- Email: [email protected]
Laser-reduced fluorescence detection of carbon monoxide npσ (n = 5–8) triplet Rydberg states
26 May 1995
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 238 (1995) 31-36
Laser-reduced fluorescence detection of carbon monoxide np~ ( n = 5-8) triplet Rydberg states A. Mellinger, C.R. Vidal Max-Planck-lnstitut fiir Extraterrestrische Physik, Giessenbachstraje, D-85740 Garching, Germany Received 9 February 1995; in final form 23 March 1995
Abstract Members of the npa 3X+ (u = 0) Rydberg series of the CO molecule in the range n = 5-8 have been detected and rotationally analysed using a three-step excitation scheme via a perturbed valence ‘doorway’ state. Starting from IZ= 6, luncoupling becomes evident. Molecular constants for a p-complex Hamiltonian have been obtained. Strong predissociation, growing with II, was found for all observed members of the series, The N-dependence of the linewidths is explained by the combined effects of l-uncoupling and a homogeneous perturbation of the np?~ ‘P+ states.
1. Introduction
npa (n = 5-8) triplet Rydberg series.
The CO molecule has long been the subject of intensive spectroscopic investigation, partly due to its importance in astrophysics [ 1,2]. Important work on
2. Experiment
absorption cross-sections in the vacuum ultraviolet (VW) and predissociation rates has been published in the last few years using conventional absorption spectroscopy [ 3,4], XUV laser spectroscopy [ 51 and multiphoton excitation [ 61. With the advance of laser techniques, a detailed analysis of high-lying Rydberg states has become feasible. Using ionization spectroscopy preceded by a three-step excitation scheme, Ebata et al. [7,8] have performed a detailed study of singlet Rydberg states in the range n = 4-10. From an experimental viewpoint, triplet states present the additional difficulty that transitions from the ground state are spin-forbidden. However, a number of triplet valence states strongly perturbed by the A ‘II state provide suitable ‘doorway’ levels which can be populated via an intercombination transition in the VW [ 91. In the present work, we have thus obtained results on the
The present pumping scheme (Fig. 1) is an extension of the two-step excitation scheme described in an earlier paper [lo]. The X’Z+ + af38+ (O-14) intercombination transition is pumped with the output of a tunable, coherent VW source [ 111. In a second step, the 3p7r c311 (u = 0) Rydberg state is pumped with the 0.5 mJ output of a Lambda Physik FL 1000 dye laser operating at 462 nm. Using suitable combinations of VW and visible lines, individual rotational levels of either parity in any one of the three c311 fine structure components can be populated. A Lambda Physik FL 2000 dye laser operating with various dyes between 480 and 750 nm at pulse energies of up to 5 m.I finally reaches the high-lying triplet Rydberg states under investigation. The fluorescence of the c 311 state into the a 311 state occurring around 240 nm is monitored with an EMR 541-F-05 photo-
0009-2614/95/$09.50 @ 1995 Elsevier Science B.V. All tights reserved SSDIOOO9-2614(95)00395-9
32
A. Mellinger, C.R. Vi&l/
Chemical Physics Letters 238 (1995) 31-36
ionization limit 110000
Rydberg states
100000
j_
60000 14950
15000
15050 wavenumber
15100
15150
[cm-‘]
Fig.
0-I
-
x1x:’
Fig. 1. Three-step excitation scheme and detection by laser-reduced fluorescence from the c 3rl state.
multiplier. An Acton Research 230-B interference filter reduces stray light from the visible lasers. Transitions from c311 into other Rydberg states result in pronounced dips in the fluorescence signal from the c 311 state. For wavelength calibration, the absorption spectrum of iodine [ 121 is recorded simultaneously. The npa states were detected in a series of mediumresolution (6~ = 0.2 cm-‘) scans with the FL 2000 laser. Individual line positions were then recorded by scanning an intracavity Ctalon resulting in an improved resolution of 0.04 cm-‘. Each scan typically covers a region of 4 cm-‘.
