Far infrared laser assignments and predictions for CO-stretching and CH3-rocking states of optically pumped 13CH3OH

INFRARED PHYSICS & TECHNOLOGY ELSEVIER Infrared Physics & Technology 37 (1996) 351-366 Far infrared laser assignments and predictions for CO-stretching and CH3-rocking states of optically pumped 13CH3OH Adriana Predoi a'b, R.M. Lees a'l, Li-Hong Xu c,2 ~Department of Physics, University of New Brunswick, Fredericton, N.B., Canada E3B 5A3 blnstitute of Optoelectronics, Bucharest, 76900 Romania CMolecular Physics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Received 2 May 1995 Abstract High-resolution Fourier transform studies of the CO-stretching and CH3-rocking bands of 13CH3OH have been applied to the assignment of far-infrared (FIR) laser transitions optically pumped by CO2 infrared (IR) lasers. The assignments are based on spectroscopic identification of the IR pump transitions at the reported offsets from the CO2 laser lines and agreement between the FIR laser wavenumbers and values calculated from IR/FIR combination-loop relations. Wavenumbers are also predicted for further potential new FIR laser lines in transition systems that could be pumped by CO2 and ~3CO2 cw and waveguide lasers. 1. Introduction The methanol molecule and its isotopic derivatives are of particular utility as far-infrared (FIR) laser sources due to the large number of coincidences between methanol infrared (IR) absorption lines and CO2 laser lines [1-3]. The complex torsion-rotation energy structure of methanol together with energy level shifts and mixings arising from interactions among the excited ITo whom correspondence should be addressed. 2On leave from the Department of Physical Sciences, University of New Brunswick, Saint John, N.B., Canada E2L 4L5. vibrational levels all contribute to a wide variety of FIR laser lines. This rich FIR emission can be further increased by the use of isotopic CO2 lasers to enlarge the number of available pumping lines. For the t3ch3oh species of methanol, over one hundred FIR laser lines optically pumped by both cw and waveguide CO2 lasers have been reported to date [2,3]. For each of the methanol isotopomers, the strong CO-stretching IR vibrational fundamental overlaps well with the CO2 laser spectrum and plays the major role in FIR laser pumping. Many of the FIR laser lines observed for IaCH3OH have been assigned via spectroscopic studies of the 01350-4495/95/$9.00 1995 Elsevier Science B.V. All rights reserved SSD1 1350-4495(95)00067-4

352 A, Predoi et al. / Infrared Physics & Technology 37 (1996) 351 366 CO-stretching band [4-16], and we have identified further such lines here. However, other vibrational bands also lie in the CO2 laser region and could account for a significant fraction of the remaining unidentified lasing transitions. In the present study, we have established through high-resolution Fourier transform (FTIR) spectroscopy that several reported FIR laser transition systems are pumped by IR absorptions of the in-plane CH 3- rocking fundamental [15], which overlaps the P- branch of the 9.4 # m CO2 laser band. The isotopic exchange of the ~2C in normal methanol by ~3C shifts the CO-stretching band sufficiently towards lower wavenumber to uncover the twin Q-branch peaks of the weak CH3-rocking fundamental and permit spectroscopic analysis of the rocking band, just as for the analogous case of CH318OH [17]. In this paper, we present new assignments of 13CH3OH FIR laser lines optically pumped in the CO-stretching and CH3-rocking IR fundamental bands. Supporting spectroscopic data are drawn primarily from our own FTIR study, supplemented by previous FIR and microwave results on the ground vibrational torsion-rotation spectrum [18-20] and earlier work in our group on the CO-stretching band [7,16,26]. These data confirm the assignments of most of the newlyidentified laser lines through combinationdifference relations for closed four-sided transition loops [21] in which the top is the observed FIR laser line in the excited vibrational state, the sides are IR absorptions or the CO2 pump line, and the bottom is a ground-state FIR or microwave transition. We have also identified IR absorptions in near coincidence with CO2 lines, and have compiled lists of predicted FIR laser lines which could be pumped by normal CO2 or isotopicallyenriched 13CO2 cw and waveguide lasers. The wavenumbers of these potential laser lines are predicted from combination loops to within the net spectroscopic uncertainty of approximately +0.001 cm-'. 2. Energy level labelling and notation The methanol energy levels are specified in this paper by the labelling (nzk, j)v, where n is the torsional quantum number, r takes values 1, 2 or 3 related to the torsional symmetry A, E~ or E2, J is the rotational angular momentum quantum number, K is the projection of J along the a-axis (the molecular near-symmetry axis) and v is the vibrational quantum number [22,23]. The correspondence between symmetry labels is given by (K+r)mod3=0, 1 and 2 for E~, A and E 2 torsional symmetry species, respectively, with the E or A symmetry being conserved in a transition between energy levels. The A levels are split into doublets for K 0 due to the coupling between I+K) and l-k) states induced by the offdiagonal (KIK + 2) asymmetry matrix elements of the rotational Hamiltonian. The specific K- doublet component is distinguished by adding a + or - superscript [22]. Since the parity of A -+ levels is -I-(-1) J n and the parity must change in a transition, the selection rules are ~ + for (AJ+An) odd and -~+ for (AJ+An) even. The parallel a-type IR transitions follow the selection rules: AJ = 0, _ 1; AK = 0; An = 0. For perpendicular b-type transitions, the selection rules are AJ = 0, _ 1; AK = _ 1; and no restriction on An. The CO-stretching band has a clear a-type parallel profile with a compact central Q-branch and P and R-branches of uniformly-spaced narrow J-multiplets extending to either side [16,24]. The weak in-plane CH3-rocking band is expected to be b-type from the perpendicular nature of the rocking motion, but instead has a predominantly parallel structure with widely spread subbranches, quite different from the CO-stretching band. This indicates significant mixing of parallel coordinates and their associated transition moments into the rocking normal mode as well as substantial changes in torsional parameters between ground and excited rocking states [15]. 3. Fourier transform spectra Fourier transform spectra of t3ch3oh were recorded from 900-1250cm -t at a resolution of 0.002cm ~ on the modified Bomem DA3.002 Fourier transform spectrometer in the laboratory of J.W.C. Johns at the National Research Council of Canada in Ottawa. One interferogram corn-

