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The C(2)1Πu state of Na2 molecule studied by polarization labelling spectroscopy method
Spectrochimica Acta Part A 57 (2001) 1829– 1831 www.elsevier.com/locate/saa
The C(2)1Pu state of Na2 molecule studied by polarization labelling spectroscopy method W. Jastrzebski a,*, P. Kowalczyk b, J.J. Camacho c, A. Pardo c, J.M.L. Poyato c a
Institute of Physics, Polish Academy of Sciences, Al. Lotniko´w 32 /46, 02 -668 Warsaw, Poland Institute of Experimental Physics, Warsaw Uni6ersity, ul. Hoz; a 69, 00 -681 Warsaw, Poland c Departamento de Quimica-Fisica Aplicada, Facultad de Ciencias, Uni6ersidad Autonoma de Madrid, Cantoblanco, E-28049 Madrid, Spain b
Received 12 December 2000; accepted 18 January 2001
Abstract The C1Pu X1+ g system of Na2 is studied by the polarization labelling spectroscopy technique. Accurate molecular constants are derived for the observed levels w= 0 – 12, J= 12 – 100 in the C1Pu state. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Polarization labelling spectroscopy; Molecular constant; Spectroscopy
1. Introduction In recent years we have studied excitation spectra of Na2 and NaK molecules in the near UV range (ca. 25 500 – 29 650 cm − 1) [1,2]. As a byproduct of our investigations on states which have not been analysed previously, we recorded several hundreds of lines belonging to the known C1Pu X1+ g system of Na2. However, during the initial assignment of the observed spectra we noticed that neither of the sets of the C state molecular constants available in the literature [3–7] can reproduce properly the line positions measured in our experiment. * Corresponding author. Tel.: +48-22-8436601 (Ext. 3217); fax: +48-22-8430926. E-mail address: [email protected] (W. Jastrzebski).
The first molecular constants describing the C(2)1Pu state of Na2 for 65 w5 19 were obtained from classical absorption spectroscopy by Wright [3]. In 1982 Verma et al. [4] corrected the vibrational numbering in the C state by observing the intensity pattern of laser induced fluorescence (LIF) in the CX band. A year later Bernage et al. [5] studied w =0–5 vibrational levels of the C state and derived molecular constants applicable to this range. Later on Effantin et al. [6] proposed an alternative set of constants describing slightly wider range of levels (05 w5 7). Finally, the C1Pu state was studied in detail by Doppler-free modulated population spectroscopy method [7]. Unfortunately, the precise data were related only to higher vibrational levels (115 w5 35). Thus each of the previous works offered only partial description of the C1Pu state of Na2, spe-
1386-1425/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 1 ) 0 0 4 0 5 - X
1830
W. Jastrzebski et al. / Spectrochimica Acta Part A 57 (2001) 1829–1831
cific to the limited range of quantum numbers w. In the present paper we verify the molecular constants relative to the bottom of the C state and extend them up to w=12. The derived set of Dunham coefficients characterizes the C state for w=0– 12 and in the wide range of rotational quantum numbers J (12 5 J 5100); the coefficients reproduce the positions of unperturbed rotational lines in the C1Pu X1+ g band system to within 0.06 cm − 1. 2. Experimental Only a brief outline of the experimental procedure is given here, as a detailed description can be found elsewhere [8]. We employed the V-type optical–optical double resonance polarization spectroscopy scheme. The fixed frequency of the probe laser (Ar+ at 457.9, 476.5, 488.0, 496.5, 501.7 or 514.5 nm) coincided with a set of known transitions in the B1Pu X1+ g system of Na2, thus labelling the involved rotational levels in the ground state. The pump laser (pulsed dye laser, 2 mJ pulse energy, 0.1cm − 1 spectral width) was tuned across the C– X band system under investigation, in the spectral range 27 550– 29 650 cm − 1. The laser frequency was calibrated