- Email: [email protected]
A study of the perturbations between the A1Σ+u and b3Πu states of Na2
Volume
126, number
6
CHEMICAL
A STUDY OF THE PERTURBATIONS OF Na,
PHYSICS
LETTERS
23 May 1986
BETWEEN THE A?$,+ AND b31t, STATES
Oliver C. MULLINS, Christopher R. MAHON and T.F. GALLAGHER Department Received
of Physrcs, University of Virginia, Charlottesvrlle,
23 January
1986; in final form 28 February
The interaction between the A’ZZ and b3Hou and, after an adjustable delay time, photoionizmg of both A and b state character. Thus the regions this technique we have investigated perturbations
VA 22901, USA
1986
states of Na, is explored by resonantly exciting A states them. For long delays signals arise only from states with where the interaction is important stand out clearly in of the A v’ = 3, 7 and 8 states by the b v’ = 10, 13 and
1. Introduction
Even weak interactions between two electronic molecular states become important when the electronic states of the same total angular momentum J and other constants of motion are nearly degenerate. This condition of near degeneracy is often fulfilled repetitively when two bound electronic potentials undergo an avoided crossing because each potential contains a series of vibrational states each with its own set of rotational states. One of the most obvious effects of the interaction is the perturbation of the regularity of the rotational structure in the observed emission or absorption bands. Not surprisingly, a common method of studying such perturbations is high-resolution spectroscopy which uncovers the small displacements of the energies due to the interaction of the two electronic states. Here we describe a method for the study of molecular perturbations which does not require the high spectral resolution required for measurements based only on energy but relies instead on the change in state wavefunctions due to perturbations. Any altered property can provide a useful signature. For example, the spin-orbit interaction between the A tB= and the b 311ustates of Na2 was first observed by exploring their magnetic properties [ 1,2]. Recently, the b 3llu state and the A-b interaction has been the subject of several high-resolution spectroscopic studies 0 009-2614/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
via A-X transitions significant fractions the spectrum. Using 14 states.
[3-81. Here, we study the A-b interaction in Na, by measuring the effects of perturbations on radiative lifetimes. Specifically, we have measured the interaction between the A u’ = 3 vibrational state with the b u’ = 10 state. Additionally, we obtain good agreement with previous work for perturbations in the A u’ = 7 and 8 vibrational states. The method we have used is pulsed tunable dye laser excitation of ground state molecules to the A or perturbed state followed after a time delay t by photoionization by an ultraviolet laser with detection of the product Na; ions. In general the wavefunction of a state which is a mixture of A and b states of specific J can be written as ti =C,$A +C2J/b
(1)
(neglecting the different 3IInu components) where $A and J/b are the nOWinteraCting A and b state wavefunctions and C, and C2 are numerical coefflcients with Cf t C’i = 1. The X state is a spin singlet and spin-forbidden transitions are weak so states are excited in proportion to CT, as long as the process is linear in the power of the first, tunable laser. No dependence of the photoionization on spin was observed, and it is, therefore, assumed to be independent of spin. This being the case, the only factor which governs the observed photoion signal is how many excited molecules are left at time t when the UV pulse arrives. This is determined by the initial production and lifetime of 501
Volume 126, number 6
CHEMICAL PHYSICS LETTERS
the state. The unperturbed A states have a lifetime ?A of = 12.4 ns while the b states have a much greater lifetime because there is no spin-conserving, dipoleallowed radiative decay. Therefore, the radiative deca rate of the state with the wavefunction eq. (1) is Y C1/rA. Combining this with the probability of excitation we find that the photoion signal Z for a specific intermediate state is given by Z=ZuCf exp(-C;r/rA).
(2)
I, is the strength of excitation of the unperturbed A
state and includes angular momentum factors, nuclear spin statistics and Boltzmann weighting. It is straightforward to show that the maximum value of Z occurs for Ci = ?A/t. For the longest delay we used, 65 ns, the maximum signal occurs for CT = 19% and a signal equal to half the maximum occurs for states with C’f = 4% and 50%. Generally, the 65 ns delay spectrum is dominated by states which are mostly triplet in character. The signal which results at long delay times results from excitation to the A state part of the wavefunction followed by a long radiative lifetime due to the b state part of the wavefunction. The method is thus sensitive to both the A and b parts of the wavefunction. This approach shares with all time-delayed detection approaches the fact that very high spectral resolution is not required. In addition, ionization rather than fluorescence detection of the long-lived states is preferable. The triplet fluorescence is dispersed in both time and wavelength and detection efficiency is reduced due to the small solid angle subtended by a detector while the photoions are all made in 5 ns and are all easily collected in a time only slightly longer than 5 ns.