A. Predoi et al. / Infrared Physics & Technology 37 (1996) 351-366 353 prised 57 coadded scans taken at a relatively high pressure of 200mTorr in order to enhance the weak CH3-rocking band. Because much of the CO-stretching band was strongly saturated at that pressure, a second spectrum of 100 scans was run from 900-1100 cm ~ at 28 mtorr to improve the accuracy of the CO-stretch measurements [16]. In both cases, the 13CH3OH sample was used as supplied by MSD Isotopes in Montreal with quoted isotopic purity of 99 atom-% ~3C. The spectra were recorded at room temperature in 4 transits of an 0.5-m White cell for a total path length of 2.0m. A calibration factor was determined by matching our experimental FTIR wavenumbers for well-resolved FIR laser pump transitions to the reported frequency offsets of those pumps from the CO2 laser line centres. Literature values for the offsets were used plus accurate new heterodyne values recently obtained at the National Institute of Standards and Technology in Boulder [25]. A mean correction ratio of 1.000000754 was determined, and the experimental wavenumbers were multiplied by this factor. The estimated uncertainty for unblended lines is _+0.0005 cm ~. The FIR wavenumbers for our combination loops were derived from FIR spectra recorded in Dr. Johns' laboratory. In the lower region, we had data at 0.002 cm -~ resolution taken in one run from 15 to 60cm ~ at a sample pressure of 400mTorr and another from 25 to 125 cm -~ at 80 mtorr. The absorption path length was 4.0 m in both cases, and 60 scans were coadded for each run. Above 125cm ~, earlier results had been recorded at lower resolution in a 15-cm absorption cell. We had a 35-scan spectrum for the 80-210cm -t region run at 0.004cm -~ resolution using 2 Torr pressure, and a 48-scan spectrum for the 200-345 cm-l region at 0.007 cm ~ resolution using 3 Torr pressure [18,19]. The FIR spectra were calibrated against known water lines. 4. FIR laser assignments for 13CH3OH As the analysis of our FTIR spectra progressed, we identified a number of IR absorptions sufficiently close to CO2 laser lines to allow optical pumping. By matching the predicted FIR emission patterns for these pump lines against the reported FIR laser lines, we then obtained new assignments and confirmations together with accurate FIR laser wavenumbers for 8 transition systems of UCH3OH pumped by 7 different CO2 laser lines. Four of the systems involve the CO-stretching mode and four the CH3-rocking mode. Our assignments and calculated wavenumbers are collected in Table 1; significant features for each system are discussed individually below. In the combination-loop method for confirming assignments, IR and FIR spectroscopic data are used to check the sum of the wavenumbers going around a closed loop of transitions. If the loop closure defect & is zero to within the net experimental uncertainty, the assignments of all transitions in the loop are confirmed. When one side of a loop is an FIR laser transition, its wavenumber can be determined to the FT spectroscopic accuracy of +0.001cm -~ from the combination difference among the other three loop transitions. This is generally a major improvement in the FIR laser wavenumber compared to the usual wavelength measurement, and allows accurate prediction of potential FIR laser lines in transition systems with newly discovered pumping coincidences. The IR and FIR data used to form loops for the assigned systems are presented in Table 2. Lines known to be overlapped in the spectrum are marked with asterisks in Table 2 and have greater measurement uncertainties. When the wavenumber from the FTIR peakfinder output for a blended line showed a clear discrepancy with neighbours in the subband difference table [l 6], a more reliable value was determined from known combination differences. Combination relations were also used to obtain accurate wavenumbers, shown in brackets, for two systems in which the groundstate Q-branch FIR transitions fall in unresolved Q-branch heads. Line blending was serious for the CH3-rocking mode, because each rocking P-subbranch is crossed sooner or later by a much stronger R-subbranch of the CO-stretching mode. Despite this problem, we believe the uncertainties associated with overlapped transitions in Table 2 should still be below +0.001 cm -~.

354 A. Predoi et al. / Infrared Physical & Technology 37 (1996) 351-366 7 cqc.qe'a eqt..qeqcq cq 0 u~ e~ 0.ta o 8 8 ~ O e~ 0 e~ 0 I -- + I ~ -- I + q-,.~ 0 =: :ff -- + -- I q- + [..L

A. Predoi et al. / Infrared Physical & Technology 37 (1996) 351-366 355 4. I. 9P(4) CO 2 pump system at -71 MHz offset Our high resolution spectrum contains a peak at 1060,5683 cm 1 lying 71 MHz below the position of the 9P(4) CO2 line. This feature is blended, but one component is the R(014,33) ~ E: transition of the CO-stretching band [16]. For the 9P(4) pump, Pereira and Scalabrin [8] reported a very strong FIR laser line with parallel polarization at a wavelength of 190.3/xm, corresponding to a wavenumber of 52.55 cm i. This was assigned earlier as the (014,34) ~ --+ (014,33) ~ E2 a-type transition, but without combination loop support [26]. With our new spectroscopic information, we can now construct the energy level and transition diagram for this system as shown in Fig. 1. With the data from Table 2, the wavenumber for the single FIR laser line L~ is determined from several independent combination loops as follows: L~ = P+c- g- A = 52.6331 = P + f + j - A = 52.6329 = P + f- b - C = 52.6329 = P - i - e - C = 52.6334 =B +d +h- C = 52.6326 = B + a - e - C = 52.6335. J (023 CO [Lb] (014) c J 3 4 5 ) ~ ~, f 3433 33 $ ==, :: A p 9P(4) i El D~ : Bi -71 MHz F== ", ci, = I i d..-. ' i 35 ',,.....- 35 ; --.'a '.-" e..'-'.~. 34.-" f_.._;~. 33 33 ~-=~..~".-'c J "'~;... "J 32 32 "'- " "-... Fig. 1. Energy level and transition diagram for the FIR laser system of ~3CH3OH pumped by the 9P(4) CO2 laser line at -71 MHz offset. The IR pump absorption is the R(014,33) E 2 transition of the CO-stretching fundamental band. Transition wavenumbers are given in Table 2. The excellent self-consistency of the independent values for La strongly supports the spectroscopic assignments of all of the loop transitions. The mean discrepancy of -0.08 cm -~ from the reported wavenumber is typical of the range expected for wavelength measurements. However, a-type transitions are relatively insensitive to the (ntk) quantum numbers, hence a single a-type FIR laser line is a slim basis for a firm assignment. Moreover, the IR absorption at 1060.5683 cm ~ consists of overlapping lines and the pump assignment is not absolutely clearcut. Fortunately, an accurate frequency for L a was recently measured by heterodyne techniques, giving a precise wavenumber of 52.63306cm -t [25]. The close agreement with the mean loopcalculated wavenumber of 52.6331 cm-1 confirms the assignment. Further support could be obtained by observing either of the potential b-type FIR laser lines [Lb] and [Lc] for this system. The polarization of [Lb] would be perpendicular and that of [Lc] parallel, with their wavenumbers related by the "triad rule" as L a ~ [Lc]- [t~,]. This rule is an approximate combination relation arising because (J + 1)K---* Jx a-type wavenumbers do not vary strongly with K. The [Lb] and [Lc] wavenumbers are predicted from the spectroscopic data in Table 2 to be: [Lb] = P + f- G = 17.4696 =P-i-a +d- E = 17.4699 = B + d - E = 17.4700 [Lc] = P + c - F = 70.1297 =P-i- D = 70.1296 =B + a-d = 70.1297. The mean [Lb] wavenumber of 17.4698cm -~ is somewhat low for convenient observation in an FIR laser, but [Lc] at 70.1297 cm 1 should be more easily observable and would provide a unique fingerprint for the proposed assignment scheme of Fig. 1. 4.2. 9P(lO) C02pump system at - IIO MHz offset The 9P(10) COz laser line position is 110 MHz above the weak but well-resolved R(039,27) c El

