- Email: [email protected]
High resolution analysis of transitions to the five lowest electronic states of samarium monoxide
JOURNAL OF MOLECULAR SPECTROSCOPY
137, l14- 126 ( 1989)
High Resolution Analysis of Transitions to the Five Lowest Electronic States of Samarium Monoxide Guo
BUJIN AND C. LINTON
PhysicsDepartment, Universityof New Brunswick,Fredericton, New Brunswick,Canada E3B 5A3 Hi resolution excitation spectra have been obtained and analyzed for 10 electronic transitions of samarium monoxide involving five low-lying and six upper states. A global fit to all the lines has yielded electronic term energies, rotational constants, and 51doubling parameters of all the states for six (and in one case seven) isotopes of samarium. The isotopic variation of the constants was examined and the B values were found to satisfy the normal isotope relations. Local perturbations in the [ 16.911 state have been assigned and analyzed. Q 1989Academicpress, I~C. INTRODUCTION
In a recent publication ( 1) we presented and discussed the assignments of 11 lowlying electronic states of the SmO molecule. The results were compared with ligand field theory calculations (2,3) and, in particular, it was found that there was excellent agreement between the energies of the observed electronic states and those calculated by Carette and Hocquet (3). The eigenfunctions were found to be consistent with the observed Q doubling of low-lying s2 = 1 states. The results were based on medium resolution resolved fluorescence spectra and high resolution excitation spectra involving the ground state (X0-) and the lowest rotational levels of the other lowest-lying states. We have recently undertaken a more detailed investigation, at high resolution, of transitions involving the lowest fi = 0, 1, and 2 states. The transitions investigated are shown in Fig. 1; it can be seen that there is more than one transition involving eachofthe[16.9]1,[17.0]2,XO~,(1)1,(1)2,and(2)0~states.‘Thisgreatlyfacilitated the analysis and provided important linkages between the states. The results of the detailed rotational analysis for the six most abundant isotopes of samarium (masses 154, 152, 150, 149, 148, 147) are presented in this paper along with a discussion of observed perturbations. EXPERIMENTAL
DETAILS
The sources of SmO (Broida oven and sputter source) and the rest of the equipment (lasers, spectrometers, etc.) are the same as those described in the previous paper ( I ). Because of the very heavy congestion in the spectra, extreme care had to be taken in selecting the appropriate monochromator wavelengths at which to detect the excitation spectra. This will be discussed in detail in the following sections.
’ The labeling of the states has been described elsewhere ( 1). The upper states are labeled [ To]il, where To is in thousands of cm-‘, and the lower states are labeled (N)Q, representing the Nth state of a given Q. CQ22-2852189$3.00 CopyriBbt0 1989 by Academic Pms, Inc. All ri&ts of reproductionin any farm rew-vcd.
114
HIGH RESOLUTION
ANALYSIS OF SmO
115
116.611
.
rib” FIG. 1. Transitions of SmO analyzed at high resolution in the present investigation, RESULTS AND ANALYSIS
Assignment of the Transitions The analysis of the R and P branches of the [ 16.91 l-X0- transition for the 154 and 152 isotopes was presented in the earlier paper ( I ) . The extension of the analysis to include the other isotopes and the Q branch will be discussed later in this section. The main result to note from the earlier analysis is the very localized perturbation at J = 5 of the [ 16.911 state which affects only the one rotational level and only the 154 isotope. The detection and analysis of the other transitions are discussed below. The [17.0]2-( 1) 1 and [ 16.91 I-( 1) 1 transitions were assigned together as the combination differences of the lower state are the same for both. Because of the G doubling, particularly in the ( 1) 1 state and the six abundant (and one less abundant) isotopes of Sm, the spectra are extremely complex with each rotational transition consisting of 12 lines. There was no way of simplifying the spectrum for the [ 17.0]2-( 1) 1 transition as detection of any band originating in the [ 17.012 state would involve both the e and f parity components. However, because of the special parity-selective properties of Q = 1-O transitions, it was possible to separate the parity components in the [ 16-91 I-( 1) 1 transition. This can most easily be understood by referring to Fig. 2. The solid lines represent the transitions involving the e levels of the upper state and the dashed lines connect the f levels. The monochromator was first carefully set to detect the Q branch of the[ 16.91 l-X0- band, which consists entirely of n = le-O-f transitions. Thus, only transitions originating from the e levels of the upper state can be detected. When the laser is scanned through the [ 16.91 I-( 1) 1 band at -5930 A,
BUJIN AND LINTON
116
[ 16.91 1
lL’”
III
J+I J-l
L
-f
‘Y==++
J+l
4
J-l
b;
f f
:
(111
xo-
FIG. 2. Schematic diagram showing parity-selective excitation of the [ 16.91 l-( 1) 1 transition. By setting the monochromator to detect the Q branch of the [16.9] l-X0- or 116.91l-(2)0+ transitions, only the e or f levels of the upper state are detected.
even though both parity components will be excited, only the lines originating from the upper state e levels will appear in the excitation spectrum. The P and R branches will go to the e levels in the ( 1) 1 state and the Q branch will go to the f levels. The monochromator was then set to detect the Q branch of the [ 16.91 l-( 2)0+ transition and only the f levels of the upper state could be detected going to the e( Q branch) and S( P and R branches) levels of the ( 1) 1 state. The success of the technique is clearly seen in Fig. 3. The top spectrum, (a), shows the complexity of the [ 17.0]2( 1) 1 spectrum in which all transitions are present. The bottom two spectra both show the same spectral region of the [ 16.9 ] 1- ( 1) 1 spectrum but detecting the f-component in (b) and the e-component in (c). It can be seen that the spectra are completely different and the two components can be assigned separately and with relative simplicity. The assignment of the spectra relied heavily on the use of narrow band-pass selectivity in detection and on combination differences. With narrow slits, the monochromator could detect only a narrow range of J in the upper state and, when the laser scanned through the R, Q, and P branches of a transition, only the lines in each branch originating in this J-range would appear in the spectrum. A preliminary assignment could then be made by trying to match the corresponding lines (i.e., same J’) in each branch. The final assignments were then made using combination difference relations. For example, the lower state combination relation
R,(J) - Qe(J+ 1) = Qf- pf(J-+ I), in which the subscripts refer to the upper state parity, must be satisfied for each transition and, as both transitions have a common lower state, it must be the same for
HIGH RESOLUTION
Pe
21
pf
1 23
ANALYSIS OF SmO
19
1
17
I
121 I
19 1 I
117
I I
(a)
20
p’
I
18
I
16 I
W I:::::: 1675Z. 5037cn-1
pe
23
: : : : : : : : : : : : : : : : : , 15760. m*ssw,
21
20
18
(c)
FIG. 3. Portions of the excitation spectra of the [ 17.0]2-( I ) 1 and [ 16.9]1-( 1) 1 transitions of SmO. (a) [17.0]2-( 1) 1 transition, P branch. (b) [16.9] If-( 1) 1 transition, P branch. (c) [16.9] le-( 1)l transition. P branch.