against the optogalvanic spectrum of argon and frequency marks provided by a 0.5 cm long Fabry–Pe´ rot interferometer. The accuracy in determination of absolute wavenumbers was better than 0.1 cm − 1. The Na2 molecules were generated in a heat-pipe oven operating at 750 K and 5 mbar of helium as a buffer gas. 3. Results and discussion The observed data consists of 706 wavenumbers corresponding to transitions between known labelled levels in the ground X1+ g state and levels in the C1Pu state. The X state constants of Kusch and Hessel [9] were used to convert each of these wavenumbers to a term value T(w, J) of a given rovibronic level (w, J) in the C state, referred to the bottom of the ground state potential well. These term values were then fitted by a leastsquares procedure with an equation of the form
T(, J) =Te + % (Ymn + lymn )( +0.5)m[J(J+ 1)−1]n m,n
(1) The lymn constants describe the \ doubling in the C1Pu state: l= 0 or 1 for f- or e-parity levels, respectively. Preliminary analysis served to eliminate a few perturbed lines. In the final fit eight constants were fitted to 698 experimental term values, providing the coefficients listed in Table 1. The standard error of the fit, equal to 0.06 cm − 1, was consistent with the precision of the measurements. It is worth noting that the experimental Y02 coefficient is in good agreement (3%) with the value calculated from the Kratzer relation [10], which holds for most electronic states in diatomic molecules with regular potential curves. Based on the derived molecular constants, the RKR potential curve of the C state was calculated. The results are shown in Table 2 which contains the Gw and Bw values as well as the RKR turning points. The C1Pu state is known to be correlated with the atomic configuration Na(3S)+ Na(3D) ([11]). Using the value of dissociation energy of the ground state of Na2 (6022 cm − 1 [12]) and excitation energy of the atomic 3D state (29 173 cm − 1 [13]) we can obtain dissociation energy of the C1Pu state from the relation
Table 1 The Dunham coefficients for the C1Pu state of Na2 obtained in the present worka Constant
Value (cm−1)
Error (%)
Te Y10 Y20 Y30 Y01 Y11 Y02 y01
29 622.13 116.310 −0.6497 0.242×10−2 0.116316 −0.8745×10−3 −0.4529×10−6 0.36×10−4
0.00003 0.005 0.179 2.738 0.003 0.032 0.071 2.993
a The quoted uncertainty of a constant is one standard deviation. To reproduce the original data, the parameters are given with more significant figures than are required by the associated standard errors.
W. Jastrzebski et al. / Spectrochimica Acta Part A 57 (2001) 1829–1831 Table 2 Rotationless RKR potential for the C1Pu state of Na2 w
0 1 2 3 4 5 6 7 8 9 10 11 12
Tw+Y00 (cm−1)
Rmin(A, )
29 622.113
3.5503a
29 680.118 29 795.136 29 908.877 30 021.355 30 132.585 30 242.581 30 351.357 30 458.928 30 565.309 30 670.514 30 774.558 30 877.456 30 979.219
3.3991 3.2975 3.2315 3.1802 3.1374 3.1003 3.0675 3.0379 3.0109 2.9860 2.9630 2.9415 2.9214
Rmax(A, )
Bw (cm−1)
3.7175 3.8515 3.9500 4.0343 4.1104 4.1810 4.2478 4.3116 4.3732 4.4329 4.4912 4.5482 4.6043
0.115915 0.115040 0.114166 0.113291 0.112417 0.111542 0.110668 0.109793 0.108919 0.108045 0.107170 0.106296 0.105421
(2)
yielding De(C1Pu) =5573 cm − 1. Thus the Dunham coefficients listed in Table 1 describe the C1Pu state to about 25% of its potential well depth.
Acknowledgements This work has been partially supported by research grants KBN (Poland) No. 2 P03B 067 16 and DGICYT (Spain) PB96-0046. The wavenumbers of the observed spectral lines in the C1Pu X1+ g system of Na2 have been deposited with
.
the British Library at Boston Spa, Wetherby, West Yorks, UK. as Supplementary Publication No.13137. Persons wishing to obtain copies of deposited material should contact Service Enquiries, British Lending Library, Boston Spa, Wetherby, West Yorks, LS23 7BQ, UK. citing the SUP number. Tel.: + 44-1937-546060; fax: +44-1937-546333. E-mail: [email protected].