3. Results and discussion The spectra show a number of dips which could be identified as 3C+ states on the basis of the selection rules for dipole transitions and the number of experimentally observed lines [ lo]. By comparing their quantum defects with those of known singlet states [ 7,8], the lines were identified as members of the npc+ 32,+ Rydberg series. Fig. 2 shows a typical medium-resolution spectrum in the 5~~7 energy region. The results from the high-resolution scans for the 5p(r and 6pa states have been compiled into the symbolic spectra of Fig. 3, where the observed lines are represented by Lorentzian profiles of the measured width and depth. This allows both a compact plot of
2. LRF spectrum in the energy region of the 5po 3X+ state. The intermediate level was c 311 (v = 0, J = 2, F3, e parity). The extra line observed is marked with a single asterisk. Also shown are three weak lines (labelled with two asterisks) which may belong to the 5pr 3E+ state.
the measured lines and an easy visualization of the linewidths, which have been expanded with respect to the energy scale. Although transitions between p Rydberg states are usually forbidden by the Al = f 1 selection rule for the angular momentum of the Rydberg electron, the 3pr c 311 state has, like other low-lying Rydberg states [ 81, sufficient d character to allow transitions to npn levels. With the potential curves of the npa Rydberg states being similar to that of the c311 intermediate state, only transitions with Au = 0 could be observed. Except for the lowest J levels, the Honl-London factors [ 131 strongly favour transitions with AJ = AN, as the c 311 state rapidly assumes Hund’s case (b) character with increasing J [ 141. Since no triplet fine structure splitting was observed within the experimental energy resolution, the Rydberg levels could be treated in the same way as singlet states, with N instead of J as the rotational quantum number. The energy levels of the c311 intermediate state were calculated using the effective molecular constants of Dabrowski et al. [ 141. As they do not give the absolute electronic and vibrational energy 7&c, the wavelengths of the c 311 --f a 311 (O-O) band recorded by Rytel and Rytel [ 151 together with the a311 molecular constants [ 161 were used to calculate a value of 92077.5(2) cm-’ for T,+ The 5pa energy levels could be accurately described by the simple relation E = T + BN( N + 1) , whereas a
A. Mellinger, C.R. Vi&d/Chemical
Physics Letters 238 (1995) 31-36
33
H= (a)
J4FF3 J4FFl J4EF2
(
P,,(4)
----VGA P&3)
J3FF3 P,,(3)
JSFFI
P,,d
d,,fW I vya
YY
R,,(3)
J3EF3
-A.
Pz*(3)
J3EF2 J2FFl J2EF3 J2EF2
J
0)
Ei 7-l
107040
107060
v J3EF3
107100
107120
” Pz(3)
P,,(2) 7
T R,,(2) y
intensity Q,,(2)
J2EF3 J2EFP
107060
-
JBEFP J2FFl
P&) v
scale
-&
1 I 0
-
v I
109100
2[N(N+
T+BIN(N+I)+zl
P,,(4)
109120
109140
109160
109160
Energy [cm-‘]
Fig. 3. Symbolic spectra of the 5p(r (a) and 6p(~ (b) states. Each line is represented by a Lotentzian profile of the measured width and depth. The linewidths have been expanded by a factor of 3 with respect to the abscissa scale. Solid and open lines denote upper levels of + and - parity, respectively. The rotational levels of the c311 intermediate state am indicated by labels of the form JjpFi, where j is the rotational quantum number, p the parity (either e or f) and i the triplet fine structure component Ft (i = 1, 2 or 3). as shown in Fig. 2 of Ref. [ 141. The assigned transitions are shown above the respective lines, with the indices denoting the fine structure component of the upper and lower level, respectively. Lines in frame (a) corresponding to the extra 3P+ state are labelled in italics.
strong contribution proportional to [ N( N + 1) ] ’ was observed for the higher npa states. This is the result of l-uncoupling, a mixing of 3X+ and 311+levels sharing a common angular momentum 1 = 1 of the Rydberg electron. Although the np7r levels were not observed, their positions could be calculated by fitting the npa levels to the p-complex Hamiltonian [ 171
2[N(N
+
I)]“*
I)]‘/2
T+C+BN(N+I) T+C+BN(N+
1) (1)
where the basis functions are [pa), ]p&) and ]pr-), and C is essentially the difference between the electronic energies of the unperturbed prr and pa states. Table 1 lists the obtained molecular constants, and Table 2 shows the observed rotational levels. For n > 6, additional perturbations, not treated in the framework of a p-complex, manifest themselves in rotational constants B significantly greater than the value of B+ = 1.977 cm-’ [ 181 for the CO+ ion. The 5pc~ state deserves special attention, since a second 38+ state was observed only 8.2 cm-’ above 5pa, as can be seen in Fig. 2, where the corresponding line is marked by a single asterisk, and in Fig. 3, where the extra lines are labelled in italics. Fitting the matrix elements of two interacting 38 states, as given by Kovacs [ 131, to the measured energy levels yielded no statistically significant interaction matrix element. The rotational constant of B = 1.8796( 8)cm-’ indicates that the additional state may also be a Rydberg state; however, no coincidence between