356 A. Predoi et al. / Infrared Physical & Technology 37 (1996) 351-366 Table 2 IR and FIR spectroscopic data for FIR laser assignments and predictions for t3ch3oh CO 2 pump Line IR transition Wavenumber ~) Line FIR transition Wavenumber ") transition system label P/Q/R (nvk, J) ~ (cm l ) label b) (nrk, J)' *-- (nzk, J)" (cm-1 ) 9P(4) - 71 MHz P R(014,33) c 1060.5683" a (014,35),-- (023,34) 72.2350 A R (014,32) c 1059.6567 b (014,34) *---(023,33) 0 70.7067 B P(014,35) 952.4682 c (014,33) *--(023,32) 69.1747 C P(014,34) ~ 954.6609 d (014,35) *--(023,35) 0 17.3831 D P(023,34) ~ 954.5735 e (014,34) 0,-- (023,34) 17.4088" E P(023,35) ~ 952.3813 f (014,33) *-- (023,33) 17.4322* F R(023,32) 1059.6133 g (014,32) ~ (023,32) 17.4532" G R (023,33) 1060.5309" h (023,35),--- (014,34) 37.4422* i (023,34) 4-- (014,33) 35.8652 j (023,33),--- (014,32) 34.2891 9P(10) - 110 MHz P R(039,27) c 1055.6214 a (039,29) *--(018,28) 96.7828 A R(039,26) ~ 1054.5200 b (039,28) *--(018,27) 95.2516" B P(039,29) ~ 966.2853 c (039,27),-- (018,26) 93.7176 C P(039,28) c 968.2960 d (039,29),-- (018,29) 51.3110 D R(018,27) ~ 1055.2319 e (039,28) *-(018,28) 51.3370 E R(018,26) c 1054.1678" f (039,27).--(018,27) 51.3610 F P(018,29) c 965.8459 g (039,26),---(018,26) 51.3835 G P(018,28) ~ 967.8970 9P(12) + 99 MHz P R(033,26) ~ 1053.9268" a (033,28),--(012,27) 62.3991" A R(033,25) c 1052.8644" b (033,27),--(012,26) 60.6700 B P(033,28) c 967.3509 c (033,26),-- (012,25) 58.9641 C P(033,27) c 969.4330 d (033,28),-- (012,28) 18.5(155 D R (012,26) c 1053.7860 e (033,27).--- (012,27) 0 18.3242" E R(012,25) c 1052.7442 f (033,26),---(012,26) 18.1679 F P(012,28) c 967.5481 g (033,25) ~-- (012,25) 18.0350 G P(012,27) ~ 969.6031" 9P(26) - 71 MHz P P(033,16) r 1041.2767" a (033,16) ~--- (012,15) 42.8776 A P(033,15) r 1042.9292" b (033,15) *--(012,14) 41.3197 B R(033,14) r 1090.0840 c (033,14),-- (012,13) 39.7620 C R(033,13) ~ 1088.5878" d (033,16) *--(012,16) 17.6273 D R(012,14) r 1091.2073" e (033,15) *--(012,15) 17.6868 E R(012,13) r 1089.6165 f (033,14),-- (012,14) 17.7027' F P(012,16) r 1042.3692" g (033,13).-- (012,13) 17.7198 G P(012,15) r 1043.9244 9P(26) - 158 MHz p P(035,17) r 1041.2738" a (035,17).-- (014,16) 52.0039 A R(035,15) r 1093.1751 b (035,16).- (014,15) 50.4327 B R(035,14) r 1091.6735 c (035,15).---(014,14) 48.8618 C P(035,16) r 1042.9126" [d] (035,17),--- (014,17) [25.2706] D R(014,15) r 1090.5688 [e] (035,16) *--(014,16) [25.2685] E R(014,14) r 1089.0776 [f] (035,15).-- (014,15) [25.2672] F P(014,17) r 1038.6715" [g] (035,14),---(014,14) [25.2667] G P(014,16) r 1040.3191

