On the 3^{1}Π_{u} state in caesium dimer
Jacek Szczepkowski, Anna Grochola, Wlodzimierz Jastrzebski, Pawel Kowalczyk
aa r X i v : . [ phy s i c s . c h e m - ph ] J a n On the 3 Π u state in caesium dimer Jacek Szczepkowski a , Anna Grochola a , Wlodzimierz Jastrzebski a, ∗ , PawelKowalczyk b, ∗∗ a Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warsaw,Poland b Institute of Experimental Physics, Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warszawa, Poland
Abstract
Polarisation labelling spectroscopy technique was employed to study the 3 Π u state of Cs molecule. The main equlibrium constants are T e = 20684 . cm − , ω e = 30 . cm − and R e = 5 . Å. Vibrational levels v = 4 − of the 3 Π u state were found to be subject to strong perturbations by the neighbouringelectronic states. Energies of 3094 rovibronic levels of the perturbed complexwere determined. Keywords: laser spectroscopy, alkali dimers, electronic states, perturbations
PACS: ∗ Corresponding author ∗∗ Corresponding author
Email addresses: [email protected] (Wlodzimierz Jastrzebski ),
[email protected] (Pawel Kowalczyk )
Preprint submitted to Spectrochimica Acta A February 1, 2021 n the present short communication we report experimental investigationof the 3 Π u electronic state of Cs . Up to now only the lowest vibrationallevels v = 0 − of this state have been observed [1] and its sole theoreticaldescription comes from an unpublished thesis by Spies [2]. Using the V-typedouble resonance polarisation labelling spectroscopy (PLS) method we were ableto extend experimental observations of the 3 Π u state up to v = 35 . As ourexperimental method is described in detail elsewhere [3, 4] we shall not presentit here. The only novelty in the present set-up comparing to that describedin Ref. [4] is that as a probe laser we used a home-built single mode externalcavity diode laser (ECDL), operating in the range − cm − andfixed on selected transitions in the B Π u ← X Σ + g band system of Cs [5, 6].The accuracy of ± . cm − was achieved by active locking of the laser toHigh Finesse WS-7 wavemeter. With the pump laser (an excimer laser pumpeddye laser on Coumarin 480 dye), tuneable between 20400 and 21600 cm − , werecorded a few thousand rotationally resolved transitions from the labelled levelsin the ground X Σ + g state to levels assigned as v = 0 − in the 3 Π u state (seean exemplary spectrum in Figure 1). Two-step calibration of the spectra usingargon and neon spectral lines as well as transmission fringes of a Fabry-Pérotetalon allowed to determine the wave numbers of the observed spectral lines withan accuracy of about 0.05 cm − . The measured wave numbers were convertedto energies of the 3 Π u state levels referred to the minimum of the X Σ + g statepotential well, using the highly accurate ground state constants [7]. As theconstants reproduce energies of rovibrational levels in the ground state withan accuracy superior to precision of our measurements, no additional errorswere introduced into our analysis of the 3 Π u state. Our study reveals thatinstead of regular ladder of levels belonging solely to the 3 Π u state we dealwith an intricate system of highly perturbed levels belonging to more electronicstates. Actually, this can be inferred from a picture of theoretical potentialenergy curves for the related energy region (Figure 2), where the bottom partof the 3 Π u state potential runs nearly in parallel with the nearby 3 Π u statepotential and in addition it is crossed by the 4 Σ + u state curve. To simplify the2nalysis to some extent, we limit our further analysis to f parity levels, proneto perturbations by Ω = 1 components of both triplet states. These levels areaccessed via Q lines in the spectra, being moreover more pronounced then Pand R lines when using our excitation scheme. Our limitation leaves out theE(3) Σ + u state from the analysis as it contains only e parity levels.Contrary to the previous report [1] we find that only the four lowest levelsof the 3 Π u state, v = 0 − , are free of observable perturbations