both transitions. As the Q branches were generally very congested, the above relation greatly assisted in assigning the lines. The same parity-selective detection technique was used to separate the branches of the [16.9] I-X0-and [16.9] 1-(2)0+transitions, asthePandRbranchesof[16.9] lX0- and Q branch of [ 16.91 I-( 2)Of come from the f levels of the upper states and the other branches are from the e levels. Comparisons of upper state combination differences in these transitions with those from the appropriate parity components of [ 16.91 l-( 1) 1 enabled us to assign all three branches, including the highly congested Q branches, of each of the 9 = 1-O transitions. The spectrum of the [ 17.0]2-( 2) 1 transition was obtained and was assigned with the help of the upper state combination differences obtained from the [ 17.0]2-( 1) 1 transition. Only two isotopes have been assigned in this transition. The assignment of transitions to the ( 1)2 state was more difficult. The [ 17.2]3( 1)2 and [ 17.6]3-( 1)2 transitions were the first transitions obtained and assigned ( I), but detailed analysis was difficult as the isotopes were not completely resolved and the R branch of the [ 17.6]3-( 1)2 transition formed a head at low J and was not assigned above J = 9. Because the ( 1)2 state is only -20 cm-’ below the (2)0+ state it is difficult to obtain a clean spectrum of the [ 16.9]1-( 1)2 transition without interference from [ 16.91 l-(2)0+. However, with very careful selection of the monochro-
118
BUJIN AND LINTON
mator wavelength, the two transitions were eventually isolated. The spectra from the e and f components of the [ 16.911 state were separated using the same methods described above for the [ 16.911-a = 1 transitions. The lines were assigned using the known combination differences of the upper state and the lower state combination differences were then used to complete the assignment of the two Q = 3-( 1)2 transitions. During the analysis, several unidentified groups of lines were observed in the regions ofthe [16.9] l-X0- (5910 A) and [17.2]3-( 1)2 (6000 A) transitions. By setting the laser on these lines, resetting the monochromator to maximize the signals, and then scanning the laser, it was possible to isolate these transitions. By comparing lower state combination differences with those of the known states, it was possible to assign the lines and show that the transitions were [16.6] l-X0- (6000 A) and [17.5] l(2)0+ (5910 A). A total of 10 transitions connecting the five lowest states have now been assigned at high resolution. It was possible to assign all seven isotopes for the [ 16.91 l-X0transition and six isotopes for the [16.9]1-( l)l, [16.9]1-(2)0+, and [17.0]2-(1)l transitions. For the other transitions, only the lines corresponding to the two most abundant isotopes, ‘54Sm0 and ‘52Sm0, have been assigned. Analysis Because of the complexity introduced by the large number of isotopes and il-doubling, the assignment and analysis were far from straightforward. However, by carefully and methodically applying the combination difference equalities, ah bands were assigned up to J - 30-40. At first, least-squares fits were performed on each band individually to check the assignments and search for more lines. After that, all the bands were fitted simultaneously using a global least-squares fitting program. The structures of the [ 17.0]2-( 1) 1 and [ 17.0]2-( 2) 1 transitions both appeared to be regular. As previously mentioned (I) the fi doubling in the a = 1 states is large and this is easily observed in Fig. 3. The transitions from the e and f levels of the [ 16.911 state show some striking differences. The perturbation in the f level at J = 5 for ‘54Sm0 has already been mentioned (I). There was also a much smaller shift, with no extra line, in the R( 4) and P(6) lines of the 116.91 l-(2)0+ transition for 154Sm0 showing that the e level at J = 5 is also slightly perturbed. This was also observed in the transitions from [16.9]letothe(l)l and(1)2states. ExaminationofthePbranchofthe [16.9]1( 1) 1 transition in Fig. 3 shows that the structure of the transitions from the f levels above J = 5 is regular. However, it is clearly observed that there is a very strong perturbation in the J = 19 region in the e levels and that it affects all isotopes. Figure 4 shows that the same perturbation is present in the Q branch of this transition and also in the P branch of the [16.9] l-(2)0+ transition. It is also observed in the Q branch of [16.9 ] l-X0- and in the [16.9 ] l-( 1)2 transition. Observations of the R branches are hampered by the formation of band heads in this region. It is clear from the above that there is a strong local perturbation at J = 19 affecting only the e levels of the [ 16.911 state. Comparison of the lower state combination differences with those from the [ 17.0]2-( 1) 1 transition (Table I) has enabled us to
119
HIGH RESOLUTION ANALYSIS OF SmO 25
2L
23
22
21
III
I
20
19
II
18
II
17 I
(a)
1::::::::::::::::::::‘
16754. m35cm-I
(b)
15770.995cm-,
23
22
21
20
19
18
I
I
I
I
I
I
II
II
23
22
21
20
19
18
I
I
I
I
I
I
(c)
15318.0015rm-1
INTERVAL = 10 Gwa
16324.9997ca-1
FIG. 4. Portions of the excitation spectra of the [ 16.911e-( 1) 1 and (2)0+ transitions showing the perturbation at J’= 19. (a) [16.9]le-(l)l, Q branch. (b) [16.9]le-(1)1, Pbranch. (c) [16.9]1e-(2)0+, P branch.
unambiguously assign the perturbed lines for all the isotopes and to conclude that they occur at J = 19 and 20 of the [ 16.911 state. The maximum perturbation occurs at J = 19 and this is clearly seen in the P( 20) transition in Fig. 4. Instead of the normal situation in which the frequency increases with decreasing isotope mass, the four lighter isotopes in the P( 20) transition are at lower frequency than the two heavier isotopes. At J = 20 (see P( 2 1)) the order is back to normal, though the separations are still anomalous. The first global least-squares fit was done without the transitions to the ( 1)2 state in order to determine the constants for the [ 16.911 state including the 0 doubling. These constants were then used with the frequencies of the [ 16.91 le-( 1)2 and ( 16.91 If-( 1)2 transitions to determine the energies of the e and f components of the ( 1)2 state in order to see if there were significant Q doubling in this state. These results showed that there was a small splitting of the e and f components which increased quadratically with J( J + 1)) which is typical of Q doubling in Q = 2 states. Once this was established, it was possible to assign the separate components of the D = 3-( 1)2 transitions. The transitions were then included in the global fit. The results of the global least-squares fit are shown in Table II. All the perturbed lines were removed from the fit but it was not possible to obtain a good fit for the [ 16.911 state unless all the e-level transitions above the perturbation were also removed. This indicates that, even though the high J isotope pattern appears normal, the e
BUJIN AND LINTON
120
TABLE I Combination Differences (cm-‘) for the [16.9] l-( 1)l and [17.0]2-( 1) 1 Transitions of ‘?3mO [16.911-(1)1:5960A IlS.911
J
1111 Q,(J)-P,(J+l)
Q=(J)-Pe(J+ll
Rt(J)-Q,(J)
Rf(Jl-Qf(J+l)
Rf(J)-QftJ+l)
Qf(J+ll-P,(J+l)
4.699 4.699 5.348 5.350
8
6.013 6.013 6.669 6.674 7.334 7.335 7.995 7.994 8.659 8.665 9.324 9.307 9.995 9.993 10.650 10.657 11.325 11.325 11.969 11.973 12.582 12.570
11 12 13 14 15 16 17 18
117.012
Rt(J)-Q,(J)
7
10
(111
Qf(J+l)-P,(J+l)
6
9
[17.012-(1)1:5930A
19
12.017
5.312 5.305 5.920 5.913 6.499 6.491 7.070 7.064 7.612 7.627 8.167 8.167 8.691 8.701 9.212 9.209 9.715 9.710 10.202 10.188 10.676 10.676 11.139 11.136 11.583 11.583 12.014
12.435
12.437
12.841
12.843
13.237