A. Predoi et al. /lnfrared Physical & Technology 37 (1996) 351-366 357 Table 2 continued CO 2 pump Line IR transition Wavenumber a) Line FIR transition Wavenumber a) transition system label P/Q/R (nrk, J) ~ (cm- l ) label b~ (n~k,j)' *-- (n~k,j)" (cm- I ) 9P(26) + 130 MHz P R(018,15) c 1041.2834 a (018,17) *-- (027,16) 86.2643 A R(018,14) c 1040.0022 b (018,16),--(027,15) 84.7008* B P(018,17) 989.4115" c (018,15),,-(027,14) 83.1361 C P(018,16) ~ 991.2670" d (018,17) ~-- (027,17) 59.5388 D Q(018,16) ~ 1016.1320" e (018,16) *-- (027,16) 59.5445* E Q(018,15) ~ 1016.4195 f (018,15) *--(027,15) 59.5493 F R(027,15) ~ 1040.8604" g (018,14) ~-- (027,14) 59.5533 G R (027,14) c 1039.6109* H P(027,17) ~ 988.9789 I P(027,16) ~ 990.8680* J Q (027,15) ~ 1016.0243* 9P(36) - 64 MHz P P(010,23) r 1031.4753 a (010,23),--(010,22) 36.0021 A R(010,21) r 1101.9307 b (010,22) ~-- (010,21) o 34.4533 B R(010,20) r 1100.5331 c (010,21) ~--- (010,20) 32.9027 C P(010,22) r 1033.1775" d (031 +,22) ~---- (010,2 I) 41.6760 D R(031+,20) r 1096.4149 e (031 +,21) *---(010,20) 40.3416 E P(031 +,22) ~ 1029.4886 f (010,23),--- (031 +,22) 28.7794 g (010,22) *--(031+,21) 27.0140 h (010,21) *---(031 +,20) 25.2504 9P(40) + 52 MHz P P(024,21) r 1027.3839 a (024,21),--(033,20) 66.4507 A R (024,19) r 1091.8360 b (024,20),-- (033,19) 64.9293 B R(024,18) r 1090.3661 c (024,19),--(033,18) 63.4003 C P(024,20) r 1029.0486" d (024,21) ~-- (033,21) 33.3885* D R (033,19) ~ 1097.4634 e (024,20),--- (033,20) 33.4410 E R(033,18) r 1096.0020 f (024,19),--(033,19) 33.4862 F P(033,21) r 1032.9133 g (024,18),-- (033,18) 33.5252 G P(033,20) r 1034.5999* 10R(18) + 29 MHz P P(029,25) c 974.6229* a (029,25),-- (038,24) 96.0449 A R(029,23) c 1051.5155 b (029,24)0,--(038,23) 94.4830 B R (029,22) c 1050.3253 c (029,23),-- (038,22) 92.9211 * C P(029,24) 976.5562 [d] (029,25) ~ (038,25) [56.81891 D R(038,23) c 1050.1104" [e] (029,24) ~-- (038,24) [56.8179] E R(038,22) c 1049.3316 [f] (029,23)0*--(038,23) [56.8175] F P(038,25) 973.2196 [g] (029,22)0,---(038,22) [56.8179] G P(038,24) c 975.5626 a' (038,25),-- (017,24) 81.9648 H Q(017,24) r 1059.9929 b' (038,24) *--(017,23) 80.4176 I R(017,23) r 1097.6710 c' (038,23),--(017,22) 78.8686 J R(017,22) r 1096.6479 d' (038,24),--(017,24) 42.7385 '~ K e(017,24) r 1022.8520" e' (038,23) *---(017,23) 42.7519 M c) P(038,24) r 980.1134 f' (038,22) ~-- (017,22) 42.7646 a)wavenumbers with asterisks are for overlapped lines, so have increased uncertainty. b)wavenumbers for transitions in brackets are calculated from combination differences. c)coriolis-induced (017,23) r~---(038,24) forbidden transition.

358 A. Predoi et al. / Infrared Physical & Technology 37 (1996) 351-366 absorption at 1055.6214cm -~. The 9P(10) line at -ll0mhz offset was reported to pump a strong FIR laser line at 95.17cm -1 with parallel polarization [6], which we assign as the (039,28)c ---~ (018,27) ~ FIR b-type transition. The following combination loops with the data from Table 2 support this assignment: Lc = P+c- E= 95.1712 =P+ f- b +e- G = 95.1708 =B+a- G=95.1711. The mean loop wavenumber of 95.1710 cm -~ is in good agreement with the reported value. Two further laser lines [Lb] and [L,] would be possible for this system, with predicted wavenumbers: [L~] = P + c - g - A = 43.4355 = P + f- b - C = 43.4348 =B+a-e-C =43.4351 [Lb] = P+ f-- D = 51.7505 =B+d- F= 51.7505 =B+a-e+b-D = 51.7508. 4.3. 9P(12) COe pump system at + 99 MHz offset The 9P(12) system is a rich one, with at least three IR coincidences at different offsets. The spectrum shows a well-resolved peak for the known R(034-,26) c A -FIR laser pump transition at -50 MHz offset [2-5,9], but also has a broad feature lying slightly higher which contains at least the R(031-,26) ~ A-, R(033,26) ~ E, and R(034+,26) A + CO-stretch absorptions [16]. The coincidence with the R(033,26) ' El transition at a reported +90 MHz offset was discovered previously and the observed FIR laser lines La and L C at 41.97 and 60.14cm ~ were assigned as the (033,27) ~o ~ (033,26) ~ and (033,27) c ~ (012,26) ~ transitions, respectively [10]. Our reinvestigation of the CO-stretching band at higher resolution has improved the agreement with the reported laser lines and allows a more accurate wavenumber prediction for the third line [Lb] of the triad: La = P+c- g-a = 41.9915 =P+ f- b- C=41.9917 = B + a - e - C = 41.9928 Lc = P + c - E = 60.1467 =P+f-b+e- G = 60.1458 =B +a- G = 60.1469 [Lb] = P+ f-d = 18.3087 B + d - F = 18.3083 B +a- e+ b- D = 18.3098 Three FIR laser lines pumped at an offset of +25 MHz from the 9P(12) CO z line were a mystery for some time, but two have recently been assigned to the R(031-,26) c A pump, perturbed by an interaction in the excited state between the (031 - )c and (334) levels [16]. The third line is still unidentified but has a high wavenumber of 158.49 cm- ~, suggesting an excited torsional transition. Its parent IR pump absorption must lie in the broad feature containing the R(031-,26) c A -, R(033,26) c E1 and R(034+,26) ~ A ~ lines, and could be either a CO-stretching or a CH;rocking transition since the CO-stretch R-branch overlaps the CH3-rock P-branch in this region. Previously proposed assignments for the 9P(12) CO:: pump are not consistent with our spectroscopic results and cannot be correct [8]. 4.4. 9P(26) COe pump systems at --71MHz, -158MHz and + 130MHz offsets The 9P(26) CO2 line also lies in the overlap region between the R-branch of the CO-stretching band and the P-branch of the CH3-rocking band. One pair of FIR laser lines is reported with cw pumping [8], and a second pair at an offset of -140 MHz pumped by a waveguide laser [6]. In Fig. 2 we show the profile from our high-pressure FTIR spectrum in the vicinity of the 9P(26) CO2 pump and its deconvolution with the line-fitting routine described by Moruzzi and Xu [27] when trial peaks were inserted for the known R (112,18) c El, R(031-,15) A-, P(035,17) r E2, P(033,16) r Et and R(018,15) E, transitions. This complicated

