- Email: [email protected]
A study of the excited 1Σ+g states in Na2
Volume 39, number 1,2
OPTICS COMMUNICATIONS
15 September 1981
A STUDY OF THE EXCITED 1 Zg STATES IN Na 2 * ql~5
A.J. T A Y L O R * , K.M. JONES and A.L. SCHAWLOW Department of Physics, Stanford University, Stanford, CA 94305, USA Received 15 June 1981 Using the technique of two-step polarization labeling spectroscopy seven excnted ~g states m Na2 have been found. Molecular constants are derived from a Dunham expansion. Tentative assignments are made to the 3p+3p, 3s+nd and 3s+ns atomic asymptotes. •
•
l
+
"
1. Introduction
2. Experiment
We present here a study of excited I y.g states in Na 2 whose energies lie between 28300 cm -1 and 37800 cm -1. These gerade states are inaccessible using one-photon absorption techniques from the l ~ g state of Na 2 because of the inversion symmetry selection rule. However, Harvey [1 ] and Woerdman [2] observed strong cw two-photon transitions in the visible, which must end on gerade states in this region. Morgan et al. [3] have observed more than a dozen such transitions. From a practical point of view, these states are important as potential sources of new laser lines [4]. Bernheim et al. [5] have shown that corresponding states in Li 2 exhibit interesting perturbations. In previous papers [ 6 - 9 ] we have reported on our study of excited gerade states in Na2, using two-step polarization labeling spectroscopy. Twenty-four new lAg, ll-lg and IZ+ states, lying between 28300 cm -1 and 38900 cm -lg, were reported. In these papers, the properties of the seventeen lAg and ll'Ig states were thoroughly discussed, while only preliminary constants were reported for the 12Eg states. Because of the recent interest in the two-photon process, we present here a more detailed, but still preliminary, description of these excited l ~ g states.
The technique of two-step polarization labeling spectroscopy, as well as the apparatus and procedure for this experiment, have been described in detail in ref. [9], and will not be discussed here. The l ~ g states were observed while pumping single vibrational-rotational transitions from the X 1 ~g+ to A I Z g states in Na 2. The v --- 1,4, 7 - 1 1 , 1 3 , 18 levels of the A state were pumped; several different values of J in each band were studied. These states were not observed when pumping the X I Z g to B III u states, although transitions to these I Z g states from the B state should be allowed. When the A IZu+ state of Na 2 is pumped, transitions are allowed to higher 1Zg states and ll-lg states. Transitions to l ~ g states can be distinguished from transitions to 1Hg states by the absence of Q branches in the former when a linearly polarized pump beam is used. Unfortunately, for probe wavelengths longer than 5500 A, transitions from the lower level of the pump transition to various levels in the A state can produce polarization signals. Q branches are also absent in these one-step transitions. We distinguish between two-step signals to higher excited 1~ g states and one-step signals to the A state in two ways. First, the constants of the X and A states are well known [10,11], so possible one-step signals are compared with predicted transition energies from the lower level of the pump transition. Secondly, if the probe is delayed relative to the pump by the lifetime of the A
~' Work supported by the National Science Foundation under Grant PHY80-10689. * Hertz Foundation Predoctoral Fellow.
47
Volume 39, number 1,2
OPTICS COMMUNICATIONS
state, (about 12 ns), then two-step signals will become weaker, while one-step signals will not be appreciably affected.