2. Experimental method The experiments were performed using a supersonic beam of sodium with the sodium oven temperature maintained at =600-650°C depending upon the particular experiment. A separate nozzle heater was employed to prevent clogging of the 0.5 mm nozzle orifice. The collimated sodium beam was intersected by the two laser beams. The second harmonic of a NdYAG laser was used to pump a Littman-type dye laser (bandwidth ti.5 GHz) which excited the A-X tran502
23 May 1986
sition. The third harmonic of the Nd-YAG laser, delayed using various path lengths, was used to photoionize the remaining excited state molecules. The pressure at the laser-molecular beam interaction region was < 10m4 Torr so collisional processes are unimportant in our experiments. The interaction region was located between a plate and a grid which were biased to produce a field of MOO V/cm thereby allowing collection of the Naz photoions. The ions were detected by a Venetian blind particle detector and the resulting signal was collected by a gated integrator, averaged, and recorded on an X-Y plotter. The frequency of the tunable laser was monitored using the optogalvanic signal from a hollow cathode, argon discharge lamp and by the transmission of the laser beam through an etalon (FSR = 20.0 GHz).
3. Experimental observations To locate perturbations coarse spectral scans are quite sufficient. As an example, in fig. 1 we show scans of the first laser wavelength over the range from 6760 to 6330 A. Fig. la, taken with no delay before the second laser pulse, is a simple excitation scan showing the A-X vibrational bands. In fig. lb, taken with a delay of 65 ns before the arrival of the second laser pulse, the perturbed regions where the wavefunctions are mixtures of substantial parts of both A and b states stand out quite clearly. (A state character in the range of r*4-50%.) Pure b states are never excited and pure A states do not live long enough to be photoionized. Strong perturbations are evident for the A state vibrational quantum number u’ = 3,6,7,8. Note the occurrence of the same perturbations in the (u’, u”) band (3,O) as well as the (3,1) hot band; higher resolution scans show this more clearly. The perturbations in the u’ = 3 and 8 states are found to be near the band head and thus of low J (the unperturbed A-X band heads occur at .I = 2) while the perturbations in the u’ = 6 and 7 states occur away from the band head and thus at larger J values. The supersonic expansion of our beam produces a rotational temperature of ~150 K, giving a population maximum at J = 18. Thus, even strong perturbations which occur for J > 45 will not be readily visible in our experiment. Including this J restriction, the coarse survey of fig. 1 agrees with ex-
Volume z 26, number 6
~0:
+e-+
CZiE&WAL PHYSfCS LETTERS
No,
A(
23 Hay 1986
No, XIV”)
(Cl Smuloted Specfrum for No Oeray
(d) S~mulatectSpectrum for 65ns Delay
Fig. 1, survey A-X ex&tation spectrum with ~bs~~~~t ~botojQ~~0~. fn (a] the photojon~a~o~ occtirs immediatejy after excitation while in (b) the photoionizatian is dekyed by 65 ns after A state excitation. Perturbed rq#ms which consist of mixed A-b states dominate (b). As with all figures here the vertical scale is expanded for the longer delay times.