and only theirpositions can be described in a compact way by molecular constants (Table 1).This suffices to determine the main characteristics of the potential energy curveof the 3 Π u state, the equilibrium distance between two caesium nuclei ( R e =5 . Å), the term energy ( T e = 20684 . cm − ) and the dissociation energy. Itis clear that the molecular 3 Π u state dissociates into atoms in 6 S and 7 Pstates [1], however the latter is split into two fine structure components distantby about 181 cm − [8]. Calculations of Spies [2] suggest correlation of the 3 Π u state with the higher 6 S+7 P / asymptote (see Figure 2). Using the atomicenergy of Cs E (7 P / ) = . ± . cm − [8] and dissociation energyof the ground state of Cs D (X Σ + g ) = . ± . cm − [9] we obtain D (3 Π u ) = D (X Σ + g ) + E (7 P / ) − T e (3 Π u ) = 4911 . − . (1)All vibrational levels of the 3 Π u state starting from v = 4 are heavily per-turbed. Energies of part of them are shown in Figure 3. The Figure evidentlyincludes both ‘main’ and ‘extra’ levels, the latter belonging to other state(s)inaccessible in direct excitation from the singlet ground state of Cs and ob-servable due to mixing of their wave functions with these of the 3 Π u state.For several vibrational levels of the 3 Π u state we tried to pick out these rota-tional levels which appeared to be only weakly affected by perturbations and todetermine rough band constants by fitting their energies to the formula E ( v, J ) = T v + B v [ J ( J + 1) − − D v [ J ( J + 1) − . (2)The results are given in Table 2. Part of them is displayed by solid lines in3 i n t en s i t y [ a r b . un i t s ] laser wave number [cm -1 ]v’=26 3227 28 29 30 31 Figure 1: A part of the polarisation spectrum of Cs recorded when the ground state level v ′′ = 2 , J ′′ = 73 was labelled by the probe laser set at the wave number 12951.237 cm − . Theexcitation scheme with linearly polarised pump laser light favours Q lines in the spectra, whichare then much more pronounced than the P and R lines. Transitions to subsequent v ′ levels inthe 3 Π u state are tentatively assigned on top of the drawing, but several extra lines presentin the spectrum reveal that the 3 Π u state is perturbed by more than one neighbouring state. E [ c m - ] R [¯] 3 Figure 2: (Colour online) Theoretical potential curves of the four electronic states of Cs related to the present experiment [2]. To guide the eye the calculated points are connectedwith solid lines. able 1: Molecular constants (in cm − ) for the 3 Π u state of Cs representing energies ofrovibrational levels in the range v = 0 − , J = 36 − , compared with theoretical values [2]. D stands for the dissociation energy. In the bottom line the equilibrium distance is alsocompared. Values in parentheses are uncertainties in units of the last digits, rms stands forthe root mean square deviation of the fit. constant experiment theory T e ω e B e α e × D e × D R e [Å] 5.27(1) 5.28Figure 3. However, a scatter of the obtained values, e.g. of T v as a functionof v , shows that our choice of perturbation-free rotational levels was ratherarbitrary. An even simpler formula E ( v, J ) = T v + B v [ J ( J + 1) − (3)was applied to levels assumed to represent the perturbers (long dashed and shortdashed lines in Figure 3). Different slopes of two sets of the corresponding linesconfirm our belief that both triplet states 3 Π u and 4 Σ + u are responsible forthe observed interactions. On the other hand the difference is not sufficient tocorrelate them with particular states.Figure 3 shows clearly that deperturbation analysis of the strongly interact-ing 3 Π u ∼ Π u ∼ Σ + u system requires a coupled channels treatment takinginto account all three interacting states and possible spin-orbit and rotationalinteractions between pairs of them. This is a serious numerical challenge thatwe have not yet attempted (see an example of such an analysis in Ref. [10]).6 E r ed = E - . x ( J ( J + )- ) [ c m - ] J(J+1)-1
Figure 3: (Colour online) Reduced term values E red = E − . × [ J ( J + 1) −