3. Results We have studied seven excited 1Z; states in Na 2 . Fig. 1 displays the electronic energies and tentative atomic asymptotes of these states, as well as the region of each state which has been examined experimentally. The data for each state is fitted to a Dunham expansion, of the form:
T(v,J) = ~.. Yi/(v+~)i (J(J+l))/. tl
The valuesof J and v for each line must be known. We know the value of J for the upper level of the pump transition from the previously determined constants of the A state, hence the value of J is known for each two-step signal. The vibrational assignment in the unknown state is less certain. We look for a sharp cut-off
3s+Sd ATOMI C ASYMPTOTE "x
3s+6s
3s+4d
40,000
3p+3p
3S+SSlI1 E
2"
×
o 30,000
~-.EXPERIMENTALLY OBSERVED REGION
--g
m
" o
3s*3p T A'~
BOTTOM OF POTENTIAL WELL
I~; EXCITED STATES
2o,oooL ~B'nu Fig. 1. Energy level diagram of excited 1 X.+ states. Included for each of the five lowest states is the bottom of the potential well, the atomic asymptote assignment, and the region studied experimentally. The two highest states are less well studied, so only the bottom of the potential well is indictaed. 48
15 September 1981
in signals to tile red when low vibrational bands of the A state are pumped to find the lowest vibrational band in the unknown state. However, bad Franck--Condon factors can produce the same effect, especially when photographic detection is used. Since we have not yet pumped the v = 0 band of the A state, we are not certain that we have found the v = 0 band in any of our states. We do see a cut-off when the v = 1 level of the A state is pumped, so it seems reasonable that the lowest level we have seen corresponds to v = 0 or v = 1. We have probably seen the lowest vibrational band for the state lowest in energy, since a cut-off occured in the same band while pumping the v = 1 and v = 4 bands in the A state. However, this is not certain, since these signals occured at the red end of a probe profile, and we were not able to go farther to tile red with commercially available dyes. For the purpose of fitting our results to a Dunham expansion, we have assigned the lowest observed band to v = 0. The coefficients along with the range of vibrational bands used for the fit of each state are listed in table 1. Unfortunately, the values of the coefficients depend on the range of v and J that is fit, as well as the number of coefficients included. The range of J in each band was limited to 10 < J < 40. However, we did not have a uniform coverage of this range in all bands. After removing a few deviant points we find that the estimated error of the fit is less than 0.5 cm --1 in agreement with the uncertainty in making a single measurement. For each state, the expansion fits the data smoothly; we find no systematic deviations from the fits within the range of J and v used. Since our data does not uniformly cover the region where we fit the constants, and since the vibrational assignment is uncertain, these constants should be regarded as preliminary. The coefficient Y30 was necessary for a good fit to state IV but was not essential for states I and 1I. The values obtained for Y30 here are comparable to those found for the X, A, B and 4dn states of Na 2. For states I and II states we have several points, (approximately fifteen apiece), with J > 60. If we refit the data with these additional points, they suggest the addition o f a Y02 = 2.1 × 10 - 7 , w i t h an increase in the Y01 term of-~0.0006 for state I, and an addition of Y02 = - 2 . 9 × 10 . 7 with an increase in Y01 o f ~ 0 . 0 0 0 5 for state II. These values are similar to the value of Y02 = - 5 × 10 - 7 , observed for the 3dTt state. Moreover,
Yi/,
Volume 39, number 1,2
OPTICS COMMUNICATIONS
15 September 1981
Table 1 .,.+ Dunham coefficients for ~-g states (all constants in units of cm -1 ) State Atomic asymptote
Vibrational bands observed
o
Y00
Yl0
1101
)'2o
Ylt
I II IIl IV V VI VII
0.-.28 0--18 0-4 0-17 0-2 0,6 0, 6
0.47 0.31 0.10 0.29 0.21 1 1
28325.61 32562.16 35095.68 31881.23 34939.67 37169.3 37763.2
108.7384 123.6736 118.612 111.4514 114.774 110.38 103.98
0.08994 0.10586 0.11087 0.10932 0.10835 0.1129 0.1116
--0.53742 -0.71313 -0.4589 -0.42985 -0.5959 -0.6 -0.6
-0.0004157 0.0001914 -0.0007353 -0.0007144 -0.001106 -0.0007427 -0.0077029
3p- 3p 3 s 4d 3s. 5d 3s--5s 3s.-6s
these observed values of Y02 agree well, (to about 15%), with the value calculated from the relation Y02 = - 4
3 -2 YO1/~ 10,