The coarse spectrumof fig 1 shows that the v’ = 3,7 and 8 states merit closer inspection. Fig. 2a shows the u’ = 7 band of the A state ; the repetitious pattern of peak heights and spacings every four lines is claarly perturbed in certain regions, the perturbations being due to the U’= 13 b %iQu state. This repetitious pattern which also occurs in Bgs. 3 and 4 is due to adjacent peaks being from the P and R branches and due to nuclear statistical effects, Symmetric nuclear spin states of the two identical nuclei must occur with oddS states of the X state while antisymmetric num
I
---.--“-l*--_I 15410
15430 ENERGY (cm-‘)
15450
Fig. 2. The Nag + e- + A@ = 7) + X(B = 0) spectrum for different pbotaior&Won delays in the redon where the A U’ = 7 states are mtiurbed by the b 3& ui = 13 states. At tie Ksp the lo~t~ns of tie P and R tram&ions for the ~ho~~x~~atio~ of the A r Z: and pertzzbed %au states are indicated. Three perturbed regions OGCWin the P and R branches which correspond to the three %lnu electronic states. (a) Zero time delay experimental spectrum. (b) 65 ns time delay exp&mental spectrum. Note that perturbed states dominate the 65 ns delay spectrum. (c> Simulation of the zero delay spectrum. fd) Simulation of the 65 ns deIay specWklm.
cfear spin states must occur with evead states of the X state. The A 1Zi-b 3115LU state interaction occurs in triplicate because for each J three b “II,, states
Volume126, number 6
CHEMICAL PHYSICS LETTERS
23 May 1986
Table 1 No;+e-$f-
b (u’)
A-b interaction energy (cm-‘)
3
10
0.81 f 0.05
7
13 14
1.33 i 0.05,1.33 f 0.02 a)
A (u’)
8 a)Fromref.
[8].
Alv’-3)a
No,
X(v”=Ol
1.34 2 0.05,1.34 b) b)Fromref.
[S].
exist corresponding to the three values of the projection G of the electronic angular momentum (here S2 = 0,l and 2). The three %I,, states become nearly degenerate with the A 12: states at slightly different values ofJ; 3110ubetweenJ= 30 and 31, 3111, between .J = 25 and 26, and 3112ubetween J = 20 and J = 2 1. The interaction of the b states with the A states is dominated by the G?= 0 part of the b state wavefunctions; aJ-dependent interaction mixes theb311 nu states and our state labels identify the component with the largest ma~itude. Not surprisingly , the range over J states of the perturbation is greatest for the 3110ustates, intermediate for 311I u states and least for 3112u states. Using the perturbation parameters listed in table 1 with the previously known spectroscopic constants [8,9] we have generated synthetic spectra to match figs. 2a and 2b, and these are shown in figs, 2c and 2d. The agreement is quite good, Close exa~nation of figs. 2b and 2d reveals an occasional significant discrepancy between theory and experiment which could not be reconciled by parameter adjustment, The simplifying assumptions of our model are apparently generally but not always applicable. In fig. 3 we show the 3-O bands for several delays of the second laser and clearly, the u’ = 3 state is also quite perturbed (due to the U’= 10 b 311ustate). Again, the perturbed regions in the zero delay spectrum of fig. 3a map into the regions of non-zero signal in the 65 ns delay spectrum of fig. 3d. In this case however only the 3110ustate is ever approximately degenerate with the A state, between J = 13 and 14. For allJ the 3111u and 3112ustates lie above the A states. Nevertheless the energeti~~y closest and therefore most perturbed states in both cases are the lower J states, and as a result we are able to see in fig. 3d the 311lu band head which occurs at J = 10 and consists of many closely spaced R branch transitions.
504
No,
c* - perturbed regmnsi
‘2:
(b)
20ns Delay
iC)
43n5 Delay
L
--.sDeio~~~~~ (d) 960
1
I
14980
15000
ENERGY
1
1502(
(cm-‘)
Fig, 3. The Nai + e + A@’ = 3) +X(6’ = 0) spectrum for different photoionization delays in the region where the A U’= 3 states are perturbed by the b 3~nu u’ = 10 states. At the top the location of the P and R transitions for photoionization of the A ’ Zi and the perturbed 3Hou states are indicated and (e) shows the corresponding energy levels at the region of maximum perturbation. The delay times are (a) 0 ns; (b) 20 ns; (c) 43 ns; and (d) 65 ns. Note the 3~ru band head in(d).
For II states of lowest J, G is a relatively good quantum number so the correspon~g 311ru and 3112u states do not interact with the A state. In fig. 4 we show simulated spectra corresponding to fig. 3, which give a satisfactory representation of the observed spectra.