the 3Z+ state and the extrapolated energies of the known triplet Rydberg states was found. The origin of this state has therefore yet to be determined. In addition, three weak and broad lines were found between 15060 and 15090 cm-t and were initially attributed to the 5pn. 3Z+ state. However, a simultaneous least-squares fit of both the 5pa and the weak lines to the p-complex Hamiltonian of Rq. ( 1) resulted in increased differences between observed and calculated energy levels for the 5pu state. Due to the low signal-to-noise ratio, the 5p7r line positions could be determined only with an accuracy of f0.5 cm-‘, but, again, the error resulting from the fit is about 3 times larger than the experimental uncertainty. From the electronic and vibrational energies T, quantum defects S,, were calculated using the usual relation
(2) a mass-reduced Rydberg constant of R = 109735 cm-’ and an ionization energy of Ei,” = 113029
34
A. Mellinger, C.R. Viaid / Chemical Physics Letters 238 (I 995) 31-36
Table 1 Rotational molecular constants (in cm-‘) for the npc~ (n =5-8) triplet Rydbetg states (u = 0). For a definition of T, C and B, see Fq. ( 1). The numbers in parentheses give the 2u uncertainties in units of the last digit. The last column gives the standard error of the differences between observed and calculated line positions. The additional %+ state near 5pu is marked by a single asterisk State
Ta
c
B
w
5PC *
107029.17(l) b 107037.41( l)b 109098.59(5) 110253.81(6) 110964.13( 10)
_c _c 91.88( 1829) 48.43(335) 33.58(412)
1.8954(8) 1.8796(8) 1.997(36) 2.057(22) 2.081(64)
0.018 0.018 0.042 0.048 0.042
6PU 7PU 8po
a The error is that of the least-squares fit only. Due to the uncertainty of the c 311 intermediate level, the total error is about 0.2 cm-t. b Even without a statistically significant C, energy levels are still defined by E = T + B[ N( N + 1) + 21 to achieve compatibility with the Hamiltonian of Eq. ( 1). c No statistically significant value obtained. Table 2 Energy levels of the npu states and differences between observed and calculated values in cm-t (o-c). The numbers represent averages of all observed lines into a given rotational level N. The column labelled with a single asterisk (*) gives the levels of the extra %,+ state; the levels in the column marked ** belong to the weak lines around 15070 cm-’ N
5pu
o-c
*
0 1 2 3 4 5 6
107032.950 107036.739 107044.334 107055.720 107070.868 107089.808 107112.574
-0.011 -0.013 0.001 0.015 -0.001 -0.015 0.006
107041.185 0.015 107044.933 0.004 107052.444 -0.004 107063.727 0.002 107078.755 -0.007 107097.554 -0.004 107120.132 0.019
a f parity.
o-c
**
6po
109102.603 109106.226 107162.1(5)a 109113.487 107172.6(5) b 109124.404 107187.9(5) a 109139.107 109157.335 109179.387
o-c
7PU
o-c
0.015 0.006 -0.006 -0.019 0.076 -0.011 -0.006
110257.949 0.022 110261.281 -0.008 110268.024 -0.060 110278.448 0.028 110292.343 -0.075 110310.192 0.009
8po
o-c
110971.321 -0.004 110977.625 0.030 110987.373 -0.008 111000.919 0.016
b e parity.
0.00
0.05
0.15
0.10
0.20
l/n*’
Fig. 4. EdlCn plot of the npu (0) and np?r (0) quantum defects versus effective quantum number n* = n - S. The additional 3Z+ state near 5pu is plotted as an open circle; the state connected with the weak lines around 15070 cm-’ is marked by an open square. The fitted lines have slopes of 0.365 and 0.352 and intercepts of 0.703 and 0.644 for the pa and PP levels, respectively. The value for 3pu was calculated from Ref. [lo].
cm-’ [ 181. When plotted versus l/n**, where n* = n - S,,, is the effective quantum number (Edlen plot, Fig. 4)) the quantum defects are described with good accuracy by a straight line of slope 0.365, which compares favourably with the value 0.318 obtained for the corresponding singlet levels [ 81. Similarly, the np?r quantum defects St,, calculated from T + C are described by a line of slope 0.352. The electronic state associated with the weak lines of Fig. 2 lies well below this line, which again casts doubt upon its interpretation as the 5p7r state. For all observed npc+ levels, the linewidth increases with the rotational quantum number N (Fig. 5). This can be explained assuming a homogeneous predissociation of the npr Rydberg states by the repulsive part of a 31T valence state potential curve. As a result of I-uncoupling, the npa levels then experience a heterogeneous perturbation. One likely candidate for the ho-
A. Mellinger, C.R. Vidal/ Chemical Physics Letters 238 (I 995) 31-36
35
in the process of diagonalizing the matrix of Eq. ( 1) and the experimental linewidths rp, = (27~~) -’ kpcTt, kpr and kp,, (or the corresponding linewidths r,, and r,,) can be determined via a least-squares fit. The results are listed in Table 3. Mixing coefficients of up to cz = 0.19 were found for the observed levels. While the values obtained for r,, are statistically insignificant except for n = 6, the np7r linewidths r,, are greater than 10 cm-‘, which is more than 50 times the linewidth of the dye laser output, even when operated without the intracavity &talon. The absence of the np7r lines in the spectra is thus explained by the large linewidths.
