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Radiative lifetimes for the B1Πu state of the Na2 molecule
Spectrochimica Acta Part A 56 (2000) 2417 – 2421 www.elsevier.nl/locate/saa
Radiative lifetimes for the B1Pu state of the Na2 molecule A. Pardo *, J.J. Camacho, J.M.L. Poyato Departamento de Quı´mica-Fı´sica Aplicada, Facultad de Ciencias, Uni6ersidad Auto´noma de Madrid, Cantoblanco, 28049 Madrid, Spain Received 24 June 1999; accepted 25 April 2000
Abstract A study of the radiative lifetimes calculation of the Na2 B1Pu state is presented. RKR electronic potentials are considered. The studied vibrational levels are for 6%=0–33 (B1Pu) and 6¦= 0–65 (X1S+ g ). The rotation is considered for values of J%= 1–225 (B1Pu). The Einstein emission coefficients are calculated for the specified B1Pu rovibrational levels (for Q line and R, P lines, for all ground state vibrational levels). With the inverse of Einstein emission coefficients sum, the radiative lifetimes are calculated. These calculated lifetimes are in good agreement with the experimental and previously calculated (with RKR potentials) lifetimes, but now great extension of considered rovibrational levels is considered. The bound– free contribution is irrelevant for Na2 lifetimes of the B1Pu state. The perturbation between Na2 B1Pu and A1S+ u states is considered. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Radiative lifetimes; Diatomic molecules; RKR potentials
1. Introduction The experimental and theoretical lifetime studies of diatomic molecules are of great interest. In the present work, we fix our attention on lifetimes for the Na2 B1Pu state. The Na2B1Pu and X1S+ g states are known in detail. Diverse laser induced fluorescence studies have produced the spectroscopic constants, including levels next to dissociation. RKR potentials for these states have been obtained by different authors. We emphasize, among many others, the X1S+ potentials by g Zemke and Stwalley (ZS) and Babaky –Hussein * Corresponding author. Tel.: +34-91-3974960; fax: + 3491-3974512. E-mail address: [email protected] (A. Pardo).
[1,2]. For the B1Pu state, the Richter–Kno¨ckel– Tiemann (RKT) potential was selected [3]. In this 1 work, the ZS (X1S+ g ) and RKT (B Pu) potentials have been used. For these potentials, the calculated rovibrational eigenvalues are in very good agreement with the experimental rovibrational energies. To calculate Einstein emission coefficients, the rovibrational wavefunctions and dipole transition moment are necessary. The theoretical (MCSCF) values for the Na2 B1Pu l X1S+ system calcug lated by Stevens–Hessel–Bertoncini–Wahl [4] are considered for dipole transition moment. These theoretical values agree with the values obtained by Demtro¨der–Stetzenbach–Stock–Witt (DSSW) [5] (utilizing experimental lifetimes with r-centroid approximation).
1386-1425/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 0 ) 0 0 2 9 3 - 6
A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
2418
The DSSW experimental lifetimes are considered to compare with those calculated in the present work. In the DSSW work, a lifetime calculation is made (with RKR potentials), finding a satisfactory agreement for the experimentally observed levels. The work presented now is based on the improvement of RKR potentials of the B and X states. Now these potentials are known with great precision (until dissociation). Furthermore, a study is made that considers the B vibrational levels for 6%=0 – 33 (for X state, 6¦ =0 – 65); referring to the rotation, this one is extended until J%= 225. The earlier radiative lifetimes (experimental and calculated) are delimited between 6%= 0–29 and 6¦= 0 – 47 (maximum J = 124). To calculate experimental energies, the spectroscopic constants of Kusch and Hessel are considered. These constants are effective approximately for J (up 100) and 6% = 0 – 29, 6¦= 0 – 45 [6]. The perturbation between Na2 B1Pu and A1S+ states is u considered [7,8].