Volume 126, number 6
Simulated
Spectra
for
CHEMICAL PHYSICS LETTERS
Na;+e--$
No,
A(v’=3l_y’Na,
X(v’=O
d
23 May 1986
( A 1Zi 1Hlb 3110U)which we have determined for the interaction of the A u’ = 3,7 and 8 states with the b u’ = 10, 13 and 14 states respectively. These values are obtained by an analysis of both the intensities and positions of the observed lines and are in good agreement with the previously obtained values
PA.
(b)
20x
Delay
(c)
43~
Delay
In conclusion this approach appears to be a straightforward way to easily identify perturbed regions and to obtain approximate values of the interaction constants with minimal spectral resolution. In conjunction with somewhat higher resolution and careful lifetime measurements using a continuously variable time delay this should prove to be a very powerful tool for the analysis of perturbed molecular spectra.
Acknowledgement
(d)
65~
Delay
II
1
Ii ,960
I
-A-bA
14980
ENERGY
It is a pleasure to acknowledge helpful conversation with R.P. Saxon. This work was supported by the National Science Foundation under grant PHY8419357.
,,la,i,J’L I15000
(cm-‘)
Fig. 4. Simulations of the Naz + e + A@’ = 3) + X(u” = 0) spectra for different photoionization delays. Compare with the experimental data shown in fig. 3.
We obtained the (8-O) spectra for different delay times and they resembled (3-O) spectra. Because the relative vibrational spacings for the A and b states are 5WA = &b, the J values of the perturbed regions repeat every fifth A vibrational state. The 3110u(u’ = 14) perturbation occurs between J = 8 and 9 and, as in fig. 3, the unresolved R transitions resulted in the largest peak in the 65 ns delay spectrum. Also, the 311lu band head, which occurs at a higher energy than the A-X band head, was visible. In table 1 we give values of the matrix elements
References [l] R.W. Wood and F.E. Hackett, Astrophys. J. 30 (1909) 399. [2] W.R. Fredrickson and CR. Stannard, Phys. Rev. 44 (1933) 632. [3] J.B. Atkinson, J. Becker and W. Demtiiider, Chem. Phys. Letters 87 (1982) 92. [4] J.B. Atkinson, J. Becker and W. Demtrijder, Chem. Phys. Letters 87 (1982) 128. [5] F. Engelke, H. Hage and C.D. Caldwell, Chem. Phys. 64 (1982) 221. [6] K. Shim&u and F. Shimizu, J. Chem. Phys. 78 (1983) 1126. (71 L. Li, S.F. Rice and R.W. Field, J. Mol. Spectry. 105 (1984) 344. [8] C. Effantin, 0. Babaky, K. Hussein, J. d’Incan and R.F. Barrow, J. Phys. B18 (1985) 4077. [9] P. Kusch and M.M.Hessel, J. Chem. Phys. 68 (1978) 2591.
505
126, number
6
CHEMICAL
A STUDY OF THE PERTURBATIONS OF Na,
PHYSICS
LETTERS
23 May 1986
BETWEEN THE A?$,+ AND b31t, STATES
Oliver C. MULLINS, Christopher R. MAHON and T.F. GALLAGHER Department Received
of Physrcs, University of Virginia, Charlottesvrlle,
23 January
1986; in final form 28 February
The interaction between the A’ZZ and b3Hou and, after an adjustable delay time, photoionizmg of both A and b state character. Thus the regions this technique we have investigated perturbations
VA 22901, USA
1986
states of Na, is explored by resonantly exciting A states them. For long delays signals arise only from states with where the interaction is important stand out clearly in of the A v’ = 3, 7 and 8 states by the b v’ = 10, 13 and
1. Introduction
Even weak interactions between two electronic molecular states become important when the electronic states of the same total angular momentum J and other constants of motion are nearly degenerate. This condition of near degeneracy is often fulfilled repetitively when two bound electronic potentials undergo an avoided crossing because each potential contains a series of vibrational states each with its own set of rotational states. One of the most obvious effects of the interaction is the perturbation of the regularity of the rotational structure in the observed emission or absorption bands. Not surprisingly, a common method of studying such perturbations is high-resolution spectroscopy which uncovers the small displacements of the energies due to the interaction of the two electronic states. Here we describe a method for the study of molecular perturbations which does not require the high spectral resolution required for measurements based only on energy but relies instead on the change in state wavefunctions due to perturbations. Any altered property can provide a useful signature. For example, the spin-orbit interaction between the A tB= and the b 311ustates of Na2 was first observed by exploring their magnetic properties [ 1,2]. Recently, the b 3llu state and the A-b interaction has been the subject of several high-resolution spectroscopic studies 0 009-2614/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
via A-X transitions significant fractions the spectrum. Using 14 states.