i "~ 0.5 i [- 101... A. Predoi et al. I Infrared Physical & Technology 37 (1996) 351-366 359... ',,! ',,,,: ; /, ~", ;! ',, :',,/ i~lll ~k, \z /sl: 9 p 6), ; ', / ~ ] t ] t t ne V i,\/ t 'Vt i R(112,18) co R(018,15)co R(031",15)co T 1 e( 35,17)r l... i, ~ ~ i, ~ ~ r I L ~ ~, I 1041.270 104L275 1041.280 1041.285 Wavenumber/cm'l Fig. 2. FTIR spectrum of t3ch3oh (dotted line) in the neighbourhood of the 9P(26) CO2 laser line, showing the spectral profile (solid line) obtained from deconvolution into individual overlapping IR absorptions (dashed lines) by the line-fitting routine of Moruzzi and Xu (Ref. [27]). The two weak rocking-band lines have appropriate relative intensities, but their wavenumberrs are shifted slightly from more accurate spectroscopic values determined from combination relations and subband difference tables. The strong R(031-,15) ~ A-line is severely saturated and distorted in this high-pressure spectrum. picture with multiple overlapping presents a difficult challenge for the line-fitting program, especially as the strong R(031-,15) ~ A line is saturated and distorted in the high-pressure spectrum. Nevertheless, the program does a creditable job of locating the two rocking-band lines forming the weak unresolved shoulder on the strong line. Although the lines are shifted in Fig. 2 from the more reliable spectroscopic positions determined from combination relations and subband difference tables [16], the wavenumber errors are relatively small and the intensities are reasonable. The P(033,16) ~ E] CH3-rocking transition in Fig. 2 is assigned as the pump for the first pair of FIR lines at 23.49cm -1 and 40.14cm ]. Our wavenumber of 1041.2767cm -] for this transition corresponds to an offset of -71 MHz from the 9P(26) CO2 line and is consistent with cw pumping. The observed FIR laser lines L~ and L, are then identified as the (033,15)r--~(033,14) r and (033,15)r---~(012,14) r transitions from the loops below, although the parallel polarization thereby required for L c is opposite to the perpendicular polarization reported [8]. L a = P+a- e- A = 23.5383 =B + c- g- C = 23.5384 =B+f-b-A =23.5378 L< = P + a - G = 40.2299 = B + c - E = 40.2295 = B + f- b + e - G = 40.2294. The third transition of the triad, [Lb]= (033,15) r ~ (012,15) r with predicted perpendicular polarization, is given by the following combination relations: [Lb] = P + d - F = 16.5798 =P+a-e+b-D= 16.5799 =B+f-D= 16.5794. A previous assignment of the 40.14 cm J laser line as the (114,10) c ~ (123,11)t transition [8] is not supported by the IR and FIR spectroscopic results. It is interesting that the above system is another example of Nature's remarkable ability to search out perturbations and make use of them for optical pumping and FIR lasing. The lower (012,14y CH3-rocking level for laser line Lc is located right at the crossover point of a J-localized Fermi resonance with the (024) c CO-stretch series [16], and has a substantial Fermi shift of about -0.05 cm-1. This disturbs the normal trends of the (012) r subbranches in the FTIR spectrum, hence the confirmation for the (012) r subband assignment provided by the FIR laser identification was extremely valuable. The second pair of FIR laser emission lines at the reported -140 MHz offset from the 9P(26) CO2 pump has wavenumbers of 52.92 and 84.80cm l and parallel polarizations [2,3]. The offset matches quite well with the value of -158MHz derived from our assignment of the second transition in the unresolved shoulder in

360 A. Predoi et al. / Infrared Physical & Technology 37 (1996) 351 366 Fig. 2 as the P(035,17) r E2 rocking-band transition at a wavenumber of 1041.2738cm-J. The 52.92cm -1 line is identified as the (035,16)r---~ (014,15) r rocking transition according to the combination loops below, in which the transitions in brackets are overlapped FIR transitions in an unresolved Q-branch head whose wavenumbers have been determined from combination relations. Lc = P+a- G = 52.9586 = A + c - E = 52.9593 = A + If] - b + [e] - G = 52.9590. Further assignment confirmation could be obtained by observation of the two other triad lines, [La] with parallel polarization and [Lb] with perpendicular polarization, at predicted wavenumbers: [L~] = P + a - [e] - C = 25.0966 = A + c - [g] - B = 25.0967 = A + [f] - b - C = 25.0970 [Lb] = P + [d] - F = 27.8729 =P + a- [e]+ b- D = 27.8731 = A + If] - D = 27.8735. At present, we have no plausible IR pump candidate at the -140MHz offset which can account for the other FIR laser line at 84.80 cm i. There is, however, a striking coincidence which leads us to a speculative proposal. In Fig. 2, the R(018,15) c Et transition is clearly resolved at 1041.2834 cm-~, 130 MHz above the 9P(26) pump. Combination loops with the IR and FIR data from Table 2 give the following wavenumbers for the (018,16) c ~ (027,15) c transition, speculatively labelled as a laser line L c: L, = P + c - G = 84.8086 =P + f- J = 84.8084 = B + a - I = 84.8078 = D + e - I = 84.8085. The 84.8083 cm ~ mean wavenumber and the predicted parallel polarization agree with those reported for the 84.80cm -~ line with the 9P(26) CO2 pump, but the offset of + 130 MHz has the opposite sign! Given the clear association of the 84.80cm -~ laser line with the feature at -140MHz offset in the optoacoustic spectrum reported by Ioli et al. [6] the similarity with wavenumber L, above would most logically be interpreted as coincidence. Nevertheless, for the record, we present loop-predicted wavenumbers for the other two triad lines [Lo] and [L~,] expected for an R(018,15) c IR pump in the event of future observation of FIR emission at the positive offset: [L~] = P - E = 24.8639 =P+c-g-A =24.8640 = D - C = 24.8650 [Lb] = P + f- F = 59.9723 =B +d- H = 59.9714 = D + b - F = 59.9724. 4.5. 9P(36) C02 pump system at -64 a4hz offset The P(010,23) r A* rocking-band transition is coincident in our FTIR spectrum with the position of the 9P(36) CO2 line at an offset of -64 MHz. The energy level diagram in Fig. 3 displays the asymmetry K-doubling for the K = 1 A levels. For this pump, FIR laser lines have been reported at 34.29 and 30.75 cm ~ with parallel polarizations [2,3]. These match well with our loop wavenumbers for the (010,22)r--~(010,21) f and (010,22)r--~ (031 +,21) r transitions: Lo = P + a - C = 34.2999 = A - b - C = 34.2999 = A + c - B = 34.3003 Lb = P + f- E = 30.7661 =A- d- E = 30.7661 =A + h- D = 30.7662. For this system, there is no third line with perpendicular polarization to complete the triad because the (031-,22) r A- level lies above the pumped (010,22) r A + level. Although another FIR laser line at 12.75cm -I was reported for the 9P(36)