for the mean contribution from the influence of the centrifugal force for the vibrationless molecule [12]. The two highest 1Zg states are not as well studied as the others; we only have data for the v = 0 and v = 6 bands o f these states. Assuming a typical value o f - 0 . 6 for Y2tl, we calculate rough values for the lowest Dunbam coefficients. (See table 1.) Assignment of asymptotes to these states is difficult because they can be formed from three separated atom configurations. The ground state o f Na 2 has the configuration KKLL(3sog) 2 , while the A state is KKLL (3SOg) (3pOg). The strongest molecular transitions should correspond to allowed atomic transitions. Thus the singly excited 1}2,,+ states observed in transitions from the A state are ~ + n d and 3s+ns, with configurations KKLL(3SOg) (t/dog) and KKLL(3SOg) (nSOg).For low n, the 3s+ns and 3s+nd asymptotes alternate in energy. We expect a similar trend for the electronic energies of these l e g states. We see from the Dunham coefficients that the vibrational constant, YI0, alternates between large (states I1 and 1II) and small (IV and V) values as Y00 increases, indicating the presence of these two kinds o f states. Moreover, signals to the first type of state are considerably stronger than those to the second type, indicating that these two kinds o f states have different F r a n c k - C o n d o n factors to the A state. An asymptote assignment is made for these states by matching the difference in electronic energies, Y00, between adjacent states to differences in energies between the 3s +ns and 3s +rid asymptotes [ 13 ]. This
Y30
--0.00083 -0.00083
assumes that the potential well depths are roughly constant. Fig. 1 displays this assignment, as well as the portion of each state observed in the experiment. The present data are also consistent with assigning states IV and V to 3s+,*d and 3s+5d asymptotes, and states 1I and III to 3s+6s and 3s+7s asymptotes. The lowest state, I, has very different Dunham coefficients form the other states in Na 2. Moreover, this state has different F r a n c k - C o n d o n factors to the A state, since typically signals to about fifteen bands o f this state were seen when pumping a single A state line. For other states usually only five bands are observed. These properties are consistent with the identification o f the lowest 1 Z ; state as having a doubly excited (3Prru)2 configuration, corresponding to the 3p +3p asymptote. One must also entertain the possibility that these are high vibrational levels of the 3s+3d state, but this seems unlikely in view of the apparent cut-off and the small value o f Y30' The above asymptote assignments should be regarded as tentative, as the only way to be certain o f their validity is to follow a few states up to their dissociation limits. Assuming this asymptote assignment, we calculate dissociation energies for these states (table 2) ¢. All energies agree to within 30% with the values predicted by a Birge-Sponer extrapolat ion [12]. It is interesting to compare the dissociation energies for the nd l ~ g * We are not certain of our vibrational assignments, .so these dissociation energies could be larger than quoted here by one vibrational spacing (-~ 110 cm -I ). There is also an uncertainty of 20 cm -t in the value of 5988 cm -I for the depth of the X state (ref. [ 10] ). Since this is used to calculate the portions of the asymptotes, error is introduced into the dissociation energies. 40
Volume 39, number 1,2
OPTICS COMMUNICATIONS
Table 2 Atomic
Dissociation energy (cm -1 )
asymptote
I
3s+4d 3s+5d 3s+5s 3s+6s 3p+3p
7975 7928 7308 7420 11576
+ ~2g states
IFig states 6728 7476 a) a) b)
a) No IHg state exists corresponding to 3s+ns asymptotes. b)We have not observed this II-lgstate. states to those for the nd lIlg states reported earlier [9]. For the II states the nd electron is in an antibonding ndllg orbital, while for the ~ states it is in a bonding Og orbital. Hence, the dissociation energy for each of these n d lllg states should be less than that for the corresponding nd 1Z+ state, as is seen in table 2. During this experiment we did not observe the two ly.g states reported earlier [6], nor were they seen by King et al. [14]. As they pointed out, the signals used to identify these states were probably X - A transitions from an overlapping pump line. We now make sure that each new state is observed using several different pump lines to avoid this kind of error. Transitions to these excited ly.g states in Na 2 have been reported and may now be identified. The twophoton transition seen by Woerdman [2] is to the (18, 50) level of state IV. Morgan et al. [3] have observed many two-photon transitions to several of these states. Using ELLIPSA, Vasudev et al. [15] have seen a ly.g state around 30000 cm -1 which probably corresponds to state I. Recently, King et al. [14] confirmed our observation of states II and IV, as well as the 5d lllg state.