References
a The first line refers to the bottom of the potential curve. R is the equilibrium distance.
1 De(C1Pu)= De(X1+ g ) + E(3D) − Te(C Pu),
1831
[1] A. Pashov, I. Jackowska, W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 58 (1998) 1048. [2] A. Pashov, W. Jastrzebski, W. Jas´niecki, V. Bednarska, P. Kowalczyk, J. Mol. Spectrosc. 203 (2000) 264. [3] C.V. Wright, Ph.D. Thesis, Oxford University, 1960. [4] K.K. Verma, T.H. Vu, W.C. Stwalley, J. Mol. Spectrosc. 91 (1982) 325. [5] P. Bernage, P. Niay, H. Bocquet, J. Mol. Spectrosc. 98 (1983) 304. [6] C. Effantin, J. d’Incan, A.J. Ross, R.F. Barrow, J. Verge`s, J. Phys. B: At. Mol. Phys. 17 (1984) 1515. [7] G.Y. Yan, B.W. Sterling, T. Kalka, A.L. Schawlow, J. Opt. Soc. Am. B 6 (1989) 1975. [8] I. Jackowska, W. Jastrzebski, R. Ferber, O. Nikolayeva, P. Kowalczyk, Mol. Phys. 89 (1996) 1719. [9] P. Kusch, M.M. Hessel, J. Chem. Phys. 68 (1978) 2591. [10] G. Herzberg, Molecular Spectra and Molecular Structure, Spectra of Diatomic Molecules, vol. 1, Van Nostrand, Princeton, 1950. [11] S. Magnier, Ph. Millie´ , O. Dulieu, F. Masnou-Seeuws, J. Chem. Phys. 98 (1993) 7113. [12] K.M. Jones, S. Maleki, S. Bize, P.D. Lett, C.J. Williams, H. Richling, H. Kno¨ ckel, E. Tiemann, H. Wang, P.L. Gould, W.C. Stwalley, Phys. Rev. A 54 (1996) R1006. [13] A.A. Radzig, P.M. Smirnov, Reference Data on Atoms, Molecules and Ions, Springer, Berlin, 1985.
The C(2)1Pu state of Na2 molecule studied by polarization labelling spectroscopy method W. Jastrzebski a,*, P. Kowalczyk b, J.J. Camacho c, A. Pardo c, J.M.L. Poyato c a
Institute of Physics, Polish Academy of Sciences, Al. Lotniko´w 32 /46, 02 -668 Warsaw, Poland Institute of Experimental Physics, Warsaw Uni6ersity, ul. Hoz; a 69, 00 -681 Warsaw, Poland c Departamento de Quimica-Fisica Aplicada, Facultad de Ciencias, Uni6ersidad Autonoma de Madrid, Cantoblanco, E-28049 Madrid, Spain b
Received 12 December 2000; accepted 18 January 2001
Abstract The C1Pu X1+ g system of Na2 is studied by the polarization labelling spectroscopy technique. Accurate molecular constants are derived for the observed levels w= 0 – 12, J= 12 – 100 in the C1Pu state. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Polarization labelling spectroscopy; Molecular constant; Spectroscopy
1. Introduction In recent years we have studied excitation spectra of Na2 and NaK molecules in the near UV range (ca. 25 500 – 29 650 cm − 1) [1,2]. As a byproduct of our investigations on states which have not been analysed previously, we recorded several hundreds of lines belonging to the known C1Pu X1+ g system of Na2. However, during the initial assignment of the observed spectra we noticed that neither of the sets of the C state molecular constants available in the literature [3–7] can reproduce properly the line positions measured in our experiment. * Corresponding author. Tel.: +48-22-8436601 (Ext. 3217); fax: +48-22-8430926. E-mail address: [email protected] (W. Jastrzebski).