4. Conclusion
0123456
N Fig. 5. Linewidths of the observed transitions into the npa (n =5-8) triplet Rydbetg states. Squares, circles and triangles denote Ft, F2 and F3 levels, respectively. For N = 6-8, interpolating curves (dashed lines) were calculated from the deperturbed linewidths (Table 3) and the mixing coefficients c2 according to
Acknowledgement
Es. (3). Table 3 Deperturbed
linewidths
(in cm-‘)
of the npu and nprr states
6~
r, r,
kPfl ’ = c:(N)
8~
0.39(7) 29.0(24)
mogeneous perturber discovered k 311 state The predissociation states can be written dissociation rates k,,
0.07(9) 10.1(11)
= cl(N)
k,, + c;(N)
Ipa)
-0.1(3) 12.7(29)
kpm
(3)
mixing coefficients
+
c2(N)
IP~+)
9
We wish to thank Professor K. Dressler for stimulating discussions, X. Li for his experimental assistance and B. Steffes for his technical support. References
of the npn= states is the recently [ 10,191. rate kpd of the l-uncoupled npa in terms of the deperturbed preand k,, as
with the N-dependent c2( N) defined by IP~‘)
The npa (n = 5-8) triplet Rydberg series has been observed spectroscopically. Accurate molecular constants have been determined, showing substantial luncoupling for n > 6. The electronic nature of a 3Z+ state found close to the 5pa levels has yet to be determined. Investigation of the d and f triplet Rydberg series of carbon monoxide is currently in progress.
ct (N) and
(4)
together with the normalization condition c:(N) + cs( N) = 1. Using the mixing coefficients obtained
[ 11 E.F. van Dieshoek and J.H. Black, Astrophys. J. 334 (1988) 771. [2] D.C. Morton and L. Noreau, Astrophys. J. Suppl. Ser. 95 (1994) 301. [3] M. Eidelsbetg and E Rostas, A&on. Astrophys. 235 (1990) 412. [4] M. Eidelsberg, J.J. Benayoun, Y. Viala, F. Rostas, PL. Smith, K. Yoshino, G. Stark and C.A. Shettle, Astron. Astrophys. 265 (1992) 839. [ 51 K.S.E. Eikema, W. Hogervotst and W. Ubachs, Chem. Phys. 181 (1994) 217. [6] M. Drabbels, J. Heinze, J.J. ter Meulen and W.L. Meerts, J. Chem. Phys. 99 (1993) 5701. [7] T. Ebata, N. Hosoi and M. Ito, J. Chem. Phys. 97 (1992) 3920. [8] M. Komatsu, T. Bbata and N. Mikami, J. Chem. Phys. 99 (1993) 9350.
36
A. Mellinger,
C.R. Vi&d/Chemical
[ 91 P. Klopotek and CR. Vidal, Can. J. Phys. 62 (1984) 1426.
Physics Letters 238 (I 995) 31-36
[ 151 T. Rytel and M. Rytel, Act. Phys. Hung. 55 (1984) 69.
[lo] A. Mellinger and C.R. Vidal, J. Chem. Phys. 101 (1994)
[ 161 C. Effantin, E Michaud, E Roux, J. D’Incan and J. Verges,
104. [ I1 ] B. Steffes, X. Li, A. Mellinger and C.R. Vidal, Appl. Phys. B (1995), in press. [ 121 S. Gerstenkom and J. Cariou, Atlas du spectre d’absorption de la molecule d’iode, CNRS report ( 1978). [ 131 1. Kovacs, Rotational structure in the spectra of diatomic molecules (Adam Hilger, London, 1969). [ 141 1. Dabrowski, M. Vervloet and D.-C. Wang, Can. J. Phys. 65 (1987) 1171.