4. Conclusion Using the technique of two-step polarization labeling spectroscopy, we have observed seven IEg states in Na 2 . For five of these states we have found preliminary constants and made atomic asymptote assignments. We are presently developing a more sensitive
50
15 September 1981
detection scheme to study these states in more detail. We intend to look for transitions from the u = 0 of the A state in order to find the bottom of the potential well of each state. To confirm the asymptote assignment, we intend to follow several of these states to their dissociation limits.
Acknowledgement We would like to thank Dr. N.W. Carlson and Professor T.W. Hansch for many helpful discussions. We would also like to thank Frans Alkemade and Ken Sherwin for their skilled technical assistance. One of us (AJT) gratefully acknowledges the support of the John and Fannie Hertz Foundation.
References [1 ] K.C. tlarvey, Thetis, M.L. report 2442, Stanford University (1975). [2] J.P. Woerdman, Chem. Phys. Letters 43 (1976) 279. [3] G.P. Morgan, H.R. Xia and A.L. Schawlow, to be submitted to Optics Communications. [4] M.A. Henesian, R.L. Herbst and R.L. Byer, J. Appl. Phys. 47 (1976) 1515. [51 R.A. Bernheim, L.P. Gold, P.B. Kelly, C. Tomczyk and D.K. Veirs, J. Chem. Phys. 74 (1981) 3259. [6] N.W. Carlson, F.V. Kowalski, R.E. Teets and A.L. Schawlow, Optics Comm. 29 (1979) 302. [71 N.W. Carlson, A.J. Taylor and A.L. Schawlow, Phys. Rev. Letters 45 (1980) 18. [8] N.W. Carlson, Thesis, G.L. report No. 3114, Stanford University (1980). [9] N.W. Carlson, A.J. Taylor, K.M. Jones and A.L. Schawlow, Physical Review A., to be published. [10] P. Kusch and M.M. Hessel, J. Chem. Phys. 68 (1978) 2591. [ 11 ] P. Kusch and M.M. ltessel, private communication. [ 12] G. Iterzberg, Molecular spectra and molecular structure, Vol. 1, Spectra of diatomic molecules (Van Nostrand, Reinhold Company (1950). [ 13 ] C.E. Moore, Atomic Energy Levels, circular of the N.B.S. (1949). [14] G.W. King, I.M. Littlewood and N.T. Littlewood, Chem. Phys. Lett. 80 (1981) 215. {15] R. Vasudev, T.M. Stachelek, W.M. McClain and J.P. Woerdman, Optics Comm. 38 (1981) 149.
OPTICS COMMUNICATIONS
15 September 1981
A STUDY OF THE EXCITED 1 Zg STATES IN Na 2 * ql~5
A.J. T A Y L O R * , K.M. JONES and A.L. SCHAWLOW Department of Physics, Stanford University, Stanford, CA 94305, USA Received 15 June 1981 Using the technique of two-step polarization labeling spectroscopy seven excnted ~g states m Na2 have been found. Molecular constants are derived from a Dunham expansion. Tentative assignments are made to the 3p+3p, 3s+nd and 3s+ns atomic asymptotes. •
•
l
+
"
1. Introduction
2. Experiment
We present here a study of excited I y.g states in Na 2 whose energies lie between 28300 cm -1 and 37800 cm -1. These gerade states are inaccessible using one-photon absorption techniques from the l ~ g state of Na 2 because of the inversion symmetry selection rule. However, Harvey [1 ] and Woerdman [2] observed strong cw two-photon transitions in the visible, which must end on gerade states in this region. Morgan et al. [3] have observed more than a dozen such transitions. From a practical point of view, these states are important as potential sources of new laser lines [4]. Bernheim et al. [5] have shown that corresponding states in Li 2 exhibit interesting perturbations. In previous papers [ 6 - 9 ] we have reported on our study of excited gerade states in Na2, using two-step polarization labeling spectroscopy. Twenty-four new lAg, ll-lg and IZ+ states, lying between 28300 cm -1 and 38900 cm -lg, were reported. In these papers, the properties of the seventeen lAg and ll'Ig states were thoroughly discussed, while only preliminary constants were reported for the 12Eg states. Because of the recent interest in the two-photon process, we present here a more detailed, but still preliminary, description of these excited l ~ g states.