Table 1 Electronic potential of the Na2 B1Pu state r (A, )
U (cm−1)
r (A, )
U (cm−1)
2.5810000 2.6285454 2.6460268 2.6656765 2.6877089 2.7123565 2.7399183 2.7708125 2.8056469 2.8453290 2.8912700 2.9458236 3.0134271 3.1046236 3.2669903 3.4131560 3.5747379 3.8001057 3.9566821 4.0924791
3058.25574 2663.08960 2513.66408 2358.03462 2193.39677 2019.05509 1825.92942 1636.00000 1430.69579 1220.44446 1001.85994 776.57767 544.64107 306.43716 62.06486 −0.00952 61.99572 306.27569 544.36317 776.14059
4.2185099 4.3397279 4.4590851 4.5787277 4.7005058 4.8262746 4.9581482 5.0988006 5.2519184 5.4229064 5.6208111 5.9800000 6.2300000 6.4800000 6.7300000 7.2300000 7.9800000 9.9800000 11.0000000
1001.27316 1219.54008 1430.50799 1633.85040 1829.08806 2015.58025 2192.80771 2359.86689 2515.58377 2659.44129 2789.32476 2942.42991 3001.34349 3032.99405 3045.80512 3036.11549 2989.16524 2860.33356 2813.71135
2. Electronic potentials For the fundamental state of the sodium molecule, the potential established by Zemke and Stwalley [1] has been considered. This potential considers spectroscopic information up to 6 = 65. The eigenvalues for the corresponding potential for J=0 present very good self-consistency. The mean (experimental –calculated vibrational terms) discrepancy is of the order of 0.03 cm − 1. When the potential is used for a rotational energy of J = 50, the mean discrepancy is about 0.3 cm − 1 (smaller) than the values calculated using the spectroscopic constants of Kusch and Hessel [6]. Correspondingly, for J=100 the discrepancies are 1.2 cm − 1 (larger). Attempts to improve this potential did not produce better consistency and the discrepancies have been taken into account as a correction factor for the calculated eigenvalue energies. As the calculated–observed differences are small, these are not significant in the calculated wavefunctions. For the B1Pu state, the potential established by Richter–Kno¨ckel–Tiemann [3] was used. This potential is the result of a very detailed analysis of the potential barrier that the B state presents in the dissociation zone. The behavioral analysis of the eigenvalues in the function of rotation (J=1, J= 50, J= 100) indicates that the discrepancies are of the order of 0.1 cm − 1 for J= 1 and J=50, and 0.17 cm − 1 for J= 100 (with the calculated values for Kusch and Hessel’s spectroscopic constant). With minor corrections (the corrected potential is shown in Table 1), these discrepancies were reduced to 0.03 cm − 1 for J =1 and J= 50, and 0.1 cm − 1 for J= 100. Taking into account these considerations, it might be expected that the calculated spectrum (using the above-mentioned electronic potentials) should be consistent with the experimental spectrum around 0.2–0.4 cm − 1 for J up to 100, discrepancy increasing for J-values above 100.
3. Calculation of radiative lifetimes To calculate the radiative lifetimes, we obtain the eigenvalues and eigenfunctions with the men1 tioned X1S+ g and B Pu electronic potentials. With
A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
Fig. 1. Representation of calculated Q lifetimes (t, s) and experimental (Q large dots, R–P medium dots) for Na2B1Pu state.
Fig. 2. Representation of calculated Q lifetimes (t, s) and previously calculated lifetimes (QSSW) for Na2B1Pu state.