J. Mol. Spectry. 92 (1982) 349. 1171 J.W.C. Johns, Rotational structure in the Rydberg series of diatomic molecules, in: Molecular spectroscopy, Vol. 2 (Chemical Society, London, 1974). [ 181 K.P Huber and G. Herzberg, Molecular structure and dynamics, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [ 191 J. Baker and E Launay, J. Mol. Spectry. 165 (1994) 75.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 238 (1995) 31-36
Laser-reduced fluorescence detection of carbon monoxide np~ ( n = 5-8) triplet Rydberg states A. Mellinger, C.R. Vidal Max-Planck-lnstitut fiir Extraterrestrische Physik, Giessenbachstraje, D-85740 Garching, Germany Received 9 February 1995; in final form 23 March 1995
Abstract Members of the npa 3X+ (u = 0) Rydberg series of the CO molecule in the range n = 5-8 have been detected and rotationally analysed using a three-step excitation scheme via a perturbed valence ‘doorway’ state. Starting from IZ= 6, luncoupling becomes evident. Molecular constants for a p-complex Hamiltonian have been obtained. Strong predissociation, growing with II, was found for all observed members of the series, The N-dependence of the linewidths is explained by the combined effects of l-uncoupling and a homogeneous perturbation of the np?~ ‘P+ states.
1. Introduction
npa (n = 5-8) triplet Rydberg series.
The CO molecule has long been the subject of intensive spectroscopic investigation, partly due to its importance in astrophysics [ 1,2]. Important work on
2. Experiment
absorption cross-sections in the vacuum ultraviolet (VW) and predissociation rates has been published in the last few years using conventional absorption spectroscopy [ 3,4], XUV laser spectroscopy [ 51 and multiphoton excitation [ 61. With the advance of laser techniques, a detailed analysis of high-lying Rydberg states has become feasible. Using ionization spectroscopy preceded by a three-step excitation scheme, Ebata et al. [7,8] have performed a detailed study of singlet Rydberg states in the range n = 4-10. From an experimental viewpoint, triplet states present the additional difficulty that transitions from the ground state are spin-forbidden. However, a number of triplet valence states strongly perturbed by the A ‘II state provide suitable ‘doorway’ levels which can be populated via an intercombination transition in the VW [ 91. In the present work, we have thus obtained results on the
The present pumping scheme (Fig. 1) is an extension of the two-step excitation scheme described in an earlier paper [lo]. The X’Z+ + af38+ (O-14) intercombination transition is pumped with the output of a tunable, coherent VW source [ 111. In a second step, the 3p7r c311 (u = 0) Rydberg state is pumped with the 0.5 mJ output of a Lambda Physik FL 1000 dye laser operating at 462 nm. Using suitable combinations of VW and visible lines, individual rotational levels of either parity in any one of the three c311 fine structure components can be populated. A Lambda Physik FL 2000 dye laser operating with various dyes between 480 and 750 nm at pulse energies of up to 5 m.I finally reaches the high-lying triplet Rydberg states under investigation. The fluorescence of the c 311 state into the a 311 state occurring around 240 nm is monitored with an EMR 541-F-05 photo-
0009-2614/95/$09.50 @ 1995 Elsevier Science B.V. All tights reserved SSDIOOO9-2614(95)00395-9
32
A. Mellinger, C.R. Vi&l/
Chemical Physics Letters 238 (1995) 31-36
ionization limit 110000
Rydberg states
100000
j_
60000 14950
15000
15050 wavenumber
15100
15150
[cm-‘]
Fig.
0-I
-
x1x:’
Fig. 1. Three-step excitation scheme and detection by laser-reduced fluorescence from the c 3rl state.
multiplier. An Acton Research 230-B interference filter reduces stray light from the visible lasers. Transitions from c311 into other Rydberg states result in pronounced dips in the fluorescence signal from the c 311 state. For wavelength calibration, the absorption spectrum of iodine [ 121 is recorded simultaneously. The npa states were detected in a series of mediumresolution (6~ = 0.2 cm-‘) scans with the FL 2000 laser. Individual line positions were then recorded by scanning an intracavity Ctalon resulting in an improved resolution of 0.04 cm-‘. Each scan typically covers a region of 4 cm-‘.
3. Results and discussion The spectra show a number of dips which could be identified as 3C+ states on the basis of the selection rules for dipole transitions and the number of experimentally observed lines [ lo]. By comparing their quantum defects with those of known singlet states [ 7,8], the lines were identified as members of the npc+ 32,+ Rydberg series. Fig. 2 shows a typical medium-resolution spectrum in the 5~~7 energy region. The results from the high-resolution scans for the 5p(r and 6pa states have been compiled into the symbolic spectra of Fig. 3, where the observed lines are represented by Lorentzian profiles of the measured width and depth. This allows both a compact plot of
2. LRF spectrum in the energy region of the 5po 3X+ state. The intermediate level was c 311 (v = 0, J = 2, F3, e parity). The extra line observed is marked with a single asterisk. Also shown are three weak lines (labelled with two asterisks) which may belong to the 5pr 3E+ state.