The technique of two-step polarization labeling spectroscopy, as well as the apparatus and procedure for this experiment, have been described in detail in ref. [9], and will not be discussed here. The l ~ g states were observed while pumping single vibrational-rotational transitions from the X 1 ~g+ to A I Z g states in Na 2. The v --- 1,4, 7 - 1 1 , 1 3 , 18 levels of the A state were pumped; several different values of J in each band were studied. These states were not observed when pumping the X I Z g to B III u states, although transitions to these I Z g states from the B state should be allowed. When the A IZu+ state of Na 2 is pumped, transitions are allowed to higher 1Zg states and ll-lg states. Transitions to l ~ g states can be distinguished from transitions to 1Hg states by the absence of Q branches in the former when a linearly polarized pump beam is used. Unfortunately, for probe wavelengths longer than 5500 A, transitions from the lower level of the pump transition to various levels in the A state can produce polarization signals. Q branches are also absent in these one-step transitions. We distinguish between two-step signals to higher excited 1~ g states and one-step signals to the A state in two ways. First, the constants of the X and A states are well known [10,11], so possible one-step signals are compared with predicted transition energies from the lower level of the pump transition. Secondly, if the probe is delayed relative to the pump by the lifetime of the A
~' Work supported by the National Science Foundation under Grant PHY80-10689. * Hertz Foundation Predoctoral Fellow.
47
Volume 39, number 1,2
OPTICS COMMUNICATIONS
state, (about 12 ns), then two-step signals will become weaker, while one-step signals will not be appreciably affected.
3. Results We have studied seven excited 1Z; states in Na 2 . Fig. 1 displays the electronic energies and tentative atomic asymptotes of these states, as well as the region of each state which has been examined experimentally. The data for each state is fitted to a Dunham expansion, of the form:
T(v,J) = ~.. Yi/(v+~)i (J(J+l))/. tl
The valuesof J and v for each line must be known. We know the value of J for the upper level of the pump transition from the previously determined constants of the A state, hence the value of J is known for each two-step signal. The vibrational assignment in the unknown state is less certain. We look for a sharp cut-off
3s+Sd ATOMI C ASYMPTOTE "x
3s+6s
3s+4d
40,000
3p+3p
3S+SSlI1 E
2"
×
o 30,000
~-.EXPERIMENTALLY OBSERVED REGION
--g
m
" o
3s*3p T A'~
BOTTOM OF POTENTIAL WELL
I~; EXCITED STATES
2o,oooL ~B'nu Fig. 1. Energy level diagram of excited 1 X.+ states. Included for each of the five lowest states is the bottom of the potential well, the atomic asymptote assignment, and the region studied experimentally. The two highest states are less well studied, so only the bottom of the potential well is indictaed. 48
15 September 1981
in signals to tile red when low vibrational bands of the A state are pumped to find the lowest vibrational band in the unknown state. However, bad Franck--Condon factors can produce the same effect, especially when photographic detection is used. Since we have not yet pumped the v = 0 band of the A state, we are not certain that we have found the v = 0 band in any of our states. We do see a cut-off when the v = 1 level of the A state is pumped, so it seems reasonable that the lowest level we have seen corresponds to v = 0 or v = 1. We have probably seen the lowest vibrational band for the state lowest in energy, since a cut-off occured in the same band while pumping the v = 1 and v = 4 bands in the A state. However, this is not certain, since these signals occured at the red end of a probe profile, and we were not able to go farther to tile red with commercially available dyes. For the purpose of fitting our results to a Dunham expansion, we have assigned the lowest observed band to v = 0. The coefficients along with the range of vibrational bands used for the fit of each state