the variation of electronic dipole moment transition by Stevens et al. and eigenvalues and eigenfunctions calculated in the present work, the radiative lifetimes are calculated for the above mentioned rovibrational levels of the B1Pu state. The calculated lifetimes are for Q transitions (DJ = 0) and for R – P transitions (DJ = 9 1). The difference between Q and R – P lifetimes for
2419
a J level is very small (only variation in the third nanosecond decimal). In radiative lifetime calculation, it is necessary to take into account the participation of the bound–free transition. This participation is practically null in the B1Pu l X1S+ transition. This is controlled by g the sum of the Frank–Condon factors. In Fig. 1, the calculated lifetimes (Q transitions) are represented for rovibrational levels of B1Pu state (6%= 0–33). In this figure, the experimental values of rovibrational levels are shown by dots (the lifetimes were also calculated for these levels in the DSSW paper). A line connects the experimental and calculated lifetimes. The experimental Q lifetimes are represented as large points to distinguish them from the R–P lifetimes (medium points). The experimental errors (0.08– 0.2 ns) are consistent with the discrepancies between experimental and calculated lifetimes. The comparison of present and previous calculated (DSSW) lifetimes is represented in Fig. 2 (the mean difference is 0.03 ns). Here, it might be appreciated the great extension of the presented calculations. In Table 2, a limited number of calculated lifetimes are collected. The calculated lifetimes for the Q transitions correspond to the P− component of the B1Pu state. For this component, no perturbations with the A1S+ u state are possible. Perturbation with the A1S+ u state is possible for the P+ component (lifetimes for R–P transitions) [7]. There is not experimental evidence for this perturbation. A similar situation was studied for H2 C1Pu and B1S+ u states [8]. The discrepancies for Q (P− component) lifetimes (experimental–calculated) are less that those for the R–P (P+ component) (Fig. 1). This is a possible indication of perturbation for the P+ component of the B1Pu state.
4. Conclusions A very extensive calculation of lifetimes for the B1Pu − X1S+ g transition is presented. The calculated lifetimes in the present work are in agreement with the previous experimental and calculated lifetimes (DSSW). Very accurate RKR
J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
6
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
6.96E−09 6.97E−09 6.99E−09 7.01E−09 7.02E−09 7.04E−09 7.05E−09 7.07E−09 7.08E−09 7.10E−09 7.11E−09 7.13E−09 7.14E−09 7.16E−09 7.17E−09 7.18E−09 7.20E−09 7.21E−09 7.23E−09 7.24E−09 7.25E−09 7.27E−09 7.29E−09 7.30E−09 7.32E−09 7.34E−09 7.36E−09 7.39E−09 7.41E−09 7.44E−09 7.47E−09 7.50E−09 7.53E−09 7.58E−09
t 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
J
Table 2 Selected lifetimes from Fig. 1
6.96E−09 6.98E−09 6.99E−09 7.01E−09 7.02E−09 7.04E−09 7.06E−09 7.07E−09 7.09E−09 7.1E−09 7.12E−09 7.13E−09 7.14E−09 7.16E−09 7.17E−09 7.19E−09 7.2E−09 7.21E−09 7.23E−09 7.24E−09 7.26E−09 7.27E−09 7.29E−09 7.3E−09 7.32E−09 7.34E−09 7.37E−09 7.39E−09 7.42E−09 7.44E−09 7.47E−09 7.5E−09 7.54E−09 7.58E−09
t 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
J 6.98E−09 6.99E−09 7.01E−09 7.02E−09 7.04E−09 7.06E−09 7.07E−09 7.09E−09 7.1E−09 7.12E−09 7.13E−09 7.14E−09 7.16E−09 7.17E−09 7.19E−09 7.2E−09 7.21E−09 7.23E−09 7.24E−09 7.26E−09 7.27E−09 7.29E−09 7.3E−09 7.32E−09 7.34E−09 7.36E−09 7.39E−09 7.41E−09 7.44E−09 7.47E−09 7.5E−09 7.53E−09 7.57E−09
t 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
J 7.03E−09 7.05E−09 7.06E−09 7.08E−09 7.09E−09 7.11E−09 7.12E−09 7.14E−09 7.15E−09 7.16E−09 7.18E−09 7.19E−09 7.21E−09 7.22E−09 7.23E−09 7.25E−09 7.26E−09 7.28E−09 7.29E−09 7.3E−09 7.32E−09 7.34E−09 7.36E−09 7.38E−09 7.4E−09 7.43E−09 7.45E−09 7.48E−09 7.51E−09 7.55E−09 7.6E−09
t 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120
J 7.24E−09 7.25E−09 7.26E−09 7.28E−09 7.29E−09 7.3E−09 7.31E−09 7.32E−09 7.34E−09 7.35E−09 7.36E−09 7.38E−09 7.39E−09 7.4E−09 7.42E−09 7.43E−09 7.45E−09 7.47E−09 7.49E−09 7.52E−09 7.56E−09 7.61E−09
t 200 200 200 200 200 200
J 7.65E−09 7.66E−09 7.67E−09 7.68E−09 7.69E−09 7.71E−09
t
210 210 210 210
J
7.71E−09 7.71E−09 7.72E−09 7.74E−09
t
2420 A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
potentials are employed. In the B1Pu electronic potential, small corrections are introduced. For the Q transitions of the B1P− u component, perturbation with levels of A1S+ u state are not possible. However, a general perturbation with 1 + the A1S+ u state is possible for the B Pu component (R–P transitions, see Ref. [7]). In addition, for some levels (with quasi-resonant energy, equal J and parity), the lifetimes are 1 a mixture of unperturbed A1S+ u and B Pu lifetimes (see Refs. [7,8]).