13.241
5.315 5.313 5.911 5.912 6.492 6.487 7.066 7.065 7.624 7.625 8.172 8.166 8.677 8.694 9.208 9.210 9.714 9.706 10.202 10.201 10.677 10.673 11.135 11.147 11.579
12.921 20
14.875
14.626 21 15.148 22
16.386
15.504 23 16.504
4.858 4.858 5.553 5.560 6.238 6.245 6.946 6.954 7.649 7.656 8.364 8.350 9.069 9.070 9.783 9.773 10.493 10.495 11.207 11.213 11.925 11.939 12.661 12.661 13.391 13.394 14.127 14.127
16.386 17.160
levels of the [ 16.911 state are still being affected by the perturbation. Thus, for this state, e levels above J = 17 were not included in the fit. The rotational constants, B, are all typical of rare-earth oxides, i.e., -0.35 cm-‘. In Table II the ratios of the B values to those for the 154Sm0 isotope are shown to agree with the reduced mass ratio, p 2, for all states for all isotopes within the experimental uncertainties. The centrifugal distortion constants, D, are not significant for the two Q = 0 states. For the other low-lying states they are well determined and -23 X lo-’ cm-‘. D is negative for all the upper states, and is particularly large ( - 10e5 cm-‘) for the [ 16.911 state. This is a phenomenon that has been observed for other rare earth oxides and is an indication of small perturbations in the upper states, where there is expected to be a very high density of states. The upper states also needed higher-order constants, H, in order to fit the lines. The Q doubling for the two low-lying D = 1 states has been shown ( 1) to be caused
HIGH RESOLUTION ANALYSIS OF SmO TABLE II Energies and Rotational and t?doubling Constants’ (cm-‘) of Observed States of SmO
121
122
BUJIN AND
LINTON
by interaction with the X0- and (2)0+ states. The approximate constants, q, determined in the previous paper ( I ) were shown to be consistent with the calculated ligand field eigenfunctions (2). More precise Q doubling constants have been determined from the global fit and are given in Table II. For the ( 1) 1 state, an extra term, p[J(J + 1 )] *, was required to fit the lines as well as the regular qJ( J + 1) term. This suggests the possibility that interaction with an fl = 2 state, probably ( 1)2, makes a small contribution to the doubling. The Q doubling in the [ 16.911 state was much smaller than that of the lower states but also required a quadratic term to give a good fit. The two s1 = 2 states were also found to have significant Q doubling which could, as expected, be fitted by thep[J(J + l)]* term. Perturbation in the [16.9] 1 State As mentioned above, two perturbations were observed in the [ 16.911 state. At J = 5, there was the weak perturbation of the f levels and an even weaker perturbation of the e levels affecting only the ‘54Sm0 isotope, and at J = 19 and 20, the much stronger perturbation described above, affecting the e levels of ah isotopes. Thef-level perturbation has been reanalyzed as the previous analysis was based on a limited data set. The shift in energy, 6E, as a result of the perturbation is given by (4)
,,=0.5AE[[l +(&)‘I”‘- l}, where AE is the separation of the perturbed and perturbing states and HI2 is the matrix element connecting the two states. The energy shift, 6E, is the difference between the observed line frequency and that calculated using the molecular constants in Table II. For the R(4) line the calculated frequency is 16 926.260 cm-’ and the actual frequency is 16 926.230 cm-‘, thus 6E = 0.030 cm-‘. The frequency of the extra line is 16 926.3 15 cm-‘, thus the unperturbed position would be at 16 926.285 cm-‘. The perturber is thus AE = 0.025 cm-’ above the 116.911 f level. Using the P branch, we obtain 6E = 0.030 cm-’ and AE = 0.026 cm-‘. Using the average of these values gives HL2 = 0.0408 cm-‘. The values obtained for 6E and hence AE are very dependent on how well the constants reproduce the actual frequencies. With a standard deviation of 0.008 cm-’ in the fit, the uncertainty in the separation, AE, of the states is 0.016 cm-’ , i.e., 62%. However, this leads to only a 5% uncertainty in H,*. Thus AE = 0.026 f 0.016 cm-’ and Hi2 = 0.0408 +- 0.0021 cm- ‘. The earlier analysis ( 1) yielded a value of AE = 0.0093 cm-‘. The relative intensities of the main and extra lines provide a further check on the values of AE and the matrix element. If the unperturbed states are labelled 11 )( [ 16.911) and 12) (perturber) and the X0- state is labelled IO), then we can write the eigenfunction of the [ 16.911 state as lW911)=
C, II)+
GP),
where Cr and CZ are the mixing co-efficients, C$ = 1 - C<, and
c:=; i
1+
HIGH RESOLUTION
ANALYSIS OF SmO
123
As the perturbing state has a very low transition probability to the ground state, the intensities of the main and extra lines are given by
Zextra= (1 - c:M_J, where I0 represents the intensity of the pure [ 16.91 l-X0ratio is thus
transition. The intensity
Zmain c: -=___ Zextra 1 - c: . Using the energy separation and matrix element determined above, we find C: = 0.65 and ZmtinlZextra= 1.86. From the spectrum, we obtain an actual ratio of 1.85. This intensity ratio is very sensitive to a change in AE, thus the agreement between theoretical and experimental intensity ratios strongly suggests that the above value of AE is probably correct. The observations indicate that the J = 5 e level is pushed up by 0.025 cm-‘. Using the R doubling constants in Table II and the results calculated from thef-level perturbation, the perturbing state is expected to be 0.032 cm-’ below the e level and the energy shift is calculated to be 0.028 cm-‘. Thus the calculations, which have ignored any possible doubling in the perturbing state, are consistent with both thef- and elevel observations. The perturber must be an fl = 1 or 2 state as D = 0 states cannot affect both parity components. The fact that only one J and one isotope is affected suggests that the B value of the perturber is considerably different from that of [ 16.9 ] 1. As we have not yet been able to assign extra lines for the e-level perturbation at J = 20, we have been unable to determine the energy separation and matrix elements. Both the direction of the line shifts and the observation that the crossover of the two states occurs at a lower J for the lighter isotopes suggest that the perturbing state is lower than the [ 16.911 state and has a larger B value. This can be more clearly understood by referring to Fig. 5. If the B value of the perturbing state is larger, then both the rotational spacing and the isotope separation will be greater than in the [ 16.911 state. In the figure, the energy levels are drawn for the light (L) and heavy (H) isotopes and the L levels are above the H levels. At J = 19, the H levels of the perturber are below and the L levels above those of [ 16.911. Thus the H levels are pushed up and the L levels down and the order is interchanged. At J = 20, all the perturbed levels are higher and all the [ 16.911 isotope levels are pushed down and the lines appear in their usual order. There are not enough data to determine whether both perturbations are caused by the same state or two different states. If a single state is responsible, we have already shown from the isotope data at J = 19 and 20 that it must be below the [ 16.911 state and have a higher B value. We can examine the J = 5 perturbation to see if it is consistent with these conclusions. The results of the global fit indicate that, in the [ 16.911 state, the e levels are above the f levels. In Fig. 6, we show a typical schematic plot of energy vs. J( J + 1) for an Q-doubled state with E, > Efand a perturbing state with negligible Q doubling that crosses the f levels at J = 5 and the e levels at J = 20. It can be seen that the perturbing state must have a lower energy and a higher B value.
