Polarisation labelling spectroscopy of rubidium dimer: Highly excited 81∑u+, 91∑u+ and 81∏u states

Journal of Molecular Structure 1208 (2020) 127858

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Polarisation labelling spectroscopy of rubidium dimer: Highly excited P 1Pþ 1Q 81 þ u, 9 u and 8 u states W. Jastrzebski a, A. Grochola a, J. Szczepkowski a, P. Kowalczyk b, * a b

w 32/46, 02-668, Warszawa, Poland Institute of Physics, Polish Academy of Sciences, Al.Lotniko Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Ul. Pasteura 5, 02-093, Warszawa, Poland

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 December 2019 Received in revised form 17 January 2020 Accepted 4 February 2020 Available online 8 February 2020

Excitation spectra of rubidium dimer were investigated in the spectral range 28000  29700 cm-1 by polarisation labelling spectroscopy technique. Three hitherto unknown electronic states were observed 1 1 þ 1 þ 1 and assigned as 8 Sþ u , 9 Su and 8 Pu . The experimental findings on the Su states were compared with theoretical predictions. The investigated electronic states are presently the highest ungerade states of Rb2 known experimentally and the 81 Pu state has not been studied theoretically as yet. © 2020 Published by Elsevier B.V.

Keywords: laser spectroscopy Alkali dimers Electronic states Potential energy curves

1. Introduction In a series of recent experiments on rubidium dimer, employing the polarisation labelling spectroscopy technique (PLS) [1], we 1 investigated electronic singlet ungerade states from 31 Pu and 3 Sþ u 1 þ 1 up to 7 Pu and 7 Su [2e7], i.e. in the range of excitation energies approximately between 22,000 and 29,000 cm-1. The measurements were accompanied by ab initio calculations of potential curves of several high-lying electronic states in Rb2 molecule [2] which helped us to plan the experiments and to interpret their results. Presently, by using a different laser system, we were able to extend the range of excitation energies up to about 29,700 cm-1. This paper deals with three previously unobserved electronic states placed in the newly explored energy region, which we assign as 1 1 þ 1 8 Sþ u , 9 Su and 8. Pu

2. Experiment As a detailed description of our experimental procedure has been presented elsewhere [1,3,8], only a brief outline is given here. We employed a V-type optical-optical double resonance

* Corresponding author. E-mail addresses: [email protected] (W. Jastrzebski), Pawel.Kowalczyk@fuw. edu.pl (P. Kowalczyk). https://doi.org/10.1016/j.molstruc.2020.127858 0022-2860/© 2020 Published by Elsevier B.V.

polarisation labelling spectroscopy method with two independent pump and probe lasers. The molecular source was a linear heat pipe oven containing rubidium vapour of natural isotopic composition. The temperature was maintained at about 300  C and a total pressure of 4 Torr was established using helium as a buffer gas. The copropagating, pump and probe laser beams were crossed at the centre of the heat pipe. The probe beam was delivered by a cw single mode ring dye laser, Coherent 899e21, operated on DCM dye at 50e200 mW and kept at fixed frequencies coinciding with cho1 sen molecular transitions in the well known B1 Pu ) X Sþ g system of Rb2, thus labelling the involved rovibrational levels in the ground electronic state. The BeX transitions induced by the probe laser could be established from a direct readout of the laser frequency (wavelength meter HighFinesse WS-7) and precise molecular 1 1 constants of the X Sþ g [9] and B Pu [10] states. As a tunable pump beam we employed frequency doubled output of the optical parametric oscillator and amplifier system (Sunlite EX, Continuum, pumped with the third harmonic of an injection seeded Nd:YAG laser, Powerlite 8000), delivering pulses at a repetition rate of 10 Hz, with 0.5 mJ energy, 10 ns duration, and spectral width below 0.16 cm-1. The pump light was tuned in the spectral range 28000  29700 cm-1 and induced transitions from the ground molecular state to the excited electronic states studied in this experiment. With a proper choice of polarisation of the pump and probe beams and a detection scheme specific to the V-type polarisation labelling method [1], we could observe excitation spectra of the rubidium