are listed in table 1. Unfortunately, the values of the coefficients depend on the range of v and J that is fit, as well as the number of coefficients included. The range of J in each band was limited to 10 < J < 40. However, we did not have a uniform coverage of this range in all bands. After removing a few deviant points we find that the estimated error of the fit is less than 0.5 cm --1 in agreement with the uncertainty in making a single measurement. For each state, the expansion fits the data smoothly; we find no systematic deviations from the fits within the range of J and v used. Since our data does not uniformly cover the region where we fit the constants, and since the vibrational assignment is uncertain, these constants should be regarded as preliminary. The coefficient Y30 was necessary for a good fit to state IV but was not essential for states I and 1I. The values obtained for Y30 here are comparable to those found for the X, A, B and 4dn states of Na 2. For states I and II states we have several points, (approximately fifteen apiece), with J > 60. If we refit the data with these additional points, they suggest the addition o f a Y02 = 2.1 × 10 - 7 , w i t h an increase in the Y01 term of-~0.0006 for state I, and an addition of Y02 = - 2 . 9 × 10 . 7 with an increase in Y01 o f ~ 0 . 0 0 0 5 for state II. These values are similar to the value of Y02 = - 5 × 10 - 7 , observed for the 3dTt state. Moreover,
Yi/,
Volume 39, number 1,2
OPTICS COMMUNICATIONS
15 September 1981
Table 1 .,.+ Dunham coefficients for ~-g states (all constants in units of cm -1 ) State Atomic asymptote
Vibrational bands observed
o
Y00
Yl0
1101
)'2o
Ylt
I II IIl IV V VI VII
0.-.28 0--18 0-4 0-17 0-2 0,6 0, 6
0.47 0.31 0.10 0.29 0.21 1 1
28325.61 32562.16 35095.68 31881.23 34939.67 37169.3 37763.2
108.7384 123.6736 118.612 111.4514 114.774 110.38 103.98
0.08994 0.10586 0.11087 0.10932 0.10835 0.1129 0.1116
--0.53742 -0.71313 -0.4589 -0.42985 -0.5959 -0.6 -0.6
-0.0004157 0.0001914 -0.0007353 -0.0007144 -0.001106 -0.0007427 -0.0077029
3p- 3p 3 s 4d 3s. 5d 3s--5s 3s.-6s
these observed values of Y02 agree well, (to about 15%), with the value calculated from the relation Y02 = - 4
3 -2 YO1/~ 10,
for the mean contribution from the influence of the centrifugal force for the vibrationless molecule [12]. The two highest 1Zg states are not as well studied as the others; we only have data for the v = 0 and v = 6 bands o f these states. Assuming a typical value o f - 0 . 6 for Y2tl, we calculate rough values for the lowest Dunbam coefficients. (See table 1.) Assignment of asymptotes to these states is difficult because they can be formed from three separated atom configurations. The ground state o f Na 2 has the configuration KKLL(3sog) 2 , while the A state is KKLL (3SOg) (3pOg). The strongest molecular transitions should correspond to allowed atomic transitions. Thus the singly excited 1}2,,+ states observed in transitions from the A state are ~ + n d and 3s+ns, with configurations KKLL(3SOg) (t/dog) and KKLL(3SOg) (nSOg).For low n, the 3s+ns and 3s+nd asymptotes alternate in energy. We expect a similar trend for the electronic energies of these l e g states. We see from the Dunham coefficients that the vibrational constant, YI0, alternates between large (states I1 and 1II) and small (IV and V) values as Y00 increases, indicating the presence of these two kinds o f states. Moreover, signals to the first type of state are considerably stronger than those to the second type, indicating that these two kinds o f states have different F r a n c k - C o n d o n factors to the A state. An asymptote assignment is made for these states by matching the difference in electronic energies, Y00, between adjacent states to differences in energies between the 3s +ns and 3s +rid asymptotes [ 13 ]. This
Y30
--0.00083 -0.00083