The first molecular constants describing the C(2)1Pu state of Na2 for 65 w5 19 were obtained from classical absorption spectroscopy by Wright [3]. In 1982 Verma et al. [4] corrected the vibrational numbering in the C state by observing the intensity pattern of laser induced fluorescence (LIF) in the CX band. A year later Bernage et al. [5] studied w =0–5 vibrational levels of the C state and derived molecular constants applicable to this range. Later on Effantin et al. [6] proposed an alternative set of constants describing slightly wider range of levels (05 w5 7). Finally, the C1Pu state was studied in detail by Doppler-free modulated population spectroscopy method [7]. Unfortunately, the precise data were related only to higher vibrational levels (115 w5 35). Thus each of the previous works offered only partial description of the C1Pu state of Na2, spe-
1386-1425/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 1 ) 0 0 4 0 5 - X
1830
W. Jastrzebski et al. / Spectrochimica Acta Part A 57 (2001) 1829–1831
cific to the limited range of quantum numbers w. In the present paper we verify the molecular constants relative to the bottom of the C state and extend them up to w=12. The derived set of Dunham coefficients characterizes the C state for w=0– 12 and in the wide range of rotational quantum numbers J (12 5 J 5100); the coefficients reproduce the positions of unperturbed rotational lines in the C1Pu X1+ g band system to within 0.06 cm − 1. 2. Experimental Only a brief outline of the experimental procedure is given here, as a detailed description can be found elsewhere [8]. We employed the V-type optical–optical double resonance polarization spectroscopy scheme. The fixed frequency of the probe laser (Ar+ at 457.9, 476.5, 488.0, 496.5, 501.7 or 514.5 nm) coincided with a set of known transitions in the B1Pu X1+ g system of Na2, thus labelling the involved rotational levels in the ground state. The pump laser (pulsed dye laser, 2 mJ pulse energy, 0.1cm − 1 spectral width) was tuned across the C– X band system under investigation, in the spectral range 27 550– 29 650 cm − 1. The laser frequency was calibrated against the optogalvanic spectrum of argon and frequency marks provided by a 0.5 cm long Fabry–Pe´ rot interferometer. The accuracy in determination of absolute wavenumbers was better than 0.1 cm − 1. The Na2 molecules were generated in a heat-pipe oven operating at 750 K and 5 mbar of helium as a buffer gas. 3. Results and discussion The observed data consists of 706 wavenumbers corresponding to transitions between known labelled levels in the ground X1+ g state and levels in the C1Pu state. The X state constants of Kusch and Hessel [9] were used to convert each of these wavenumbers to a term value T(w, J) of a given rovibronic level (w, J) in the C state, referred to the bottom of the ground state potential well. These term values were then fitted by a leastsquares procedure with an equation of the form
T(, J) =Te + % (Ymn + lymn )( +0.5)m[J(J+ 1)−1]n m,n
(1) The lymn constants describe the \ doubling in the C1Pu state: l= 0 or 1 for f- or e-parity levels, respectively. Preliminary analysis served to eliminate a few perturbed lines. In the final fit eight constants were fitted to 698 experimental term values, providing the coefficients listed in Table 1. The standard error of the fit, equal to 0.06 cm − 1, was consistent with the precision of the measurements. It is worth noting that the experimental Y02 coefficient is in good agreement (3%) with the value calculated from the Kratzer relation [10], which holds for most electronic states in diatomic molecules with regular potential curves. Based on the derived molecular constants, the RKR potential curve of the C state was calculated. The results are shown in Table 2 which contains the Gw and Bw values as well as the RKR turning points. The C1Pu state is known to be correlated with the atomic configuration Na(3S)+ Na(3D) ([11]). Using the value of dissociation energy of the ground state of Na2 (6022 cm − 1 [12]) and excitation energy of the atomic 3D state (29 173 cm − 1 [13]) we can obtain dissociation energy of the C1Pu state from the relation
Table 1 The Dunham coefficients for the C1Pu state of Na2 obtained in the present worka Constant
Value (cm−1)
Error (%)
Te Y10 Y20 Y30 Y01 Y11 Y02 y01
29 622.13 116.310 −0.6497 0.242×10−2 0.116316 −0.8745×10−3 −0.4529×10−6 0.36×10−4
0.00003 0.005 0.179 2.738 0.003 0.032 0.071 2.993
a The quoted uncertainty of a constant is one standard deviation. To reproduce the original data, the parameters are given with more significant figures than are required by the associated standard errors.