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dimer originating only from the levels labelled in the X Sþ g state. The frequency of the laser light inducing the observed spectra (i.e. of the pump beam) was determined from the optogalvanic spectrum of argon recorded simultaneously with the molecular spectra. The linearity of the laser scan was additionally controlled with a rot interferometer providing frequency markers separated Fabry-Pe by 1 cm-1. Both auxiliary signals were recorded using the fundamental output of the OPO/OPA system. With these input data the accuracy of the determination of the pump laser frequency was better than 0.1 cm-1 and the apparatus provided us with rotationally resolved molecular spectra with both resolution and accuracy limited only by the pump laser linewidth.

ground state to an accuracy of ±0:001 cm-1 [9]. Therefore the term values of the excited states could be calculated from the measured wavenumbers n of the observed lines as 00

00

00

T 0 ðv0 ; J 0 Þ ¼ T ðv ; J Þ þ n:

(1)

The excited state energies were represented by standard Dunham polynomial expansions of the form

Tðv; JÞ ¼ Te þ

h in X Ymn ,rmþ2n ðv þ 0:5Þm JðJ þ 1Þ  L2 ;

(2)

m;n 1

3. Results and analysis The investigated spectral range was dominated at its low fre1 quency limit by strong progressions belonging to the known 7 Sþ u 1 1 þ 1 ) X Sþ and 7 P ) X S band systems [5] which gradually u g g faded away at higher frequencies. Besides, weaker spectral lines could be occasionally observed. By improving sensitivity of our system we were able to record more of them (Fig. 1) and finally to arrange the weak lines into three separate band systems, two of 1 1 þ them corresponding to two different Sþ u ) X Sg transitions (as proved by the presence of only P and R lines in the spectra) and one 1 to a 1 Pu ) X Sþ g transition (characterized by the existence of Q lines). Aided by recent theoretical calculations of properties of highly excited states of rubidium dimer [2], we could identify the 1 1 þ 1 þ two excited Sþ u states as 8 Su and 9 Su . Unfortunately, the calculations do not cover sufficiently high 1 Pu states so our assignment of the observed state as 81 Pu is only tentative, based on the fact that the last but one state of this symmetry known experimentally is definitely 71 Pu [5]. 00 1 In each of the observed excitation spectra the starting X Sþ g (v ; 00 J ) level was identified by frequency of the labelling laser and its energy T 00 was known from precise molecular constants of the

1 where L2 ¼ 0 or 1 for Sþ u and Pu states, respectively. The factor r accounts for the isotope effects and is equal to 1 for 85 Rb2 and pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m8585 =m8587 x 0.9942 for 85Rb87Rb, with m standing for the molecular reduced mass. In case of the 1 Pu state the above formula is valid only for f parity levels whereas for levels of e parity the term r2 qJðJ þ 1Þ, describing the lambda doubling effects, was appended. The coefficients Te , Ymn and q were fitted for each state by a least squares procedure. As can be expected for highly excited electronic states, we observed numerous perturbations of the rovibrational levels in each state. In very few cases when the ‘main’ and ‘extra’ lines were seen and assigned, they could be illustrated by a textbook diagram of energy shifts (Fig. 2), but usually the perturbations were manifested simply by impossibility of fitting energies of some levels using molecular constants describing the majority of them. For the most regular 81 Pu state we were able to select 415 spectral lines in 1 85 the 81 Pu ) X Sþ Rb2 and 109 for g system (306 lines for 85 87 Rb Rb) which provided consistent description of the 81 Pu state levels within formula (2) with rms ¼ 0.14 cm-1, comparable to the experimental uncertainty. This left 79 outlying lines (from the total of 494), corresponding mainly to transitions to two consecutive vibrational levels in the 81 Pu state (v0 ¼ 11 and 12, see Fig. 3), 1 apparently heavily perturbed. For the 8 Sþ u state the choice of

1

Fig. 1. A fragment of the polarisation spectrum of rubidium dimer in which relatively strong transitions to the 8 Sþ u state can be observed. The three vibrational progressions with 1 1 þ 1 þ 1 þ 1 þ 85 1 the assignment of the upper levels shown on top correspond to 8 Sþ Rb2 from the ground state level v00 ¼ 3, J 00 ¼ 55 u ) X Sg , 7 Su ) X Sg and 7 Pu ) X Sg transitions in -1 labelled by the probe laser set at the wavenumber 14980.395 cm .