the measured lines and an easy visualization of the linewidths, which have been expanded with respect to the energy scale. Although transitions between p Rydberg states are usually forbidden by the Al = f 1 selection rule for the angular momentum of the Rydberg electron, the 3pr c 311 state has, like other low-lying Rydberg states [ 81, sufficient d character to allow transitions to npn levels. With the potential curves of the npa Rydberg states being similar to that of the c311 intermediate state, only transitions with Au = 0 could be observed. Except for the lowest J levels, the Honl-London factors [ 131 strongly favour transitions with AJ = AN, as the c 311 state rapidly assumes Hund’s case (b) character with increasing J [ 141. Since no triplet fine structure splitting was observed within the experimental energy resolution, the Rydberg levels could be treated in the same way as singlet states, with N instead of J as the rotational quantum number. The energy levels of the c311 intermediate state were calculated using the effective molecular constants of Dabrowski et al. [ 141. As they do not give the absolute electronic and vibrational energy 7&c, the wavelengths of the c 311 --f a 311 (O-O) band recorded by Rytel and Rytel [ 151 together with the a311 molecular constants [ 161 were used to calculate a value of 92077.5(2) cm-’ for T,+ The 5pa energy levels could be accurately described by the simple relation E = T + BN( N + 1) , whereas a
A. Mellinger, C.R. Vi&d/Chemical
Physics Letters 238 (1995) 31-36
33
H= (a)
J4FF3 J4FFl J4EF2
(
P,,(4)
----VGA P&3)
J3FF3 P,,(3)
JSFFI
P,,d
d,,fW I vya
YY
R,,(3)
J3EF3
-A.
Pz*(3)
J3EF2 J2FFl J2EF3 J2EF2
J
0)
Ei 7-l
107040
107060
v J3EF3
107100
107120
” Pz(3)
P,,(2) 7
T R,,(2) y
intensity Q,,(2)
J2EF3 J2EFP
107060
-
JBEFP J2FFl
P&) v
scale
-&
1 I 0
-
v I
109100
2[N(N+
T+BIN(N+I)+zl
P,,(4)
109120
109140
109160
109160
Energy [cm-‘]
Fig. 3. Symbolic spectra of the 5p(r (a) and 6p(~ (b) states. Each line is represented by a Lotentzian profile of the measured width and depth. The linewidths have been expanded by a factor of 3 with respect to the abscissa scale. Solid and open lines denote upper levels of + and - parity, respectively. The rotational levels of the c311 intermediate state am indicated by labels of the form JjpFi, where j is the rotational quantum number, p the parity (either e or f) and i the triplet fine structure component Ft (i = 1, 2 or 3). as shown in Fig. 2 of Ref. [ 141. The assigned transitions are shown above the respective lines, with the indices denoting the fine structure component of the upper and lower level, respectively. Lines in frame (a) corresponding to the extra 3P+ state are labelled in italics.
strong contribution proportional to [ N( N + 1) ] ’ was observed for the higher npa states. This is the result of l-uncoupling, a mixing of 3X+ and 311+levels sharing a common angular momentum 1 = 1 of the Rydberg electron. Although the np7r levels were not observed, their positions could be calculated by fitting the npa levels to the p-complex Hamiltonian [ 171
2[N(N
+
I)]“*
I)]‘/2
T+C+BN(N+I) T+C+BN(N+
1) (1)
where the basis functions are [pa), ]p&) and ]pr-), and C is essentially the difference between the electronic energies of the unperturbed prr and pa states. Table 1 lists the obtained molecular constants, and Table 2 shows the observed rotational levels. For n > 6, additional perturbations, not treated in the framework of a p-complex, manifest themselves in rotational constants B significantly greater than the value of B+ = 1.977 cm-’ [ 181 for the CO+ ion. The 5pc~ state deserves special attention, since a second 38+ state was observed only 8.2 cm-’ above 5pa, as can be seen in Fig. 2, where the corresponding line is marked by a single asterisk, and in Fig. 3, where the extra lines are labelled in italics. Fitting the matrix elements of two interacting 38 states, as given by Kovacs [ 131, to the measured energy levels yielded no statistically significant interaction matrix element. The rotational constant of B = 1.8796( 8)cm-’ indicates that the additional state may also be a Rydberg state; however, no coincidence between the 3Z+ state and the extrapolated energies of the known triplet Rydberg states was found. The origin of this state has therefore yet to be determined. In addition, three weak and broad lines were found between 15060 and 15090 cm-t and were initially attributed to the 5pn. 3Z+ state. However, a simultaneous least-squares fit of both the 5pa and the weak lines to the p-complex Hamiltonian of Rq. ( 1) resulted in increased differences between observed and calculated energy levels for the 5pu state. Due to the low signal-to-noise ratio, the 5p7r line positions could be determined only with an accuracy of f0.5 cm-‘, but, again, the error resulting from the fit is about 3 times larger than the experimental uncertainty. From the electronic and vibrational energies T, quantum defects S,, were calculated using the usual relation