Acknowledgements The authors gratefully acknowledge the support
.
2421
received from the DGICYT (Spain) (project No. PB96-0046) for this research.
References [1] W.T. Zemke, W.C. Stwalley, J. Chem. Phys. 100 (1994) 2661. [2] O. Babaky, K. Hussein, Can. J. Phys. 67 (1989) 912. [3] H. Richter, H. Kno¨ckel, E. Tiemann, Chem. Phys. 157 (1991) 217. [4] W.J. Stevens, M.M. Hessel, P.J. Bertoncini, A.C. Wahl, J. Chem. Phys. 66 (1977) 1477. [5] W. Demtro¨der, W. Stetzenbach, M. Stock, J. Witt, J. Mol. Spectrosc. 61 (1976) 382. [6] P. Kusch, M.M. Hessel, J. Chem. Phys. 68 (1978) 2591. [7] K. Dressler, L. Wolniewicz, J. Chem. Phys. 82 (1985) 4720. [8] A. Pardo, J. Mol. Spectrosc. 195 (1999) 68.
Radiative lifetimes for the B1Pu state of the Na2 molecule A. Pardo *, J.J. Camacho, J.M.L. Poyato Departamento de Quı´mica-Fı´sica Aplicada, Facultad de Ciencias, Uni6ersidad Auto´noma de Madrid, Cantoblanco, 28049 Madrid, Spain Received 24 June 1999; accepted 25 April 2000
Abstract A study of the radiative lifetimes calculation of the Na2 B1Pu state is presented. RKR electronic potentials are considered. The studied vibrational levels are for 6%=0–33 (B1Pu) and 6¦= 0–65 (X1S+ g ). The rotation is considered for values of J%= 1–225 (B1Pu). The Einstein emission coefficients are calculated for the specified B1Pu rovibrational levels (for Q line and R, P lines, for all ground state vibrational levels). With the inverse of Einstein emission coefficients sum, the radiative lifetimes are calculated. These calculated lifetimes are in good agreement with the experimental and previously calculated (with RKR potentials) lifetimes, but now great extension of considered rovibrational levels is considered. The bound– free contribution is irrelevant for Na2 lifetimes of the B1Pu state. The perturbation between Na2 B1Pu and A1S+ u states is considered. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Radiative lifetimes; Diatomic molecules; RKR potentials
1. Introduction The experimental and theoretical lifetime studies of diatomic molecules are of great interest. In the present work, we fix our attention on lifetimes for the Na2 B1Pu state. The Na2B1Pu and X1S+ g states are known in detail. Diverse laser induced fluorescence studies have produced the spectroscopic constants, including levels next to dissociation. RKR potentials for these states have been obtained by different authors. We emphasize, among many others, the X1S+ potentials by g Zemke and Stwalley (ZS) and Babaky –Hussein * Corresponding author. Tel.: +34-91-3974960; fax: + 3491-3974512. E-mail address: [email protected] (A. Pardo).