124
BWJIN AND LINTON J L-_-_-L
20
19
L
-
H_-__-H---e-H H LfTfT;;---
L -+
T-T dH
18
L----L----t H----H-_--H
FIG. 5. Schematic diagram showing the opposite shifts in the heavy (H) and light ( L) isotope energies as a result of a local perturbation. The perturbing state is on the right. At J = 19, the lighter isotopes of the perturber are above and the heavier isotopes are below the perturbed state in energy. The dashed lines represent the unperturbed energies and the solid lines the perturbed energies of the two states. The H, L labels on the left and right refer to the perturbed levels of the two states and the center labels refer to the unperturbed levels.
This is consistent with the J = 20 isotope data and it is therefore a possibility that both perturbations are caused by the same state. From the rotational and Q-doubling constants in Table II, the energy separation of the J = 5f and J = 20e levels in the [ 16.911 state is 134.649 cm-‘. If the two states were in exact resonance at these levels and we ignore centrifugal distortion, we obtain that, for the perturbing state, B - 0.345 cm-’ and that (at J = 0) it is 0.16 cm-’ below the [ 16.911 state. Centrifugal distortion would not affect these constants at this level of accuracy. We have ignored the fact that the perturber is 0.026 cm-’ above [ 16.911 at J = 5. However, it is also above [ 16.911 at J = 20 so the correction to the calculated J = 5-20 separation would be small. If there is significant fl doubling in the perturbing state, the f levels must be above the e levels and the B value will be higher and the energy lower than calculated above. If a single state is responsible for both perturbations, it cannot be an Q = 0 state as this would perturb only one component. Because the perturbation at J = 20 is much greater than at J = 5, it would appear that the matrix element is J-dependent, suggesting
...
30
Perturber
420 J(J+l)
FIG. 6. Schematic plot of energy vs. J(J + 1) for an Q-doubled Q = 1 state and a perturbing state with degenerate e and f components. The crossing points represent perturbations at J = 5 (f) and J = 20 (e).
HIGH RESOLUTION ANALYSIS OF SmO
125
a heterogeneous perturbation. Thus, the most likely assignment would be Q = 2. However, there are difficulties with this assignment. If the B value calculated for the perturber is correct, there should be significant and observable perturbations at J = 4 and 6 and none are observed. The J = 20 matrix element calculated from that at J = 5 would not be large enough to account for the observed shifts at J = 19 and 20. Calculations are difficult as the high-order rotational constants of the [ 16.911 state, even though they fit the observed spectrum, are not physically realistic and may not give the true unperturbed energies. Molecular Constants In Table II, it can be seen that the B values for both the Q = 0 states, X0- and (2)0+, are slightly less than those for the other states. However. though these constants reflect the J( J + 1) dependence of the energy levels, they include a contribution from the interaction with the neighboring 0 = 1 states responsible for the Q doubling. This interaction lowers the levels of each Q = 0 state and lowers the effective B value. To take this into account, the Q doubling constants, q, should be added to the quoted ‘effective’ B values to give the true constants. Thus for ‘54Sm0 B[XO-] - 0.35968 1 cm-’ and B[(2)Of] - 0.364557. All the term values in the table represent the energy of the v = 0 level of the state relative to the 2) = 0 level of the ground state, which has been set at zero for each isotope. However, this is not a true representation of the ground state energy as, because of the vibrational isotope shift of -0.5( 1 - p)q, the energy of the v = 0 level of the ground state will increase with decreasing mass. For example, assuming that op - 830 cm-‘, the value of r, relative to 154Sm0, for X0- of “‘SmO, should be 0.257 cm-‘. The term energies of all the states in Table II increase with decreasing mass which suggests that the vibrational frequencies are slightly higher than that of the ground state. This would be very surprising if true for the upper states. However, because of the large number of states and probable interactions between them, it is felt that the constants (e.g., the negative D values) all probably contain perturbation terms of similar functional form and that the term values do not reflect the true positions of the unperturbed electronic states. For the lower states, the isotope shifts are possibly more meaningful. CONCLUSIONS
The above analysis has shown that, with very careful wavelength-selective detection, it is possible to analyze all isotopes in a spectrum even when there are many closelying states and D doubling. The analysis shows that the B values for all the states vary according to the calculated isotopic dependence. The Q doubling in the low-lying R = 1 states can be understood in terms of the interaction with neighboring D = 0 states and is consistent with Ligand Field calculations. The Q doubling in the ( I)2 state can be qualitatively understood in terms of its interaction with the low-lying Q = 1 states but it is felt that more and higher quality data are needed in order to analyze it quantitatively. The perturbations in the [ 16.911 state are qualitatively consistent with a lower-lying Q = 2 perturber with a larger B value, but there are quantitative difficulties, and this assignment is far from conclusive. The large number of isotopic
BUJIN AND LINTON
126
lines mask many of the extra lines needed to evaluate the matrix elements at the J = 20 perturbation. This paper has presented the first detailed rotational analysis of the samarium oxide spectrum. There are stiII many unresolved questions requiring further study. More detailed experiments, for example, optical optical double resonance, are required to assign extra lines in the perturbed regions. The Q branch of the [ 16.91 lJ--( 1) 1 transition was found to be very intense whereas that in [ 16.91 le-( 1) 1 was very weak. This is not yet understood and requires further investigation. Many other low-lying states have been observed in resolved fluorescence in the 6000-6700-A region and it is hoped to obtain excitation spectra involving these states in the near future using Kiton red and DCM dyes. Several of these transitions involve the [ 17.213 and [ 17.613 states which, in the present analysis, appeared to show some n doubling. However, this is uncertain as for lower J’s the isotopic structure was not clearly resolved, resulting in a poorer fit. Observation of more transitions involving these Q = 3 states will considerably improve the analysis. Transitions involving u = 1 levels of the lowest states also appear in this region and analysis of these for the different isotopes should provide reliable vibrational frequencies for the upper and lower states. Work is proceeding along these directions and will be reported in future publications.
ACKNOWLEDGMENTS This work has been funded by the Natural Sciences and Engineering Research Council of Canada. Some of the work was performed in the laboratory of Professor R. W. Field at MIT under a grant from the National Science Foundation (PHY 83-20098). RECEIVED:
April 10, 1989 REFERENCES
1. 2. 3. 4.
C. LINTON,Guo BUJIN,R. S. RANA, AND J. A. GRAY, J. Mol. Spectrosc. 126, 310-392 ( 1987). M. DULICK,E. MURAD, AND R. F. BARROW,J. Chem. Phys. 85385-390 (1986). P. CAREITEAND A. HOCQUET,J. Mol. Spectrosc. 131, 301-324, ( 1988). H. LEFEBVRE-BRION ANDR. W. FIELD,“Perturbations in the Spectraof DiatomicMolecules,”Academic Press, 1986.