i i A. Predoi et al. / lnfi'ared Physical & Technology 37 (1996) 351 366 361 J (010)r 22 (031) r J ~ L a ~ -21 ~ + 21 The a-type transition [L,] completing triad is predicted as [La] = P+ a- e- C = 31.3450 the laser 9P(36) -64 MHz i ]A : is = ic 23 #, '~-._,, "'--. f - "-.../,. + 22 21 C~,' ~... ""h, e.--"... +20 20 ' "'" Fig. 3. Energy level and transition diagram for the FIR laser system of t3ch3oh pumped by the 9P(36) CO 2 laser line at -64 MHz offset. The IR pump absorption is the P(010,23) r A transition of the in-plane CH 3-rocking fundamental. Transition wavenumbers are given in Table 2. pump, it does not appear to belong to this system and does not have a reported offset. A proposed CO-stretching assignment for this latter transition [8] is not supported by our spectroscopic data. 4.6. 9P(40) CO: pump system at + 52 MHz offset The 9P(40) CO2 line pumps two FIR laser lines at a reported offset of + 35 MHz [4]. In our FTIR spectrum, the P(024,21y EL transition in the rocking-band P-branch appears at 1027.3839 cm 1 at an offset of 52 MHz in reasonable agreement with the reported value. This identifies the FIR laser lines as the (024,20)r--+ (033,20) r and (024,20)r-+ (033,19) r transitions, consistent with their observed polarizations and the combination loops below: Lb = P +d- F = 27.8591 id =P+a- e+ b- D--- 27.8595 =A + f- D = 27.8588 Lc = P + a - G = 59.2347 =A+c-E= 59.2343 = A + f- b + e - G = 59.2340. E =A +c- g- B = 31.3450 =A + f- b-c = 31.3443. 4. 7. lor(18) C02pump system at + 29 MHz offset The four observed FIR laser lines pumped by the 10R(18) CO2 line have been previously discussed in the literature [11,13,26]. Three of the FIR lines were tentatively assigned to a system having the P(029,25) c E2 CO-stretching transition as pump [26] and the fourth was brought into the picture through theoretical arguments involving C'oriolis resonance between the (038,J) c and (027,J) r stacks of levels [13]. Our data provide further support for this scheme, but the full spectroscopic situation for the Coriolis-coupled subbands is still not resolved. However, the P(029,25) c E: pump assignment was confirmed earlier by IR-IR double resonance experiments [11], and this transition is clearly identified in our FTIR spectrum at the expected offset. The energy level and transition structure for this system is shown in Fig. 4. Coriolis mixing between the (038,J) ~ CO-stretching and (027,Jy CH 3- rocking levels allows b-type FIR emission from the pumped (029,24) c E 2 level down to both the (038) c and (027) r stacks. Also, the a-type (029,24) ~ ~ (029,23) c FIR laser line is observed at 37.23 cm -~. Our data of Table 2 give the wavenumbers for this line from loop combination relations as follows: L, = P + a -- [e] - C = 37.2937 =P+ a- G + E- [g]- B = 37.2936 =P + [d] +D- F- b- C = 37.2934 La = A + c - [g] - B = 37.2934 = A + [f] - b - C = 37.2938. The frequencies of the two b-type FIR lines Lb and L, down to the (038,24) ~ and (038,23) ~ levels have both been accurately measured by heterodyning [4]. With wavenumbers for the ground-state

362 A. Predoi et al. / Infrared Physical & Technology 37 (1996) 351-366 J [Ld] ~ ~ L a 24 J [La] = P+a- M + K- H = 53.4135 =P +a- b'-i = 53.4144 i Le ', : Lc i, 23 $ t ~ 2 3,t I ~ p//'lc i p 10R(18) : ", T i ', B A +29 MHz ; : ', i : cl ; " J : HI ' ', E ',, ', I F; I i : ji Ii! M', GI! KI i i i ", ': i i ':.,! 2s a'," ',,,.;i "" 24~1 *'~'" /'b 24 '-d' F'23 ",;f-';.~ :,".--",",,"..4 22 23 'e; c'.- 22 ':"g"- (029) CO 22 "~;'- (038) co (017) r Fig. 4. Energy level and transition diagram for the FIR laser system of 13CH3OH pumped by the 10R(18) CO 2 laser line at 29 MHz offset. The IR pump absorption is the P(029,25y E 2 transition of the CH 3 rocking fundamental. The (029,24) c ---, (017,24y and (029,24) ~ ---, (017,23y FIR laser transitions arise through intensity borrowing due to Coriolis mixing between the (038,J) ~ and (017,J)' levels. (029),----(038) subband from our FIR spectra, the IR transitions D to G in the (038) c subband shown in Fig. 4 could then be predicted from combination relations. When the FTIR spectrum was inspected, lines were indeed found at the predicted locations. Further, with the accurate frequency reported for FIR laser line Le to the Coriolis-hybridized (027,23y level plus our ground-state FIR data for the (038) ~ --- (027) subband, we could also calculate the wavenumbers for the rocking-band lines H to K plus the perturbation-induced transition M in Fig. 4. Again, lines were found at those locations, so that the energy level pattern of Fig. 4 has spectroscopic support. The pattern is further confirmed by the self-consistency of loop relations for the other FIR laser transitions in the system, as follows: L b = P + [d] - F = 58.2222 = P + a - [el + b - D = 58.2225 = A + [f] - D = 58.2226 Lc=P + a - G = 95.1052 =A+c- E = 95.1050 =A + [f] - b + [el - G = 95.1053 24 =P+[d]+a'-H = 53.4137 =A + [f] + e'- I = 53.4139 Le = P + a - M = 90.5544 =P+a+ d'- K = 90.5543 =A+c + f'- J= 90.5533 =A + If] + c' - J = 90.5537. However, a problem remains for this system in that the IR wavenumbers do not match the trends of line series in the spectrum which are assigned at lower J to the (038) c and (027y subbands but which cannot be followed up to J' values of 24. The spectroscopic situation is still ambiguous, therefore, and until the full (038) c and (027) r subbands are confidently identified the state labelling in Fig. 4 cannot be considered as definitively confirmed. 5. Predicted FIR laser lines for =3CH3OH Our FTIR study of 13C-methanol has revealed several near-coincidences between IR absorptions and CO2 or ~3CO2 laser lines which could lead to further optically-pumped FIR laser transition systems. For these predicted systems, our IR and FIR data sets permit combination-loop calculation of the wavenumbers of the potential new FIR laser lines to virtually the full spectroscopic precision. We present these predicted FIR laser wavenumbers in Table 3 for transitions which could be pumped by normal CO2 cw and waveguide lasers, and in Table 4 for those which could be pumped by ~3CO2 lasers. Four of the schemes merit specific comments. 5.1. Predicted 9R(4) C02 pump ~Tstem at - 123 MHz offset The 9R(4) CO2 line lies 123 MHz above the well-resolved Q(14) member of the (037) r A rocking-band Q branch. This system carries special spectroscopic interest, because the (037) r rocking-