W. Jastrzebski et al. / Spectrochimica Acta Part A 57 (2001) 1829–1831 Table 2 Rotationless RKR potential for the C1Pu state of Na2 w
0 1 2 3 4 5 6 7 8 9 10 11 12
Tw+Y00 (cm−1)
Rmin(A, )
29 622.113
3.5503a
29 680.118 29 795.136 29 908.877 30 021.355 30 132.585 30 242.581 30 351.357 30 458.928 30 565.309 30 670.514 30 774.558 30 877.456 30 979.219
3.3991 3.2975 3.2315 3.1802 3.1374 3.1003 3.0675 3.0379 3.0109 2.9860 2.9630 2.9415 2.9214
Rmax(A, )
Bw (cm−1)
3.7175 3.8515 3.9500 4.0343 4.1104 4.1810 4.2478 4.3116 4.3732 4.4329 4.4912 4.5482 4.6043
0.115915 0.115040 0.114166 0.113291 0.112417 0.111542 0.110668 0.109793 0.108919 0.108045 0.107170 0.106296 0.105421
(2)
yielding De(C1Pu) =5573 cm − 1. Thus the Dunham coefficients listed in Table 1 describe the C1Pu state to about 25% of its potential well depth.
Acknowledgements This work has been partially supported by research grants KBN (Poland) No. 2 P03B 067 16 and DGICYT (Spain) PB96-0046. The wavenumbers of the observed spectral lines in the C1Pu X1+ g system of Na2 have been deposited with
.
the British Library at Boston Spa, Wetherby, West Yorks, UK. as Supplementary Publication No.13137. Persons wishing to obtain copies of deposited material should contact Service Enquiries, British Lending Library, Boston Spa, Wetherby, West Yorks, LS23 7BQ, UK. citing the SUP number. Tel.: + 44-1937-546060; fax: +44-1937-546333. E-mail: [email protected].
References
a The first line refers to the bottom of the potential curve. R is the equilibrium distance.
1 De(C1Pu)= De(X1+ g ) + E(3D) − Te(C Pu),
1831
[1] A. Pashov, I. Jackowska, W. Jastrzebski, P. Kowalczyk, Phys. Rev. A 58 (1998) 1048. [2] A. Pashov, W. Jastrzebski, W. Jas´niecki, V. Bednarska, P. Kowalczyk, J. Mol. Spectrosc. 203 (2000) 264. [3] C.V. Wright, Ph.D. Thesis, Oxford University, 1960. [4] K.K. Verma, T.H. Vu, W.C. Stwalley, J. Mol. Spectrosc. 91 (1982) 325. [5] P. Bernage, P. Niay, H. Bocquet, J. Mol. Spectrosc. 98 (1983) 304. [6] C. Effantin, J. d’Incan, A.J. Ross, R.F. Barrow, J. Verge`s, J. Phys. B: At. Mol. Phys. 17 (1984) 1515. [7] G.Y. Yan, B.W. Sterling, T. Kalka, A.L. Schawlow, J. Opt. Soc. Am. B 6 (1989) 1975. [8] I. Jackowska, W. Jastrzebski, R. Ferber, O. Nikolayeva, P. Kowalczyk, Mol. Phys. 89 (1996) 1719. [9] P. Kusch, M.M. Hessel, J. Chem. Phys. 68 (1978) 2591. [10] G. Herzberg, Molecular Spectra and Molecular Structure, Spectra of Diatomic Molecules, vol. 1, Van Nostrand, Princeton, 1950. [11] S. Magnier, Ph. Millie´ , O. Dulieu, F. Masnou-Seeuws, J. Chem. Phys. 98 (1993) 7113. [12] K.M. Jones, S. Maleki, S. Bize, P.D. Lett, C.J. Williams, H. Richling, H. Kno¨ ckel, E. Tiemann, H. Wang, P.L. Gould, W.C. Stwalley, Phys. Rev. A 54 (1996) R1006. [13] A.A. Radzig, P.M. Smirnov, Reference Data on Atoms, Molecules and Ions, Springer, Berlin, 1985.