137, l14- 126 ( 1989)
High Resolution Analysis of Transitions to the Five Lowest Electronic States of Samarium Monoxide Guo
BUJIN AND C. LINTON
PhysicsDepartment, Universityof New Brunswick,Fredericton, New Brunswick,Canada E3B 5A3 Hi resolution excitation spectra have been obtained and analyzed for 10 electronic transitions of samarium monoxide involving five low-lying and six upper states. A global fit to all the lines has yielded electronic term energies, rotational constants, and 51doubling parameters of all the states for six (and in one case seven) isotopes of samarium. The isotopic variation of the constants was examined and the B values were found to satisfy the normal isotope relations. Local perturbations in the [ 16.911 state have been assigned and analyzed. Q 1989Academicpress, I~C. INTRODUCTION
In a recent publication ( 1) we presented and discussed the assignments of 11 lowlying electronic states of the SmO molecule. The results were compared with ligand field theory calculations (2,3) and, in particular, it was found that there was excellent agreement between the energies of the observed electronic states and those calculated by Carette and Hocquet (3). The eigenfunctions were found to be consistent with the observed Q doubling of low-lying s2 = 1 states. The results were based on medium resolution resolved fluorescence spectra and high resolution excitation spectra involving the ground state (X0-) and the lowest rotational levels of the other lowest-lying states. We have recently undertaken a more detailed investigation, at high resolution, of transitions involving the lowest fi = 0, 1, and 2 states. The transitions investigated are shown in Fig. 1; it can be seen that there is more than one transition involving eachofthe[16.9]1,[17.0]2,XO~,(1)1,(1)2,and(2)0~states.‘Thisgreatlyfacilitated the analysis and provided important linkages between the states. The results of the detailed rotational analysis for the six most abundant isotopes of samarium (masses 154, 152, 150, 149, 148, 147) are presented in this paper along with a discussion of observed perturbations. EXPERIMENTAL
DETAILS
The sources of SmO (Broida oven and sputter source) and the rest of the equipment (lasers, spectrometers, etc.) are the same as those described in the previous paper ( I ). Because of the very heavy congestion in the spectra, extreme care had to be taken in selecting the appropriate monochromator wavelengths at which to detect the excitation spectra. This will be discussed in detail in the following sections.
’ The labeling of the states has been described elsewhere ( 1). The upper states are labeled [ To]il, where To is in thousands of cm-‘, and the lower states are labeled (N)Q, representing the Nth state of a given Q. CQ22-2852189$3.00 CopyriBbt0 1989 by Academic Pms, Inc. All ri&ts of reproductionin any farm rew-vcd.
114
HIGH RESOLUTION
ANALYSIS OF SmO
115
116.611
.
rib” FIG. 1. Transitions of SmO analyzed at high resolution in the present investigation, RESULTS AND ANALYSIS
Assignment of the Transitions The analysis of the R and P branches of the [ 16.91 l-X0- transition for the 154 and 152 isotopes was presented in the earlier paper ( I ) . The extension of the analysis to include the other isotopes and the Q branch will be discussed later in this section. The main result to note from the earlier analysis is the very localized perturbation at J = 5 of the [ 16.911 state which affects only the one rotational level and only the 154 isotope. The detection and analysis of the other transitions are discussed below. The [17.0]2-( 1) 1 and [ 16.91 I-( 1) 1 transitions were assigned together as the combination differences of the lower state are the same for both. Because of the G doubling, particularly in the ( 1) 1 state and the six abundant (and one less abundant) isotopes of Sm, the spectra are extremely complex with each rotational transition consisting of 12 lines. There was no way of simplifying the spectrum for the [ 17.0]2-( 1) 1 transition as detection of any band originating in the [ 17.012 state would involve both the e and f parity components. However, because of the special parity-selective properties of Q = 1-O transitions, it was possible to separate the parity components in the [ 16-91 I-( 1) 1 transition. This can most easily be understood by referring to Fig. 2. The solid lines represent the transitions involving the e levels of the upper state and the dashed lines connect the f levels. The monochromator was first carefully set to detect the Q branch of the[ 16.91 l-X0- band, which consists entirely of n = le-O-f transitions. Thus, only transitions originating from the e levels of the upper state can be detected. When the laser is scanned through the [ 16.91 I-( 1) 1 band at -5930 A,
BUJIN AND LINTON
116
[ 16.91 1
lL’”
III
J+I J-l
L
-f
‘Y==++
J+l
4
J-l
b;
f f
:
(111
xo-
FIG. 2. Schematic diagram showing parity-selective excitation of the [ 16.91 l-( 1) 1 transition. By setting the monochromator to detect the Q branch of the [16.9] l-X0- or 116.91l-(2)0+ transitions, only the e or f levels of the upper state are detected.
even though both parity components will be excited, only the lines originating from the upper state e levels will appear in the excitation spectrum. The P and R branches will go to the e levels in the ( 1) 1 state and the Q branch will go to the f levels. The monochromator was then set to detect the Q branch of the [ 16.91 l-( 2)0+ transition and only the f levels of the upper state could be detected going to the e( Q branch) and S( P and R branches) levels of the ( 1) 1 state. The success of the technique is clearly seen in Fig. 3. The top spectrum, (a), shows the complexity of the [ 17.0]2( 1) 1 spectrum in which all transitions are present. The bottom two spectra both show the same spectral region of the [ 16.9 ] 1- ( 1) 1 spectrum but detecting the f-component in (b) and the e-component in (c). It can be seen that the spectra are completely different and the two components can be assigned separately and with relative simplicity. The assignment of the spectra relied heavily on the use of narrow band-pass selectivity in detection and on combination differences. With narrow slits, the monochromator could detect only a narrow range of J in the upper state and, when the laser scanned through the R, Q, and P branches of a transition, only the lines in each branch originating in this J-range would appear in the spectrum. A preliminary assignment could then be made by trying to match the corresponding lines (i.e., same J’) in each branch. The final assignments were then made using combination difference relations. For example, the lower state combination relation
R,(J) - Qe(J+ 1) = Qf
HIGH RESOLUTION
Pe
21
pf
1 23
ANALYSIS OF SmO
19
1
17
I
121 I
19 1 I
117
I I
(a)
20
p’
I
18
I
16 I
W I:::::: 1675Z. 5037cn-1
pe
23
: : : : : : : : : : : : : : : : : , 15760. m*ssw,
21
20
18
(c)
FIG. 3. Portions of the excitation spectra of the [ 17.0]2-( I ) 1 and [ 16.9]1-( 1) 1 transitions of SmO. (a) [17.0]2-( 1) 1 transition, P branch. (b) [16.9] If-( 1) 1 transition, P branch. (c) [16.9] le-( 1)l transition. P branch.