A. Predoi et at. / Infrared Physical & Technology 37 (1996) 351-366 363 mode levels are coupled to and mixed with the (028) ~ CO-stretch levels by a significant Coriolis resonance. Intensity borrowing from the main (037,14) ~ ~ (037,137 transition then makes the cross-mode (037,14) r~ (028,13) transition weakly allowed. Thus, the four FIR laser emissions listed in Table 3 might be observed for C-13 methanol pumped by the 9R(4) line of a waveguide CO2 laser. These include the usual allowed triad of rocking-mode FIR lines from the upper (037,14) ~ level, plus the fourth Coriolis-induced transition to the (028,15) level. A further Coriolis-induced transition, (037,14)r----~ (028,14) ~, is of too long a wavelength to be detectable. 5.2. 9P(6) C02 pum p system at -I14MHz offset This is not strictly speaking a new system but already has two reported FIR laser lines at wave- lengths of 205 and 113.4/~m [2,3], corresponding to wavenumbers of 48.8 and 88.18 cm-l '/'he first is waveguide-pumped by 9P(6) at an offset of -120(10) MHz [6], and the second is pumped cw [8]. We include the system here because of ambiguity in the assignment, despite clear identification of an overlapping IR absorption in the spectrum. The 9P(6) CO 2 line lies at the upper edge of the R(31) CO-stretch multiplet, and the 48.8 cm -~ laser line L~ was partially assigned by Mukhopadhyay et ai. as an a-type (nrk,32) ~ --~ (nzk,31) ~ transition [10]. However, the approximate excited-state B-value, given by the relation B,~ L,/2J' = 0.762 cm -~, is significantly less than the 0.778 cm-~ typical of the CO-stretching state [16]. In our spectrum, a well-isolated feature at 1058.9449 cm -~ at an offset of - 114 MHz is identified as a blend of the R(033,31) ~ and P(030,3) ~ transitions. This suggests a (033,32)c ---~ (033,31) ~ Table 3 Predicted FIR laser lines for ]3CH3OH optically pumped by a CO 2 laser CO 2 CO 2 Offset IR absorption IR transition Predicted FIR laser pump pump v L vl-vm hr assignment Rel transition line (cm i ) (MHz) (cm t ) (nrk, j)v Pol (n 'T 'K ",J ')' --* (n "r"k ",J ")~ 9R(30) 1084.63515 130 1084.6395 R(015,12) r I[ (015,13) r ~ (015,12) r 3- ~ (024,13) r II ~ (024,12) r 9R(4) 1067.53911-123 1067.5350 Q(037,14) r 3_ (037,14) r ---* (037,13) T II ~ (016,14) T J_ ~ (016,13) r 3- ---, (028,13) co 9R(0) 1064.50885 190 1064.5152 Q(015,6) r II (015,6) r ~ (024,6) r 3- ---. (024,5) r II ~ (036,6) c 9P(6) 1058.94871-114 1058.9449 R(033,31) c II (033,32) c ---. (033,31) c 3- --., (012,32) 0 II ---. (012,31) c 9P(12) 1053.92350 174 1053.9293 R(034+,26) c II (034+,26) ---* (034+,26) 3- ~ (013-,27) c II ~ (013+,26) c 9P(18) 1048.66081 180 1048.6668 P(O15,10) r II (015,9) r ~ (015,8) ~ 3- ~ (024,9) r FI ~ (024,8) ~ 9P(20) 1046.85423-97 1046.8510 R (027,20) ~ I] (027,21) ~ ~ (027,20) ~ 3- ~ (036.21) ~ II ~ (036,20) c 9P(36) 1031.47743 62 1031.4795 P(038,22) r II (038,21) ~ -* (038,20) ~ 3- --. (017,21) ~ II ~ (017,207 11 -* (029,20) ~ a)weakly allowed via Coriolis mixing between CH~-rocking K levels and CO-stretching (K + 1) levels. Predicted VFIR (cm -I ) 20.3901 31.2207 51.6113 21.8787 40.6449 62.6012 18.9408 a) 31.2177 40.6332 16.2268 ") 49.7493 19.4411 68.9151 41.9299 21.4018 63.5804 14.1219 31.2202 45.3414 32.5915 49.1 043 81.6980 32.8175 47.9137 80.7453 26.9014 a)