[1,2]. For the B1Pu state, the Richter–Kno¨ckel– Tiemann (RKT) potential was selected [3]. In this 1 work, the ZS (X1S+ g ) and RKT (B Pu) potentials have been used. For these potentials, the calculated rovibrational eigenvalues are in very good agreement with the experimental rovibrational energies. To calculate Einstein emission coefficients, the rovibrational wavefunctions and dipole transition moment are necessary. The theoretical (MCSCF) values for the Na2 B1Pu l X1S+ system calcug lated by Stevens–Hessel–Bertoncini–Wahl [4] are considered for dipole transition moment. These theoretical values agree with the values obtained by Demtro¨der–Stetzenbach–Stock–Witt (DSSW) [5] (utilizing experimental lifetimes with r-centroid approximation).
1386-1425/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 1 4 2 5 ( 0 0 ) 0 0 2 9 3 - 6
A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
2418
The DSSW experimental lifetimes are considered to compare with those calculated in the present work. In the DSSW work, a lifetime calculation is made (with RKR potentials), finding a satisfactory agreement for the experimentally observed levels. The work presented now is based on the improvement of RKR potentials of the B and X states. Now these potentials are known with great precision (until dissociation). Furthermore, a study is made that considers the B vibrational levels for 6%=0 – 33 (for X state, 6¦ =0 – 65); referring to the rotation, this one is extended until J%= 225. The earlier radiative lifetimes (experimental and calculated) are delimited between 6%= 0–29 and 6¦= 0 – 47 (maximum J = 124). To calculate experimental energies, the spectroscopic constants of Kusch and Hessel are considered. These constants are effective approximately for J (up 100) and 6% = 0 – 29, 6¦= 0 – 45 [6]. The perturbation between Na2 B1Pu and A1S+ states is u considered [7,8].
Table 1 Electronic potential of the Na2 B1Pu state r (A, )
U (cm−1)
r (A, )
U (cm−1)
2.5810000 2.6285454 2.6460268 2.6656765 2.6877089 2.7123565 2.7399183 2.7708125 2.8056469 2.8453290 2.8912700 2.9458236 3.0134271 3.1046236 3.2669903 3.4131560 3.5747379 3.8001057 3.9566821 4.0924791
3058.25574 2663.08960 2513.66408 2358.03462 2193.39677 2019.05509 1825.92942 1636.00000 1430.69579 1220.44446 1001.85994 776.57767 544.64107 306.43716 62.06486 −0.00952 61.99572 306.27569 544.36317 776.14059
4.2185099 4.3397279 4.4590851 4.5787277 4.7005058 4.8262746 4.9581482 5.0988006 5.2519184 5.4229064 5.6208111 5.9800000 6.2300000 6.4800000 6.7300000 7.2300000 7.9800000 9.9800000 11.0000000
1001.27316 1219.54008 1430.50799 1633.85040 1829.08806 2015.58025 2192.80771 2359.86689 2515.58377 2659.44129 2789.32476 2942.42991 3001.34349 3032.99405 3045.80512 3036.11549 2989.16524 2860.33356 2813.71135
2. Electronic potentials For the fundamental state of the sodium molecule, the potential established by Zemke and Stwalley [1] has been considered. This potential considers spectroscopic information up to 6 = 65. The eigenvalues for the corresponding potential for J=0 present very good self-consistency. The mean (experimental –calculated vibrational terms) discrepancy is of the order of 0.03 cm − 1. When the potential is used for a rotational energy of J = 50, the mean discrepancy is about 0.3 cm − 1 (smaller) than the values calculated using the spectroscopic constants of Kusch and Hessel [6]. Correspondingly, for J=100 the discrepancies are 1.2 cm − 1 (larger). Attempts to improve this potential did not produce better consistency and the discrepancies have been taken into account as a correction factor for the calculated eigenvalue energies. As the calculated–observed differences are small, these are not significant in the calculated wavefunctions. For the B1Pu state, the potential established by Richter–Kno¨ckel–Tiemann [3] was used. This potential is the result of a very detailed analysis of the potential barrier that the B state presents in the dissociation zone. The behavioral analysis of the eigenvalues in the function of rotation (J=1, J= 50, J= 100) indicates that the discrepancies are of the order of 0.1 cm − 1 for J= 1 and J=50, and 0.17 cm − 1 for J= 100 (with the calculated values for Kusch and Hessel’s spectroscopic constant). With minor corrections (the corrected potential is shown in Table 1), these discrepancies were reduced to 0.03 cm − 1 for J =1 and J= 50, and 0.1 cm − 1 for J= 100. Taking into account these considerations, it might be expected that the calculated spectrum (using the above-mentioned electronic potentials) should be consistent with the experimental spectrum around 0.2–0.4 cm − 1 for J up to 100, discrepancy increasing for J-values above 100.