both transitions. As the Q branches were generally very congested, the above relation greatly assisted in assigning the lines. The same parity-selective detection technique was used to separate the branches of the [16.9] I-X0-and [16.9] 1-(2)0+transitions, asthePandRbranchesof[16.9] lX0- and Q branch of [ 16.91 I-( 2)Of come from the f levels of the upper states and the other branches are from the e levels. Comparisons of upper state combination differences in these transitions with those from the appropriate parity components of [ 16.91 l-( 1) 1 enabled us to assign all three branches, including the highly congested Q branches, of each of the 9 = 1-O transitions. The spectrum of the [ 17.0]2-( 2) 1 transition was obtained and was assigned with the help of the upper state combination differences obtained from the [ 17.0]2-( 1) 1 transition. Only two isotopes have been assigned in this transition. The assignment of transitions to the ( 1)2 state was more difficult. The [ 17.2]3( 1)2 and [ 17.6]3-( 1)2 transitions were the first transitions obtained and assigned ( I), but detailed analysis was difficult as the isotopes were not completely resolved and the R branch of the [ 17.6]3-( 1)2 transition formed a head at low J and was not assigned above J = 9. Because the ( 1)2 state is only -20 cm-’ below the (2)0+ state it is difficult to obtain a clean spectrum of the [ 16.9]1-( 1)2 transition without interference from [ 16.91 l-(2)0+. However, with very careful selection of the monochro-
118
BUJIN AND LINTON
mator wavelength, the two transitions were eventually isolated. The spectra from the e and f components of the [ 16.911 state were separated using the same methods described above for the [ 16.911-a = 1 transitions. The lines were assigned using the known combination differences of the upper state and the lower state combination differences were then used to complete the assignment of the two Q = 3-( 1)2 transitions. During the analysis, several unidentified groups of lines were observed in the regions ofthe [16.9] l-X0- (5910 A) and [17.2]3-( 1)2 (6000 A) transitions. By setting the laser on these lines, resetting the monochromator to maximize the signals, and then scanning the laser, it was possible to isolate these transitions. By comparing lower state combination differences with those of the known states, it was possible to assign the lines and show that the transitions were [16.6] l-X0- (6000 A) and [17.5] l(2)0+ (5910 A). A total of 10 transitions connecting the five lowest states have now been assigned at high resolution. It was possible to assign all seven isotopes for the [ 16.91 l-X0transition and six isotopes for the [16.9]1-( l)l, [16.9]1-(2)0+, and [17.0]2-(1)l transitions. For the other transitions, only the lines corresponding to the two most abundant isotopes, ‘54Sm0 and ‘52Sm0, have been assigned. Analysis Because of the complexity introduced by the large number of isotopes and il-doubling, the assignment and analysis were far from straightforward. However, by carefully and methodically applying the combination difference equalities, ah bands were assigned up to J - 30-40. At first, least-squares fits were performed on each band individually to check the assignments and search for more lines. After that, all the bands were fitted simultaneously using a global least-squares fitting program. The structures of the [ 17.0]2-( 1) 1 and [ 17.0]2-( 2) 1 transitions both appeared to be regular. As previously mentioned (I) the fi doubling in the a = 1 states is large and this is easily observed in Fig. 3. The transitions from the e and f levels of the [ 16.911 state show some striking differences. The perturbation in the f level at J = 5 for ‘54Sm0 has already been mentioned (I). There was also a much smaller shift, with no extra line, in the R( 4) and P(6) lines of the 116.91 l-(2)0+ transition for 154Sm0 showing that the e level at J = 5 is also slightly perturbed. This was also observed in the transitions from [16.9]letothe(l)l and(1)2states. ExaminationofthePbranchofthe [16.9]1( 1) 1 transition in Fig. 3 shows that the structure of the transitions from the f levels above J = 5 is regular. However, it is clearly observed that there is a very strong perturbation in the J = 19 region in the e levels and that it affects all isotopes. Figure 4 shows that the same perturbation is present in the Q branch of this transition and also in the P branch of the [16.9] l-(2)0+ transition. It is also observed in the Q branch of [16.9 ] l-X0- and in the [16.9 ] l-( 1)2 transition. Observations of the R branches are hampered by the formation of band heads in this region. It is clear from the above that there is a strong local perturbation at J = 19 affecting only the e levels of the [ 16.911 state. Comparison of the lower state combination differences with those from the [ 17.0]2-( 1) 1 transition (Table I) has enabled us to
119
HIGH RESOLUTION ANALYSIS OF SmO 25
2L
23
22
21
III
I
20
19
II
18
II
17 I
(a)
1::::::::::::::::::::‘
16754. m35cm-I
(b)
15770.995cm-,
23
22
21
20
19
18
I
I
I
I
I
I
II
II
23
22
21
20
19
18
I
I
I
I
I
I
(c)
15318.0015rm-1
INTERVAL = 10 Gwa
16324.9997ca-1
FIG. 4. Portions of the excitation spectra of the [ 16.911e-( 1) 1 and (2)0+ transitions showing the perturbation at J’= 19. (a) [16.9]le-(l)l, Q branch. (b) [16.9]le-(1)1, Pbranch. (c) [16.9]1e-(2)0+, P branch.
unambiguously assign the perturbed lines for all the isotopes and to conclude that they occur at J = 19 and 20 of the [ 16.911 state. The maximum perturbation occurs at J = 19 and this is clearly seen in the P( 20) transition in Fig. 4. Instead of the normal situation in which the frequency increases with decreasing isotope mass, the four lighter isotopes in the P( 20) transition are at lower frequency than the two heavier isotopes. At J = 20 (see P( 2 1)) the order is back to normal, though the separations are still anomalous. The first global least-squares fit was done without the transitions to the ( 1)2 state in order to determine the constants for the [ 16.911 state including the 0 doubling. These constants were then used with the frequencies of the [ 16.91 le-( 1)2 and ( 16.91 If-( 1)2 transitions to determine the energies of the e and f components of the ( 1)2 state in order to see if there were significant Q doubling in this state. These results showed that there was a small splitting of the e and f components which increased quadratically with J( J + 1)) which is typical of Q doubling in Q = 2 states. Once this was established, it was possible to assign the separate components of the D = 3-( 1)2 transitions. The transitions were then included in the global fit. The results of the global least-squares fit are shown in Table II. All the perturbed lines were removed from the fit but it was not possible to obtain a good fit for the [ 16.911 state unless all the e-level transitions above the perturbation were also removed. This indicates that, even though the high J isotope pattern appears normal, the e
BUJIN AND LINTON
120
TABLE I Combination Differences (cm-‘) for the [16.9] l-( 1)l and [17.0]2-( 1) 1 Transitions of ‘?3mO [16.911-(1)1:5960A IlS.911
J
1111 Q,(J)-P,(J+l)
Q=(J)-Pe(J+ll
Rt(J)-Q,(J)
Rf(Jl-Qf(J+l)
Rf(J)-QftJ+l)
Qf(J+ll-P,(J+l)
4.699 4.699 5.348 5.350
8
6.013 6.013 6.669 6.674 7.334 7.335 7.995 7.994 8.659 8.665 9.324 9.307 9.995 9.993 10.650 10.657 11.325 11.325 11.969 11.973 12.582 12.570
11 12 13 14 15 16 17 18
117.012
Rt(J)-Q,(J)
7
10
(111
Qf(J+l)-P,(J+l)
6
9
[17.012-(1)1:5930A
19
12.017
5.312 5.305 5.920 5.913 6.499 6.491 7.070 7.064 7.612 7.627 8.167 8.167 8.691 8.701 9.212 9.209 9.715 9.710 10.202 10.188 10.676 10.676 11.139 11.136 11.583 11.583 12.014
12.435
12.437
12.841
12.843
13.237