[3-81. Here, we study the A-b interaction in Na, by measuring the effects of perturbations on radiative lifetimes. Specifically, we have measured the interaction between the A u’ = 3 vibrational state with the b u’ = 10 state. Additionally, we obtain good agreement with previous work for perturbations in the A u’ = 7 and 8 vibrational states. The method we have used is pulsed tunable dye laser excitation of ground state molecules to the A or perturbed state followed after a time delay t by photoionization by an ultraviolet laser with detection of the product Na; ions. In general the wavefunction of a state which is a mixture of A and b states of specific J can be written as ti =C,$A +C2J/b
(1)
(neglecting the different 3IInu components) where $A and J/b are the nOWinteraCting A and b state wavefunctions and C, and C2 are numerical coefflcients with Cf t C’i = 1. The X state is a spin singlet and spin-forbidden transitions are weak so states are excited in proportion to CT, as long as the process is linear in the power of the first, tunable laser. No dependence of the photoionization on spin was observed, and it is, therefore, assumed to be independent of spin. This being the case, the only factor which governs the observed photoion signal is how many excited molecules are left at time t when the UV pulse arrives. This is determined by the initial production and lifetime of 501
Volume 126, number 6
CHEMICAL PHYSICS LETTERS
the state. The unperturbed A states have a lifetime ?A of = 12.4 ns while the b states have a much greater lifetime because there is no spin-conserving, dipoleallowed radiative decay. Therefore, the radiative deca rate of the state with the wavefunction eq. (1) is Y C1/rA. Combining this with the probability of excitation we find that the photoion signal Z for a specific intermediate state is given by Z=ZuCf exp(-C;r/rA).
(2)
I, is the strength of excitation of the unperturbed A
state and includes angular momentum factors, nuclear spin statistics and Boltzmann weighting. It is straightforward to show that the maximum value of Z occurs for Ci = ?A/t. For the longest delay we used, 65 ns, the maximum signal occurs for CT = 19% and a signal equal to half the maximum occurs for states with C’f = 4% and 50%. Generally, the 65 ns delay spectrum is dominated by states which are mostly triplet in character. The signal which results at long delay times results from excitation to the A state part of the wavefunction followed by a long radiative lifetime due to the b state part of the wavefunction. The method is thus sensitive to both the A and b parts of the wavefunction. This approach shares with all time-delayed detection approaches the fact that very high spectral resolution is not required. In addition, ionization rather than fluorescence detection of the long-lived states is preferable. The triplet fluorescence is dispersed in both time and wavelength and detection efficiency is reduced due to the small solid angle subtended by a detector while the photoions are all made in 5 ns and are all easily collected in a time only slightly longer than 5 ns.
2. Experimental method The experiments were performed using a supersonic beam of sodium with the sodium oven temperature maintained at =600-650°C depending upon the particular experiment. A separate nozzle heater was employed to prevent clogging of the 0.5 mm nozzle orifice. The collimated sodium beam was intersected by the two laser beams. The second harmonic of a NdYAG laser was used to pump a Littman-type dye laser (bandwidth ti.5 GHz) which excited the A-X tran502
23 May 1986
sition. The third harmonic of the Nd-YAG laser, delayed using various path lengths, was used to photoionize the remaining excited state molecules. The pressure at the laser-molecular beam interaction region was < 10m4 Torr so collisional processes are unimportant in our experiments. The interaction region was located between a plate and a grid which were biased to produce a field of MOO V/cm thereby allowing collection of the Naz photoions. The ions were detected by a Venetian blind particle detector and the resulting signal was collected by a gated integrator, averaged, and recorded on an X-Y plotter. The frequency of the tunable laser was monitored using the optogalvanic signal from a hollow cathode, argon discharge lamp and by the transmission of the laser beam through an etalon (FSR = 20.0 GHz).