3. Calculation of radiative lifetimes To calculate the radiative lifetimes, we obtain the eigenvalues and eigenfunctions with the men1 tioned X1S+ g and B Pu electronic potentials. With
A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
Fig. 1. Representation of calculated Q lifetimes (t, s) and experimental (Q large dots, R–P medium dots) for Na2B1Pu state.
Fig. 2. Representation of calculated Q lifetimes (t, s) and previously calculated lifetimes (QSSW) for Na2B1Pu state.
the variation of electronic dipole moment transition by Stevens et al. and eigenvalues and eigenfunctions calculated in the present work, the radiative lifetimes are calculated for the above mentioned rovibrational levels of the B1Pu state. The calculated lifetimes are for Q transitions (DJ = 0) and for R – P transitions (DJ = 9 1). The difference between Q and R – P lifetimes for
2419
a J level is very small (only variation in the third nanosecond decimal). In radiative lifetime calculation, it is necessary to take into account the participation of the bound–free transition. This participation is practically null in the B1Pu l X1S+ transition. This is controlled by g the sum of the Frank–Condon factors. In Fig. 1, the calculated lifetimes (Q transitions) are represented for rovibrational levels of B1Pu state (6%= 0–33). In this figure, the experimental values of rovibrational levels are shown by dots (the lifetimes were also calculated for these levels in the DSSW paper). A line connects the experimental and calculated lifetimes. The experimental Q lifetimes are represented as large points to distinguish them from the R–P lifetimes (medium points). The experimental errors (0.08– 0.2 ns) are consistent with the discrepancies between experimental and calculated lifetimes. The comparison of present and previous calculated (DSSW) lifetimes is represented in Fig. 2 (the mean difference is 0.03 ns). Here, it might be appreciated the great extension of the presented calculations. In Table 2, a limited number of calculated lifetimes are collected. The calculated lifetimes for the Q transitions correspond to the P− component of the B1Pu state. For this component, no perturbations with the A1S+ u state are possible. Perturbation with the A1S+ u state is possible for the P+ component (lifetimes for R–P transitions) [7]. There is not experimental evidence for this perturbation. A similar situation was studied for H2 C1Pu and B1S+ u states [8]. The discrepancies for Q (P− component) lifetimes (experimental–calculated) are less that those for the R–P (P+ component) (Fig. 1). This is a possible indication of perturbation for the P+ component of the B1Pu state.