- - 113 364 A. Predoi et al. / Infrared Physical & Technology 37 (1996) 351-366 Table 4. Predicted FIR laser lines for ~3CH3OH optically pumped by a ~3CO2 laser 13-CO 2 13-CO 2 Offset IR absorption IR transition Predicted FIR laser Predicted pump pump v L v L v~r V~R assignment Rel transition vv~ R line (cm -I) (MHz) (cm t) (nzk, j)~ Pol (n'z'k',j')'~--*.(n"r"k",j") ~ (cm -1) 13-9R(56) 1050.33420-99 1050.3309 R(035,23) c II (035,24) c ~ (035,23) ~ 37.2551 3_ ~ (014,24) c 25.0838 l[ ~ (014,23) c 62.3262 13-9R(52) 1048.78036 142 1048.7851 R(134,24) c II (134,25) e -~ (134,24) c 38.8802 Z ~ (113,25) c 59.3406 ]l ---* (113,24) ~ 98.0746 13-9R(48) 1047.11983 --145 1047.1150 R(011,20) c Ir (011,21) ~ ~ (011,20) c 32.4651 tl --* (020,20) ~ 28.1099 13-9R(40) 1043.47269 78 1043.4753 R(024,17) c II (024,18) ~ --* (024,17) ~ 27.9725 ± ---, (033,18) ~ 33.3573 II ---, (033,17) c 61.3570 13-9R(38) 1042.49196 118 1042.4959 R(034=,16) ~ Ii (034+,17) ~ ~ (034+,16) c 26.4240 ± ---, (013,17) ~ 21.4465 Ii ---* (013+,16f 47.8879 rl (034-,17) ~ ~ (034,16f 26.4237 ± ~ (013+,17) c 21.4676 II ---, (013,16) c 47.8731 1042.4882 R(112,19) c II (112,20) 0 ~ (I 12,19) ~ 31.0274 13-9R(36) 1041.48334 173 1041.4891 R(039,15) c II (039,16) ~ ---, (039,15) ~ 24.8587 ± --~ (018,16) ~ 51.7489 II ---, (018,15) ~ 76.6130 13-9R(20) 1032.39450-159 1032.3892 P(016,19y II (016,18) ~ ---* (016,17) ~ 28.2117 3" ~ (025,18) r 40.0878 II ~ (025,17) r 68.3069 13-9R(18) 1031.12930 158 1031.1346 P(03l+,21) r il (031+,20) r ---* (031+,19) ~ 31.0452 13-9R(8) 1024.36774-119 1024.3638 P(033,26) ~ II (033,25) ~ --* (033,24) ~ 39.2032 J_ ~ (012,25) ~ 17.3512 II ---, (012,24) ~ 56.4298 assignment for the reported FIR laser line, since the J' value for the rocking transition is too low to give emission in the FIR. However, combination loops in the transition scheme for an R(033,31) c pump give the mean La wavenumber of 49.7493 cm-~ shown in Table 3, in serious disagreement with the reported value. Since we are confident of the (033) c subband identification, it would be useful to reexamine this system. Observation of either of the b-type lines of the triad, predicted to occur at [Lb] = 19.4411 and [L,] = 68.9151 cm J, would confirm our proposal. 5.3. Predicted 9P(36) C02 pump system at + 62 MHz offset The 9P(36) line has already been shown in Table 1 to pump the P(010,23) r A transition at -62 MHz offset. However, it is also situated just below the P(038,22) r E2 rocking-band absorption, and could pump this line to generate three and possibly four FIR laser lines as listed in Table 3. The small offset would make these FIR laser transitions accessible to cw pumping. This system also involves Coriolis coupling between the rocking and CO-stretching modes, here between the (038) r and (029) c E2 states. Predictions for the triad of rocking-state FIR lines from the (038,21) r upper level plus the fourth Coriolis-induced transition to the (029,20) c level are given in Table 3 from well-determined combination loop relations. 5.4. Predicted 13-9R(38) 13C02 pump system at + 118 and - II3MHz offsets The 13-9R(38) line of the ~3CO: waveguide laser potentially pumps two CO-stretching systems at

A. Predoi et al. /' Infrared Physical & Technology 37 (1996) 351-366 365 "~ 0.5 R(l12 19) co 13-9R(38) i R(034 -+, 16)co I I,,,,I... E,~,,I,,,,I... [... I,,,,I,~ I~,,,I,,, 1042,44 1042.46 1042.48 1042,50 1042.52 Wavenumber (crnq) Fig. 5. FTIR spectrum of t3ch3oh in the vicinity of the 13-9R(38) 13CO2 laser line showing the two nearby IR absorptions for potential optical pumping. The apparent breadth and doublet structure of the R(034+,16) c A * absorption are artifacts due to strong saturation of the n = 0 transition in this high-pressure spectrum. The horizontal scale is uncalibrated, so should be multiplied by the 1.000000754 correction factor. offsets of 118 and - 113 MHz. Our high pressure FTIR spectrum in the vicinity of 13-9R(38) is shown in Fig. 5. Note that the horizontal scale is uncalibrated and the n = 0 line shapes are distorted due to strong saturation. The R(034±,16) c A transition at 118 MHz offset is a close K-doublet with very small splitting, and both components would be pumped simultaneously. The b-type FIR transitions go down to (013) c A doublet levels having larger asymmetry splittings, which would be clearly resolved in heterodyne frequency measurements. The other coincident transition is the R(112,19) c Et torsionally-excited absorption. The fact that this is so close to the R(16) member of the (034) c subband yet differs in J by 3 units illustrates the substantial downshift of the n = 1 CO-stretch subbands in the spectrum. This has already been noted to lead to potential slips in assignments based only on energy level calculations with a Hamiltonian derived from n = 0 observations [8,26]. 6. Conclusions The results of high-resolution FTIR spectroscopic studies of the CO-stretching and in-plane CH3-rocking bands of 13CH3OH have allowed new assignments for optically-pumped FIR laser lines. Results are given for eight well-determined IRpump/FIR-laser transitions systems and one speculative proposal. The laser assignments have been tested and confirmed by combination relations for closed loops of measured IR and FIR transitions, whose wavenumbers are also reported. With the FTIR spectral observations, near-coincidences between ~3CH3OH IR absorptions and CO2 laser transitions have been identified for a number of possible pump lines of CO2 and 13CO2 cw and waveguide lasers. Our accurate Fourier transform data were then utilized in transition combination loops to predict potential new FIR laser lines for these pump systems. Three of the systems involve Coriolis resonance between the CH3-rocking K levels and CO-stretching (K+ 1) levels, hence possible perturbation-induced FIR laser emissions would be of particular spectroscopic interest in probing the interactions directly in the excited states. Acknowledgements Support of this research by the Natural Sciences and Engineering Research Council of Canada and the University of New Brunswick Research Fund is gratefully acknowledged. We thank J.W.C. Johns of the Steacie Institute of Molecular Sciences, National Research Council Canada, for access to the Bomem Fourier transform spectrometer and Mario NoEl for assistance in recording the IR and FIR spectra. We are also pleased to acknowledge continuing collaboration and interaction with G. Moruzzi of the University of Pisa in the use and development of his elegant PC-based line-fitting and spectral plotting routines. References [1] G. Moruzzi, J.C.S. Moraes and F. Strumia, Int. J. Infrared Millimeter Waves 13 (1992) 1269.

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