3. Experimental observations To locate perturbations coarse spectral scans are quite sufficient. As an example, in fig. 1 we show scans of the first laser wavelength over the range from 6760 to 6330 A. Fig. la, taken with no delay before the second laser pulse, is a simple excitation scan showing the A-X vibrational bands. In fig. lb, taken with a delay of 65 ns before the arrival of the second laser pulse, the perturbed regions where the wavefunctions are mixtures of substantial parts of both A and b states stand out quite clearly. (A state character in the range of r*4-50%.) Pure b states are never excited and pure A states do not live long enough to be photoionized. Strong perturbations are evident for the A state vibrational quantum number u’ = 3,6,7,8. Note the occurrence of the same perturbations in the (u’, u”) band (3,O) as well as the (3,1) hot band; higher resolution scans show this more clearly. The perturbations in the u’ = 3 and 8 states are found to be near the band head and thus of low J (the unperturbed A-X band heads occur at .I = 2) while the perturbations in the u’ = 6 and 7 states occur away from the band head and thus at larger J values. The supersonic expansion of our beam produces a rotational temperature of ~150 K, giving a population maximum at J = 18. Thus, even strong perturbations which occur for J > 45 will not be readily visible in our experiment. Including this J restriction, the coarse survey of fig. 1 agrees with ex-
Volume z 26, number 6
~0:
+e-+
CZiE&WAL PHYSfCS LETTERS
No,
A(
23 Hay 1986
No, XIV”)
(Cl Smuloted Specfrum for No Oeray
(d) S~mulatectSpectrum for 65ns Delay
Fig. 1, survey A-X ex&tation spectrum with ~bs~~~~t ~botojQ~~0~. fn (a] the photojon~a~o~ occtirs immediatejy after excitation while in (b) the photoionizatian is dekyed by 65 ns after A state excitation. Perturbed rq#ms which consist of mixed A-b states dominate (b). As with all figures here the vertical scale is expanded for the longer delay times.
The coarse spectrumof fig 1 shows that the v’ = 3,7 and 8 states merit closer inspection. Fig. 2a shows the u’ = 7 band of the A state ; the repetitious pattern of peak heights and spacings every four lines is claarly perturbed in certain regions, the perturbations being due to the U’= 13 b %iQu state. This repetitious pattern which also occurs in Bgs. 3 and 4 is due to adjacent peaks being from the P and R branches and due to nuclear statistical effects, Symmetric nuclear spin states of the two identical nuclei must occur with oddS states of the X state while antisymmetric num
I
---.--“-l*--_I 15410
15430 ENERGY (cm-‘)
15450
Fig. 2. The Nag + e- + A@ = 7) + X(B = 0) spectrum for different pbotaior&Won delays in the redon where the A U’ = 7 states are mtiurbed by the b 3& ui = 13 states. At tie Ksp the lo~t~ns of tie P and R tram&ions for the ~ho~~x~~atio~ of the A r Z: and pertzzbed %au states are indicated. Three perturbed regions OGCWin the P and R branches which correspond to the three %lnu electronic states. (a) Zero time delay experimental spectrum. (b) 65 ns time delay exp&mental spectrum. Note that perturbed states dominate the 65 ns delay spectrum. (c> Simulation of the zero delay spectrum. fd) Simulation of the 65 ns deIay specWklm.
cfear spin states must occur with evead states of the X state. The A 1Zi-b 3115LU state interaction occurs in triplicate because for each J three b “II,, states
Volume126, number 6
CHEMICAL PHYSICS LETTERS
23 May 1986
Table 1 No;+e-$f-
b (u’)
A-b interaction energy (cm-‘)
3
10
0.81 f 0.05
7
13 14
1.33 i 0.05,1.33 f 0.02 a)
A (u’)
8 a)Fromref.
[8].
Alv’-3)a
No,
X(v”=Ol
1.34 2 0.05,1.34 b) b)Fromref.
