of the t = 1, 3, 4 levels in the c3Rg+ state of He2.
t=1 Tta Bt Dt 104 Ht 108 Lt 1012 ct 105 cDt 108 kt 102 kDt 106
r a b
t=3
t=4
This work
Ref. [15]
Ref. [9]
This work
Ref. [9]
This work
Ref. [9]
12369.50264(89)b 6.556864(14) 5.80751(36) 4.49 3.68 8.0805 2.2828 3.6664342 6.5887 0.0020
12369.4987(25) 6.556820(63) 5.8067(49) 4.49(135) 3.68(120) 8.0805 2.2828 3.6664342 6.5887
12369.50(2) 6.556 (2) 5.76(2) 1.3(1)
14988.7411(21) 5.839938(76) 7.2707(70) 1.18(22) 184.0(22) 8.0805 2.2828 3.6664342 6.5887 0.0037
14988.80(2) 5.837(1) 6.98(5) 13(1)
16084.6134(24) 5.34436(21) 9.190(47) 19.7(36) 687(88) 8.0805 2.2828 3.6664342 6.5887 0.0034
16084.63(2) 5.340(1) 8.57(4) 54(2)
The energy of t = 0 level in the a3Ru+ state is set to 0. Numbers in parentheses denote one standard deviation in unit of the last quoted digit. If the numbers are missing, the values are fixed at those of Ref. [15].
4. Conclusion In summary, the (1, 0), (3, 1), (4, 2) and a portion of (2, 0) bands in the c3Rg+–a3Ru+ system of He2 were recorded in the region 12 090–13 300 cm1 by OH-CMS. Fifty-two spectral lines of the (1, 0), (3, 1) and (4, 2) bands were non-linear least-squares fitted, yielding about one order of magnitude improved constants of the t = 3 and 4 levels in the c3Rg+ state. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 10574045), the National Key Basic Research and Development Program of China (Grant Nos. 2006CB921604 and 2010CB922903), and the Basic Key Program of Shanghai Municipality (Grant No. 07JC14017). One of the authors (C.L.L.) is grateful to the support of the PhD Program Scholarship Fund of ECNU 2009, and another (L.H.D.) would like to thank the support of the National Science Foundation for Post-doctoral Scientist of China. References [1] H.L. Williams, T. Korona, R. Bukowski, B. Jeziorski, K. Szalewicz, Chem. Phys. Lett. 262 (1996) 431–436.
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