assumes that the potential well depths are roughly constant. Fig. 1 displays this assignment, as well as the portion of each state observed in the experiment. The present data are also consistent with assigning states IV and V to 3s+,*d and 3s+5d asymptotes, and states 1I and III to 3s+6s and 3s+7s asymptotes. The lowest state, I, has very different Dunham coefficients form the other states in Na 2. Moreover, this state has different F r a n c k - C o n d o n factors to the A state, since typically signals to about fifteen bands o f this state were seen when pumping a single A state line. For other states usually only five bands are observed. These properties are consistent with the identification o f the lowest 1 Z ; state as having a doubly excited (3Prru)2 configuration, corresponding to the 3p +3p asymptote. One must also entertain the possibility that these are high vibrational levels of the 3s+3d state, but this seems unlikely in view of the apparent cut-off and the small value o f Y30' The above asymptote assignments should be regarded as tentative, as the only way to be certain o f their validity is to follow a few states up to their dissociation limits. Assuming this asymptote assignment, we calculate dissociation energies for these states (table 2) ¢. All energies agree to within 30% with the values predicted by a Birge-Sponer extrapolat ion [12]. It is interesting to compare the dissociation energies for the nd l ~ g * We are not certain of our vibrational assignments, .so these dissociation energies could be larger than quoted here by one vibrational spacing (-~ 110 cm -I ). There is also an uncertainty of 20 cm -t in the value of 5988 cm -I for the depth of the X state (ref. [ 10] ). Since this is used to calculate the portions of the asymptotes, error is introduced into the dissociation energies. 40
Volume 39, number 1,2
OPTICS COMMUNICATIONS
Table 2 Atomic
Dissociation energy (cm -1 )
asymptote
I
3s+4d 3s+5d 3s+5s 3s+6s 3p+3p
7975 7928 7308 7420 11576
+ ~2g states
IFig states 6728 7476 a) a) b)
a) No IHg state exists corresponding to 3s+ns asymptotes. b)We have not observed this II-lgstate. states to those for the nd lIlg states reported earlier [9]. For the II states the nd electron is in an antibonding ndllg orbital, while for the ~ states it is in a bonding Og orbital. Hence, the dissociation energy for each of these n d lllg states should be less than that for the corresponding nd 1Z+ state, as is seen in table 2. During this experiment we did not observe the two ly.g states reported earlier [6], nor were they seen by King et al. [14]. As they pointed out, the signals used to identify these states were probably X - A transitions from an overlapping pump line. We now make sure that each new state is observed using several different pump lines to avoid this kind of error. Transitions to these excited ly.g states in Na 2 have been reported and may now be identified. The twophoton transition seen by Woerdman [2] is to the (18, 50) level of state IV. Morgan et al. [3] have observed many two-photon transitions to several of these states. Using ELLIPSA, Vasudev et al. [15] have seen a ly.g state around 30000 cm -1 which probably corresponds to state I. Recently, King et al. [14] confirmed our observation of states II and IV, as well as the 5d lllg state.
4. Conclusion Using the technique of two-step polarization labeling spectroscopy, we have observed seven IEg states in Na 2 . For five of these states we have found preliminary constants and made atomic asymptote assignments. We are presently developing a more sensitive
50
15 September 1981
detection scheme to study these states in more detail. We intend to look for transitions from the u = 0 of the A state in order to find the bottom of the potential well of each state. To confirm the asymptote assignment, we intend to follow several of these states to their dissociation limits.
Acknowledgement We would like to thank Dr. N.W. Carlson and Professor T.W. Hansch for many helpful discussions. We would also like to thank Frans Alkemade and Ken Sherwin for their skilled technical assistance. One of us (AJT) gratefully acknowledges the support of the John and Fannie Hertz Foundation.
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