13.241
5.315 5.313 5.911 5.912 6.492 6.487 7.066 7.065 7.624 7.625 8.172 8.166 8.677 8.694 9.208 9.210 9.714 9.706 10.202 10.201 10.677 10.673 11.135 11.147 11.579
12.921 20
14.875
14.626 21 15.148 22
16.386
15.504 23 16.504
4.858 4.858 5.553 5.560 6.238 6.245 6.946 6.954 7.649 7.656 8.364 8.350 9.069 9.070 9.783 9.773 10.493 10.495 11.207 11.213 11.925 11.939 12.661 12.661 13.391 13.394 14.127 14.127
16.386 17.160
levels of the [ 16.911 state are still being affected by the perturbation. Thus, for this state, e levels above J = 17 were not included in the fit. The rotational constants, B, are all typical of rare-earth oxides, i.e., -0.35 cm-‘. In Table II the ratios of the B values to those for the 154Sm0 isotope are shown to agree with the reduced mass ratio, p 2, for all states for all isotopes within the experimental uncertainties. The centrifugal distortion constants, D, are not significant for the two Q = 0 states. For the other low-lying states they are well determined and -23 X lo-’ cm-‘. D is negative for all the upper states, and is particularly large ( - 10e5 cm-‘) for the [ 16.911 state. This is a phenomenon that has been observed for other rare earth oxides and is an indication of small perturbations in the upper states, where there is expected to be a very high density of states. The upper states also needed higher-order constants, H, in order to fit the lines. The Q doubling for the two low-lying D = 1 states has been shown ( 1) to be caused
HIGH RESOLUTION ANALYSIS OF SmO TABLE II Energies and Rotational and t?doubling Constants’ (cm-‘) of Observed States of SmO
121
122
BUJIN AND
LINTON
by interaction with the X0- and (2)0+ states. The approximate constants, q, determined in the previous paper ( I ) were shown to be consistent with the calculated ligand field eigenfunctions (2). More precise Q doubling constants have been determined from the global fit and are given in Table II. For the ( 1) 1 state, an extra term, p[J(J + 1 )] *, was required to fit the lines as well as the regular qJ( J + 1) term. This suggests the possibility that interaction with an fl = 2 state, probably ( 1)2, makes a small contribution to the doubling. The Q doubling in the [ 16.911 state was much smaller than that of the lower states but also required a quadratic term to give a good fit. The two s1 = 2 states were also found to have significant Q doubling which could, as expected, be fitted by thep[J(J + l)]* term. Perturbation in the [16.9] 1 State As mentioned above, two perturbations were observed in the [ 16.911 state. At J = 5, there was the weak perturbation of the f levels and an even weaker perturbation of the e levels affecting only the ‘54Sm0 isotope, and at J = 19 and 20, the much stronger perturbation described above, affecting the e levels of ah isotopes. Thef-level perturbation has been reanalyzed as the previous analysis was based on a limited data set. The shift in energy, 6E, as a result of the perturbation is given by (4)
,,=0.5AE[[l +(&)‘I”‘- l}, where AE is the separation of the perturbed and perturbing states and HI2 is the matrix element connecting the two states. The energy shift, 6E, is the difference between the observed line frequency and that calculated using the molecular constants in Table II. For the R(4) line the calculated frequency is 16 926.260 cm-’ and the actual frequency is 16 926.230 cm-‘, thus 6E = 0.030 cm-‘. The frequency of the extra line is 16 926.3 15 cm-‘, thus the unperturbed position would be at 16 926.285 cm-‘. The perturber is thus AE = 0.025 cm-’ above the 116.911 f level. Using the P branch, we obtain 6E = 0.030 cm-’ and AE = 0.026 cm-‘. Using the average of these values gives HL2 = 0.0408 cm-‘. The values obtained for 6E and hence AE are very dependent on how well the constants reproduce the actual frequencies. With a standard deviation of 0.008 cm-’ in the fit, the uncertainty in the separation, AE, of the states is 0.016 cm-’ , i.e., 62%. However, this leads to only a 5% uncertainty in H,*. Thus AE = 0.026 f 0.016 cm-’ and Hi2 = 0.0408 +- 0.0021 cm- ‘. The earlier analysis ( 1) yielded a value of AE = 0.0093 cm-‘. The relative intensities of the main and extra lines provide a further check on the values of AE and the matrix element. If the unperturbed states are labelled 11 )( [ 16.911) and 12) (perturber) and the X0- state is labelled IO), then we can write the eigenfunction of the [ 16.911 state as lW911)=
C, II)+
GP),
where Cr and CZ are the mixing co-efficients, C$ = 1 - C<, and
c:=; i
1+
HIGH RESOLUTION
ANALYSIS OF SmO
123
As the perturbing state has a very low transition probability to the ground state, the intensities of the main and extra lines are given by
Zextra= (1 - c:M_J, where I0 represents the intensity of the pure [ 16.91 l-X0ratio is thus
transition. The intensity
Zmain c: -=___ Zextra 1 - c: . Using the energy separation and matrix element determined above, we find C: = 0.65 and ZmtinlZextra= 1.86. From the spectrum, we obtain an actual ratio of 1.85. This intensity ratio is very sensitive to a change in AE, thus the agreement between theoretical and experimental intensity ratios strongly suggests that the above value of AE is probably correct. The observations indicate that the J = 5 e level is pushed up by 0.025 cm-‘. Using the R doubling constants in Table II and the results calculated from thef-level perturbation, the perturbing state is expected to be 0.032 cm-’ below the e level and the energy shift is calculated to be 0.028 cm-‘. Thus the calculations, which have ignored any possible doubling in the perturbing state, are consistent with both thef- and elevel observations. The perturber must be an fl = 1 or 2 state as D = 0 states cannot affect both parity components. The fact that only one J and one isotope is affected suggests that the B value of the perturber is considerably different from that of [ 16.9 ] 1. As we have not yet been able to assign extra lines for the e-level perturbation at J = 20, we have been unable to determine the energy separation and matrix elements. Both the direction of the line shifts and the observation that the crossover of the two states occurs at a lower J for the lighter isotopes suggest that the perturbing state is lower than the [ 16.911 state and has a larger B value. This can be more clearly understood by referring to Fig. 5. If the B value of the perturbing state is larger, then both the rotational spacing and the isotope separation will be greater than in the [ 16.911 state. In the figure, the energy levels are drawn for the light (L) and heavy (H) isotopes and the L levels are above the H levels. At J = 19, the H levels of the perturber are below and the L levels above those of [ 16.911. Thus the H levels are pushed up and the L levels down and the order is interchanged. At J = 20, all the perturbed levels are higher and all the [ 16.911 isotope levels are pushed down and the lines appear in their usual order. There are not enough data to determine whether both perturbations are caused by the same state or two different states. If a single state is responsible, we have already shown from the isotope data at J = 19 and 20 that it must be below the [ 16.911 state and have a higher B value. We can examine the J = 5 perturbation to see if it is consistent with these conclusions. The results of the global fit indicate that, in the [ 16.911 state, the e levels are above the f levels. In Fig. 6, we show a typical schematic plot of energy vs. J( J + 1) for an Q-doubled state with E, > Efand a perturbing state with negligible Q doubling that crosses the f levels at J = 5 and the e levels at J = 20. It can be seen that the perturbing state must have a lower energy and a higher B value.