[S].
exist corresponding to the three values of the projection G of the electronic angular momentum (here S2 = 0,l and 2). The three %I,, states become nearly degenerate with the A 12: states at slightly different values ofJ; 3110ubetweenJ= 30 and 31, 3111, between .J = 25 and 26, and 3112ubetween J = 20 and J = 2 1. The interaction of the b states with the A states is dominated by the G?= 0 part of the b state wavefunctions; aJ-dependent interaction mixes theb311 nu states and our state labels identify the component with the largest ma~itude. Not surprisingly , the range over J states of the perturbation is greatest for the 3110ustates, intermediate for 311I u states and least for 3112u states. Using the perturbation parameters listed in table 1 with the previously known spectroscopic constants [8,9] we have generated synthetic spectra to match figs. 2a and 2b, and these are shown in figs, 2c and 2d. The agreement is quite good, Close exa~nation of figs. 2b and 2d reveals an occasional significant discrepancy between theory and experiment which could not be reconciled by parameter adjustment, The simplifying assumptions of our model are apparently generally but not always applicable. In fig. 3 we show the 3-O bands for several delays of the second laser and clearly, the u’ = 3 state is also quite perturbed (due to the U’= 10 b 311ustate). Again, the perturbed regions in the zero delay spectrum of fig. 3a map into the regions of non-zero signal in the 65 ns delay spectrum of fig. 3d. In this case however only the 3110ustate is ever approximately degenerate with the A state, between J = 13 and 14. For allJ the 3111u and 3112ustates lie above the A states. Nevertheless the energeti~~y closest and therefore most perturbed states in both cases are the lower J states, and as a result we are able to see in fig. 3d the 311lu band head which occurs at J = 10 and consists of many closely spaced R branch transitions.
504
No,
c* - perturbed regmnsi
‘2:
(b)
20ns Delay
iC)
43n5 Delay
L
--.sDeio~~~~~ (d) 960
1
I
14980
15000
ENERGY
1
1502(
(cm-‘)
Fig, 3. The Nai + e + A@’ = 3) +X(6’ = 0) spectrum for different photoionization delays in the region where the A U’= 3 states are perturbed by the b 3~nu u’ = 10 states. At the top the location of the P and R transitions for photoionization of the A ’ Zi and the perturbed 3Hou states are indicated and (e) shows the corresponding energy levels at the region of maximum perturbation. The delay times are (a) 0 ns; (b) 20 ns; (c) 43 ns; and (d) 65 ns. Note the 3~ru band head in(d).
For II states of lowest J, G is a relatively good quantum number so the correspon~g 311ru and 3112u states do not interact with the A state. In fig. 4 we show simulated spectra corresponding to fig. 3, which give a satisfactory representation of the observed spectra.
Volume 126, number 6
Simulated
Spectra
for
CHEMICAL PHYSICS LETTERS
Na;+e--$
No,
A(v’=3l_y’Na,
X(v’=O
d
23 May 1986
( A 1Zi 1Hlb 3110U)which we have determined for the interaction of the A u’ = 3,7 and 8 states with the b u’ = 10, 13 and 14 states respectively. These values are obtained by an analysis of both the intensities and positions of the observed lines and are in good agreement with the previously obtained values
PA.
(b)
20x
Delay
(c)
43~
Delay
In conclusion this approach appears to be a straightforward way to easily identify perturbed regions and to obtain approximate values of the interaction constants with minimal spectral resolution. In conjunction with somewhat higher resolution and careful lifetime measurements using a continuously variable time delay this should prove to be a very powerful tool for the analysis of perturbed molecular spectra.
Acknowledgement
(d)
65~
Delay
II
1
Ii ,960
I
-A-bA
14980
ENERGY
It is a pleasure to acknowledge helpful conversation with R.P. Saxon. This work was supported by the National Science Foundation under grant PHY8419357.
,,la,i,J’L I15000
(cm-‘)
Fig. 4. Simulations of the Naz + e + A@’ = 3) + X(u” = 0) spectra for different photoionization delays. Compare with the experimental data shown in fig. 3.
We obtained the (8-O) spectra for different delay times and they resembled (3-O) spectra. Because the relative vibrational spacings for the A and b states are 5WA = &b, the J values of the perturbed regions repeat every fifth A vibrational state. The 3110u(u’ = 14) perturbation occurs between J = 8 and 9 and, as in fig. 3, the unresolved R transitions resulted in the largest peak in the 65 ns delay spectrum. Also, the 311lu band head, which occurs at a higher energy than the A-X band head, was visible. In table 1 we give values of the matrix elements
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