W. Jastrzebski et al. / Journal of Molecular Structure 1208 (2020) 127858

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Table 1 1 1 þ Deviations of the experimental energies of levels in the 81 Pu , 8 Sþ u and 9 Su states from their fitted positions, analysed in three different ways: rms deviations of the fit (rms), rms deviations only for lines of 85 Rb87 Rb (rms iso) and average deviations for 85 Rb87Rb (av iso), calculated for three different numberings v ¼ v0 þ n with n ranging from 1 to 1. Here v0 denotes the finally chosen, ‘correct’ numbering. All deviations are given in cm-1. state

n

rms

rms iso

av iso

81 P u

1 0 1 1 0 1 1 0 1

0.178 0.142 0.177 0.270 0.254 0.263 0.74 0.73 0.74

0.21 0.13 0.21 0.27 0.19 0.24 0.68 0.66 0.66

 0:17 1:3 10-3 0.17  0:20 2:3 10-2 0.15  0:13 1:2 10-2 0.15

1

8 Sþ u 1

9 Sþ u

Fig. 2. Differences between the measured and expected term values for rotational 1 levels in the v0 ¼ 11 level of the 8 Sþ u state. Note that in this case pairs of main and extra lines could be unambiguously assigned for a few J values.

‘unperturbed’ lines was more difficult. From 497 lines observed in 1 1 þ the 8 Sþ u ) X Sg system we picked finally 392 of them (330 for 85 Rb2 and 62 for 85Rb87Rb) but the description of the excited state by the Dunham coefficients was less satisfactory, yielding 1 rms ¼ 0.25 cm-1. The 9 Sþ u state turned out to be perturbed so 1 1 þ heavily that any attempt to group the lines from the 9 Sþ u ) X Sg system into ‘more regular’ and ‘less regular’ ones had failed. Therefore we fitted molecular constants to all 325 observed spectral lines (232 for 85 Rb2 and 93 for 85Rb87Rb) with rms ¼ 0.73 cm-1, exceeding the experimental error by more than four times. Note that the relatively weak molecular spectra, in most cases preventing observation of transitions to the perturbing electronic states (probably of triplet symmetry), did not allow us to apply any deperturbation procedure to states under investigation.

1

In view of weak and perturbed spectra unambiguous determination of vibrational numbering of levels in each state was not straightforward. Generally the numberings were based on mass scaling of Dunham coefficients for different isotopologues, shown explicitly in formula (2). Fits of Dunham coefficients to term energies when assuming various numberings should provide the lowest rms deviation for the correct one. However, we examined also two other characteristics of different fits (in each case fits to all levels belonging to both isotopologues): an rms deviation calculated only for levels of the less abundant isotopologue 85 Rb87Rb and an average deviation calculated also only for 85Rb87Rb. The simultaneous minima of all three characteristics confirmed the num1 berings (see Table 1) although the numbering of levels in the 9 Sþ u state must be treated with some caution and a change by ±1 cannot be excluded. The corresponding Dunham coefficients for the three electronic states are listed in Table 2 together with the ranges of v and J quantum numbers of rovibrational levels used for their determination. For each state we used the smallest number of coefficients that reproduce the measured level energies. The values of the coefficients were rounded using a procedure suggested by Le

Fig. 3. Range of v0 and J 0 for levels observed in the 81 Pu (a) and 8 Sþ u (b) states. Open circles (red online) indicate levels included in the fits of Dunham coefficients.

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W. Jastrzebski et al. / Journal of Molecular Structure 1208 (2020) 127858 Table 2 1 1 þ 85 Molecular constants (in cm-1) for the 81 Pu , 8 Sþ Rb2 determined in the present work. The range of rovibrational levels used for their determination is u and 9 Su states of indicated. The numbers in parentheses correspond to one standard deviation in units of the last digits, rms stands for the root mean square deviation of the fit. Note that the 1 constants for the 9 Sþ u state have no physical meaning and can be used as numerical parameters only within the indicated (v, J) limits. 1

1

Constant

81 Pu

8 Sþ u

9 Sþ u

Te Y10 Y20 Y30

28750.85(7) 46.430(15) 0.08058(124)

28142.77(16) 51.911(29) 0.4451(19)

28750.46(11) 29.174(105) 0.1306(27)

 0:366ð32Þ  103 0.016895(11)