124
BWJIN AND LINTON J L-_-_-L
20
19
L
-
H_-__-H---e-H H LfTfT;;---
L -+
T-T dH
18
L----L----t H----H-_--H
FIG. 5. Schematic diagram showing the opposite shifts in the heavy (H) and light ( L) isotope energies as a result of a local perturbation. The perturbing state is on the right. At J = 19, the lighter isotopes of the perturber are above and the heavier isotopes are below the perturbed state in energy. The dashed lines represent the unperturbed energies and the solid lines the perturbed energies of the two states. The H, L labels on the left and right refer to the perturbed levels of the two states and the center labels refer to the unperturbed levels.
This is consistent with the J = 20 isotope data and it is therefore a possibility that both perturbations are caused by the same state. From the rotational and Q-doubling constants in Table II, the energy separation of the J = 5f and J = 20e levels in the [ 16.911 state is 134.649 cm-‘. If the two states were in exact resonance at these levels and we ignore centrifugal distortion, we obtain that, for the perturbing state, B - 0.345 cm-’ and that (at J = 0) it is 0.16 cm-’ below the [ 16.911 state. Centrifugal distortion would not affect these constants at this level of accuracy. We have ignored the fact that the perturber is 0.026 cm-’ above [ 16.911 at J = 5. However, it is also above [ 16.911 at J = 20 so the correction to the calculated J = 5-20 separation would be small. If there is significant fl doubling in the perturbing state, the f levels must be above the e levels and the B value will be higher and the energy lower than calculated above. If a single state is responsible for both perturbations, it cannot be an Q = 0 state as this would perturb only one component. Because the perturbation at J = 20 is much greater than at J = 5, it would appear that the matrix element is J-dependent, suggesting
...
30
Perturber
420 J(J+l)
FIG. 6. Schematic plot of energy vs. J(J + 1) for an Q-doubled Q = 1 state and a perturbing state with degenerate e and f components. The crossing points represent perturbations at J = 5 (f) and J = 20 (e).
HIGH RESOLUTION ANALYSIS OF SmO
125
a heterogeneous perturbation. Thus, the most likely assignment would be Q = 2. However, there are difficulties with this assignment. If the B value calculated for the perturber is correct, there should be significant and observable perturbations at J = 4 and 6 and none are observed. The J = 20 matrix element calculated from that at J = 5 would not be large enough to account for the observed shifts at J = 19 and 20. Calculations are difficult as the high-order rotational constants of the [ 16.911 state, even though they fit the observed spectrum, are not physically realistic and may not give the true unperturbed energies. Molecular Constants In Table II, it can be seen that the B values for both the Q = 0 states, X0- and (2)0+, are slightly less than those for the other states. However. though these constants reflect the J( J + 1) dependence of the energy levels, they include a contribution from the interaction with the neighboring 0 = 1 states responsible for the Q doubling. This interaction lowers the levels of each Q = 0 state and lowers the effective B value. To take this into account, the Q doubling constants, q, should be added to the quoted ‘effective’ B values to give the true constants. Thus for ‘54Sm0 B[XO-] - 0.35968 1 cm-’ and B[(2)Of] - 0.364557. All the term values in the table represent the energy of the v = 0 level of the state relative to the 2) = 0 level of the ground state, which has been set at zero for each isotope. However, this is not a true representation of the ground state energy as, because of the vibrational isotope shift of -0.5( 1 - p)q, the energy of the v = 0 level of the ground state will increase with decreasing mass. For example, assuming that op - 830 cm-‘, the value of r, relative to 154Sm0, for X0- of “‘SmO, should be 0.257 cm-‘. The term energies of all the states in Table II increase with decreasing mass which suggests that the vibrational frequencies are slightly higher than that of the ground state. This would be very surprising if true for the upper states. However, because of the large number of states and probable interactions between them, it is felt that the constants (e.g., the negative D values) all probably contain perturbation terms of similar functional form and that the term values do not reflect the true positions of the unperturbed electronic states. For the lower states, the isotope shifts are possibly more meaningful. CONCLUSIONS
The above analysis has shown that, with very careful wavelength-selective detection, it is possible to analyze all isotopes in a spectrum even when there are many closelying states and D doubling. The analysis shows that the B values for all the states vary according to the calculated isotopic dependence. The Q doubling in the low-lying R = 1 states can be understood in terms of the interaction with neighboring D = 0 states and is consistent with Ligand Field calculations. The Q doubling in the ( I)2 state can be qualitatively understood in terms of its interaction with the low-lying Q = 1 states but it is felt that more and higher quality data are needed in order to analyze it quantitatively. The perturbations in the [ 16.911 state are qualitatively consistent with a lower-lying Q = 2 perturber with a larger B value, but there are quantitative difficulties, and this assignment is far from conclusive. The large number of isotopic
BUJIN AND LINTON
126
lines mask many of the extra lines needed to evaluate the matrix elements at the J = 20 perturbation. This paper has presented the first detailed rotational analysis of the samarium oxide spectrum. There are stiII many unresolved questions requiring further study. More detailed experiments, for example, optical optical double resonance, are required to assign extra lines in the perturbed regions. The Q branch of the [ 16.91 lJ--( 1) 1 transition was found to be very intense whereas that in [ 16.91 le-( 1) 1 was very weak. This is not yet understood and requires further investigation. Many other low-lying states have been observed in resolved fluorescence in the 6000-6700-A region and it is hoped to obtain excitation spectra involving these states in the near future using Kiton red and DCM dyes. Several of these transitions involve the [ 17.213 and [ 17.613 states which, in the present analysis, appeared to show some n doubling. However, this is uncertain as for lower J’s the isotopic structure was not clearly resolved, resulting in a poorer fit. Observation of more transitions involving these Q = 3 states will considerably improve the analysis. Transitions involving u = 1 levels of the lowest states also appear in this region and analysis of these for the different isotopes should provide reliable vibrational frequencies for the upper and lower states. Work is proceeding along these directions and will be reported in future publications.
ACKNOWLEDGMENTS This work has been funded by the Natural Sciences and Engineering Research Council of Canada. Some of the work was performed in the laboratory of Professor R. W. Field at MIT under a grant from the National Science Foundation (PHY 83-20098). RECEIVED:
April 10, 1989 REFERENCES
1. 2. 3. 4.
C. LINTON,Guo BUJIN,R. S. RANA, AND J. A. GRAY, J. Mol. Spectrosc. 126, 310-392 ( 1987). M. DULICK,E. MURAD, AND R. F. BARROW,J. Chem. Phys. 85385-390 (1986). P. CAREITEAND A. HOCQUET,J. Mol. Spectrosc. 131, 301-324, ( 1988). H. LEFEBVRE-BRION ANDR. W. FIELD,“Perturbations in the Spectraof DiatomicMolecules,”Academic Press, 1986.