4. Conclusions A very extensive calculation of lifetimes for the B1Pu − X1S+ g transition is presented. The calculated lifetimes in the present work are in agreement with the previous experimental and calculated lifetimes (DSSW). Very accurate RKR
J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
6
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
6.96E−09 6.97E−09 6.99E−09 7.01E−09 7.02E−09 7.04E−09 7.05E−09 7.07E−09 7.08E−09 7.10E−09 7.11E−09 7.13E−09 7.14E−09 7.16E−09 7.17E−09 7.18E−09 7.20E−09 7.21E−09 7.23E−09 7.24E−09 7.25E−09 7.27E−09 7.29E−09 7.30E−09 7.32E−09 7.34E−09 7.36E−09 7.39E−09 7.41E−09 7.44E−09 7.47E−09 7.50E−09 7.53E−09 7.58E−09
t 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
J
Table 2 Selected lifetimes from Fig. 1
6.96E−09 6.98E−09 6.99E−09 7.01E−09 7.02E−09 7.04E−09 7.06E−09 7.07E−09 7.09E−09 7.1E−09 7.12E−09 7.13E−09 7.14E−09 7.16E−09 7.17E−09 7.19E−09 7.2E−09 7.21E−09 7.23E−09 7.24E−09 7.26E−09 7.27E−09 7.29E−09 7.3E−09 7.32E−09 7.34E−09 7.37E−09 7.39E−09 7.42E−09 7.44E−09 7.47E−09 7.5E−09 7.54E−09 7.58E−09
t 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
J 6.98E−09 6.99E−09 7.01E−09 7.02E−09 7.04E−09 7.06E−09 7.07E−09 7.09E−09 7.1E−09 7.12E−09 7.13E−09 7.14E−09 7.16E−09 7.17E−09 7.19E−09 7.2E−09 7.21E−09 7.23E−09 7.24E−09 7.26E−09 7.27E−09 7.29E−09 7.3E−09 7.32E−09 7.34E−09 7.36E−09 7.39E−09 7.41E−09 7.44E−09 7.47E−09 7.5E−09 7.53E−09 7.57E−09
t 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
J 7.03E−09 7.05E−09 7.06E−09 7.08E−09 7.09E−09 7.11E−09 7.12E−09 7.14E−09 7.15E−09 7.16E−09 7.18E−09 7.19E−09 7.21E−09 7.22E−09 7.23E−09 7.25E−09 7.26E−09 7.28E−09 7.29E−09 7.3E−09 7.32E−09 7.34E−09 7.36E−09 7.38E−09 7.4E−09 7.43E−09 7.45E−09 7.48E−09 7.51E−09 7.55E−09 7.6E−09
t 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120
J 7.24E−09 7.25E−09 7.26E−09 7.28E−09 7.29E−09 7.3E−09 7.31E−09 7.32E−09 7.34E−09 7.35E−09 7.36E−09 7.38E−09 7.39E−09 7.4E−09 7.42E−09 7.43E−09 7.45E−09 7.47E−09 7.49E−09 7.52E−09 7.56E−09 7.61E−09
t 200 200 200 200 200 200
J 7.65E−09 7.66E−09 7.67E−09 7.68E−09 7.69E−09 7.71E−09
t
210 210 210 210
J
7.71E−09 7.71E−09 7.72E−09 7.74E−09
t
2420 A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
A. Pardo et al. / Spectrochimica Acta Part A 56 (2000) 2417–2421
potentials are employed. In the B1Pu electronic potential, small corrections are introduced. For the Q transitions of the B1P− u component, perturbation with levels of A1S+ u state are not possible. However, a general perturbation with 1 + the A1S+ u state is possible for the B Pu component (R–P transitions, see Ref. [7]). In addition, for some levels (with quasi-resonant energy, equal J and parity), the lifetimes are 1 a mixture of unperturbed A1S+ u and B Pu lifetimes (see Refs. [7,8]).
Acknowledgements The authors gratefully acknowledge the support
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received from the DGICYT (Spain) (project No. PB96-0046) for this research.
References [1] W.T. Zemke, W.C. Stwalley, J. Chem. Phys. 100 (1994) 2661. [2] O. Babaky, K. Hussein, Can. J. Phys. 67 (1989) 912. [3] H. Richter, H. Kno¨ckel, E. Tiemann, Chem. Phys. 157 (1991) 217. [4] W.J. Stevens, M.M. Hessel, P.J. Bertoncini, A.C. Wahl, J. Chem. Phys. 66 (1977) 1477. [5] W. Demtro¨der, W. Stetzenbach, M. Stock, J. Witt, J. Mol. Spectrosc. 61 (1976) 382. [6] P. Kusch, M.M. Hessel, J. Chem. Phys. 68 (1978) 2591. [7] K. Dressler, L. Wolniewicz, J. Chem. Phys. 82 (1985) 4720. [8] A. Pardo, J. Mol. Spectrosc. 195 (1999) 68.