0:4316ð39Þ  102 0.015656(19)

0.016326(86)

 0:365ð4Þ  104

 0:399ð9Þ  104

 0:731ð38Þ  104

0.25 1  29 44  109

0.73 12  28 49  123

Y01 Y11 Y02

 0:103ð6Þ  107

q

 0:117ð3Þ  103 0.14 0  24 49  122

rms range of v range of J

Table 3 1 85 1 Rotationless RKR potential energy curves for the 8 Sþ Rb2 . The u and 8 Pu states of first line refers to the bottoms of the potential curves, the corresponding R values are the equilibrium distances. v

0 1 2 3 5 7 9 11 14 17 20 23 26 29

1

8 Sþ u state

81 Pu state

E (cm-1)

R (Å)

Rþ (Å)

28142.77 28168.53 28219.56 28269.74 28319.10 28415.44 28508.80 28599.36 28687.35 28814.96 28937.93 29056.97 29172.78 29286.05 29397.48

5.036 4.916 4.830 4.773 4.727 4.651 4.589 4.535 4.486 4.421 4.362 4.309 4.261 4.218 4.178

5.163 5.263 5.336 5.397 5.503 5.597 5.684 5.766 5.882 5.993 6.099 6.201 6.299 6.392

E (cm-1)

R (Å)

Rþ (Å)

28750.85 28774.04 28820.31 28866.41 28912.35 29003.72 29094.39 29184.35 29273.58 29406.03 29536.74 29665.65 29792.71

4.831 4.704 4.615 4.555 4.508 4.433 4.372 4.320 4.275 4.214 4.161 4.113 4.069

4.966 5.069 5.142 5.204 5.307 5.397 5.477 5.552 5.656 5.754 5.847 5.936

Roy [11]. 1 1 For the 8 Sþ u and 8 Pu states, for which the data bases included low vibrational levels, potential curves were constructed using the standard Rydberg-Klein-Rees method (Table 3). In the case of the 1 9 Sþ u state, somewhat surprisingly, only levels with v  12 were observed. Moreover, the distance of subsequent levels in this range was increasing with growing v, indicating that the determined Dunham coefficients Y10 and Y20 lack their physical meaning of vibrational constant and anharmonicity. Therefore no reliable potential could be constructed for this state. The two experimental potentials are displayed in Fig. 4 together with the available theo1 1 þ retical curves for the Sþ u states. The agreement for the 8 Su state is very satisfactory. It may be noticed that the range of energies for the 1 observed levels in the 9 Sþ u state, indicated in Fig. 4 by dotted horizontal lines, coincides rather well with the region where the theoretical potential curve is distorted by an anticrossing with the 1 potential of the next state of the same symmetry, 10 Sþ u . The distance of consecutive vibrational levels calculated from the theo1 retical 9 Sþ u state potential also changes irregularly, although this effect is not so pronounced as in our experiment. The anticrossing of potential curves, which would be connected inherently with a change of transition dipole moment for transition from the ground state, may explain also why the lowest vibrational levels of the 1 9 Sþ u state remained unobserved. CRediT authorship contribution statement W. Jastrzebski: Conceptualization, Methodology, Investigation, Writing - original draft, Writing - review & editing, Supervision, Funding acquisition. A. Grochola: Formal analysis. J. Szczepkowski: Investigation, Software. P. Kowalczyk: Conceptualization, Methodology, Investigation, Formal analysis, Writing - original draft, Writing - review & editing, Supervision. Acknowledgements This work was partially supported by the National Science Centre of Poland (Grant No. 2016/21/B/ST2/02190). The paper is dedicated to the memory of the late Jon Hougen.  dobry’ (‘good day’), spoken with We shall miss his warm ‘dzien perfect Polish pronunciation, with which he used to greet us at various molecular conferences.

1

Fig. 4. (Colour online) The RKR potential energy curves of the 81 Pu and 8 Sþ u states obtained in the present work (black open circles and open triangles, respectively, each set connected by a dashed line) drawn alongside the available theoretical potentials [2] (solid lines, blue online). The horizontal dotted lines indicate the region of energies of 1 vibrational levels in the 9 Sþ u state observed in our experiment.

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.molstruc.2020.127858.

W. Jastrzebski et al. / Journal of Molecular Structure 1208 (2020) 127858

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