(2) a mass-reduced Rydberg constant of R = 109735 cm-’ and an ionization energy of Ei,” = 113029
34
A. Mellinger, C.R. Viaid / Chemical Physics Letters 238 (I 995) 31-36
Table 1 Rotational molecular constants (in cm-‘) for the npc~ (n =5-8) triplet Rydbetg states (u = 0). For a definition of T, C and B, see Fq. ( 1). The numbers in parentheses give the 2u uncertainties in units of the last digit. The last column gives the standard error of the differences between observed and calculated line positions. The additional %+ state near 5pu is marked by a single asterisk State
Ta
c
B
w
5PC *
107029.17(l) b 107037.41( l)b 109098.59(5) 110253.81(6) 110964.13( 10)
_c _c 91.88( 1829) 48.43(335) 33.58(412)
1.8954(8) 1.8796(8) 1.997(36) 2.057(22) 2.081(64)
0.018 0.018 0.042 0.048 0.042
6PU 7PU 8po
a The error is that of the least-squares fit only. Due to the uncertainty of the c 311 intermediate level, the total error is about 0.2 cm-t. b Even without a statistically significant C, energy levels are still defined by E = T + B[ N( N + 1) + 21 to achieve compatibility with the Hamiltonian of Eq. ( 1). c No statistically significant value obtained. Table 2 Energy levels of the npu states and differences between observed and calculated values in cm-t (o-c). The numbers represent averages of all observed lines into a given rotational level N. The column labelled with a single asterisk (*) gives the levels of the extra %,+ state; the levels in the column marked ** belong to the weak lines around 15070 cm-’ N
5pu
o-c
*
0 1 2 3 4 5 6
107032.950 107036.739 107044.334 107055.720 107070.868 107089.808 107112.574
-0.011 -0.013 0.001 0.015 -0.001 -0.015 0.006
107041.185 0.015 107044.933 0.004 107052.444 -0.004 107063.727 0.002 107078.755 -0.007 107097.554 -0.004 107120.132 0.019
a f parity.
o-c
**
6po
109102.603 109106.226 107162.1(5)a 109113.487 107172.6(5) b 109124.404 107187.9(5) a 109139.107 109157.335 109179.387
o-c
7PU
o-c
0.015 0.006 -0.006 -0.019 0.076 -0.011 -0.006
110257.949 0.022 110261.281 -0.008 110268.024 -0.060 110278.448 0.028 110292.343 -0.075 110310.192 0.009
8po
o-c
110971.321 -0.004 110977.625 0.030 110987.373 -0.008 111000.919 0.016
b e parity.
0.00
0.05
0.15
0.10
0.20
l/n*’
Fig. 4. EdlCn plot of the npu (0) and np?r (0) quantum defects versus effective quantum number n* = n - S. The additional 3Z+ state near 5pu is plotted as an open circle; the state connected with the weak lines around 15070 cm-’ is marked by an open square. The fitted lines have slopes of 0.365 and 0.352 and intercepts of 0.703 and 0.644 for the pa and PP levels, respectively. The value for 3pu was calculated from Ref. [lo].
cm-’ [ 181. When plotted versus l/n**, where n* = n - S,,, is the effective quantum number (Edlen plot, Fig. 4)) the quantum defects are described with good accuracy by a straight line of slope 0.365, which compares favourably with the value 0.318 obtained for the corresponding singlet levels [ 81. Similarly, the np?r quantum defects St,, calculated from T + C are described by a line of slope 0.352. The electronic state associated with the weak lines of Fig. 2 lies well below this line, which again casts doubt upon its interpretation as the 5p7r state. For all observed npc+ levels, the linewidth increases with the rotational quantum number N (Fig. 5). This can be explained assuming a homogeneous predissociation of the npr Rydberg states by the repulsive part of a 31T valence state potential curve. As a result of I-uncoupling, the npa levels then experience a heterogeneous perturbation. One likely candidate for the ho-
A. Mellinger, C.R. Vidal/ Chemical Physics Letters 238 (I 995) 31-36
35
in the process of diagonalizing the matrix of Eq. ( 1) and the experimental linewidths rp, = (27~~) -’ kpcTt, kpr and kp,, (or the corresponding linewidths r,, and r,,) can be determined via a least-squares fit. The results are listed in Table 3. Mixing coefficients of up to cz = 0.19 were found for the observed levels. While the values obtained for r,, are statistically insignificant except for n = 6, the np7r linewidths r,, are greater than 10 cm-‘, which is more than 50 times the linewidth of the dye laser output, even when operated without the intracavity &talon. The absence of the np7r lines in the spectra is thus explained by the large linewidths.
4. Conclusion
0123456
N Fig. 5. Linewidths of the observed transitions into the npa (n =5-8) triplet Rydbetg states. Squares, circles and triangles denote Ft, F2 and F3 levels, respectively. For N = 6-8, interpolating curves (dashed lines) were calculated from the deperturbed linewidths (Table 3) and the mixing coefficients c2 according to
Acknowledgement
Es. (3). Table 3 Deperturbed
linewidths
(in cm-‘)
of the npu and nprr states
6~
r, r,
kPfl ’ = c:(N)
8~
0.39(7) 29.0(24)
mogeneous perturber discovered k 311 state The predissociation states can be written dissociation rates k,,
0.07(9) 10.1(11)
= cl(N)
k,, + c;(N)
Ipa)
-0.1(3) 12.7(29)
kpm
(3)
mixing coefficients
+
c2(N)
IP~+)
9
We wish to thank Professor K. Dressler for stimulating discussions, X. Li for his experimental assistance and B. Steffes for his technical support. References
of the npn= states is the recently [ 10,191. rate kpd of the l-uncoupled npa in terms of the deperturbed preand k,, as
with the N-dependent c2( N) defined by IP~‘)
The npa (n = 5-8) triplet Rydberg series has been observed spectroscopically. Accurate molecular constants have been determined, showing substantial luncoupling for n > 6. The electronic nature of a 3Z+ state found close to the 5pa levels has yet to be determined. Investigation of the d and f triplet Rydberg series of carbon monoxide is currently in progress.
ct (N) and
(4)
together with the normalization condition c:(N) + cs( N) = 1. Using the mixing coefficients obtained
[ 11 E.F. van Dieshoek and J.H. Black, Astrophys. J. 334 (1988) 771. [2] D.C. Morton and L. Noreau, Astrophys. J. Suppl. Ser. 95 (1994) 301. [3] M. Eidelsbetg and E Rostas, A&on. Astrophys. 235 (1990) 412. [4] M. Eidelsberg, J.J. Benayoun, Y. Viala, F. Rostas, PL. Smith, K. Yoshino, G. Stark and C.A. Shettle, Astron. Astrophys. 265 (1992) 839. [ 51 K.S.E. Eikema, W. Hogervotst and W. Ubachs, Chem. Phys. 181 (1994) 217. [6] M. Drabbels, J. Heinze, J.J. ter Meulen and W.L. Meerts, J. Chem. Phys. 99 (1993) 5701. [7] T. Ebata, N. Hosoi and M. Ito, J. Chem. Phys. 97 (1992) 3920. [8] M. Komatsu, T. Bbata and N. Mikami, J. Chem. Phys. 99 (1993) 9350.
36
A. Mellinger,
C.R. Vi&d/Chemical
[ 91 P. Klopotek and CR. Vidal, Can. J. Phys. 62 (1984) 1426.
Physics Letters 238 (I 995) 31-36
[ 151 T. Rytel and M. Rytel, Act. Phys. Hung. 55 (1984) 69.
[lo] A. Mellinger and C.R. Vidal, J. Chem. Phys. 101 (1994)
[ 161 C. Effantin, E Michaud, E Roux, J. D’Incan and J. Verges,
104. [ I1 ] B. Steffes, X. Li, A. Mellinger and C.R. Vidal, Appl. Phys. B (1995), in press. [ 121 S. Gerstenkom and J. Cariou, Atlas du spectre d’absorption de la molecule d’iode, CNRS report ( 1978). [ 131 1. Kovacs, Rotational structure in the spectra of diatomic molecules (Adam Hilger, London, 1969). [ 141 1. Dabrowski, M. Vervloet and D.-C. Wang, Can. J. Phys. 65 (1987) 1171.
J. Mol. Spectry. 92 (1982) 349. 1171 J.W.C. Johns, Rotational structure in the Rydberg series of diatomic molecules, in: Molecular spectroscopy, Vol. 2 (Chemical Society, London, 1974). [ 181 K.P Huber and G. Herzberg, Molecular structure and dynamics, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [ 191 J. Baker and E Launay, J. Mol. Spectry. 165 (1994) 75.