\documentstyle[prl,aps]{revtex} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=Latex.dll} %TCIDATA{LastRevised=Wed Feb 03 16:39:06 1999} %TCIDATA{} %TCIDATA{CSTFile=revtxtci.cst} \begin{document} \author{D. Azinovi\'{c}, S. Milo\v {s}evi\'{c}, and G. Pichler} \address{Institute of Physics, P.O.Box 304, Zagreb, Croatia} \author{M.C. van Hemert} \address{Department of Chemistry, Gorleaus Laboratory, University of Leiden, P.O.Box\\ 9502, 2300 RA Leiden, The Netherlands} \author{R. D\"{u}ren} \address{Max-Planck-Institut f\"{u}r Str\"{o}mungsforschung, D-37018-G\"{o}ttingen,\\ Germany} \title{LiAr, LiKr and LiXe excimers: Photochemical formation of the 3$% ^{2}\Sigma^{+} $-1$^{2}\Sigma ^{+}$ bands} \date{\today } \maketitle \begin{abstract} We investigated the photochemical formation of lithium-rare gas excimers in the 3$^{2}\Sigma ^{+}$state through the reaction of Li$_{2}$(2(C)$^{1}\Pi _{u}$) and the ground-state rare gas atom. Lithium-rare gas vapor mixture was prepared in the heat-pipe oven. We populated the 2(C)$^{1}\Pi _{u}$ state of the Li$_{2}$ molecule using the XeCl excimer laser wavelength at 308 nm or the PTP dye laser wavelength at about 335 nm. The 3$^{2}\Sigma ^{+} $-1$^{2}\Sigma ^{+}$ transitions were observed with peaks at 414, 420 and 435 nm for LiAr, LiKr and LiXe, respectively. We estimated thermally averaged rate constants for these photochemical reactions, which are (2.3$% \pm $1.1) 10$^{-10}$cm$^{3}$s$^{-1}$ for LiAr, (6.9$\pm $3.2) 10$^{-10}$cm$% ^{3}$s$^{-1}$ for LiKr and (19$\pm $9) 10$^{-10}$cm$^{3}$s$^{-1}$ for LiXe. {\it Ab initio }potential-energy curves and transition dipole moments for LiKr were calculated applying the SCF MRDCI method. Available data for the LiAr and LiKr excimers are presented, including potential-energy curves, electronic transition dipole moments, and spectroscopic constants. Possible photochemical formation of these molecules in the excited states is discussed. We performed the quantum mechanical spectral simulations of the LiAr and LiKr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transitions, using {\it % ab initio} potential-energy curves. \end{abstract} \pacs{PACS numbers: 33.20.Kf; 82.20.Pm; 34.20.Cf} \newpage \section{Introduction} The alkali-rare gas (RG) molecular bands have been extensively studied for the past thirty years which was systematized in the review paper published by Rostas \cite{ros82}. Alkali-RG 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transitions, investigated by applying the laser induced fluorescence method or electric discharge, were reported by Tam et al.\cite{tam75,tam76a,tam76b}% , Webster and Rostas \cite{web78} and Wang and Havey \cite{wan84}. In our previous work we studied the photochemical formation of the 2$^{2}\Pi $-1$^{2}\Sigma ^{+}$ excimer bands of LiZn \cite{mil92}, LiCd \cite{hem92}, NaZn \cite{azi93}. The IIB atoms and rare gases have a closed outer electronic shell. The structure and spectra of alkali-IIB and alkali-rare gas molecules appear to be similar and one can compare the features of those two groups of molecules. The potential well for the 2$^{2}\Pi $ state of alkali-IIB excimers is deeper than the 3$^{2}\Sigma ^{+}$ state and the wells overlap partly. In contrast, the wells of the alkali-RG 3$^{2}\Sigma ^{+}$ and 2$^{2}\Pi $ states do not overlap and it is possible to study transitions from these states separately. After our investigation of alkali-IIB excimers, we expected to observe the LiRG produced in a similar photochemical reaction. Tam et al. \cite{tam76a} were the first to observe photochemically produced alkali-RG bands. They excited the K$_{2}$ 2$^{1}\Pi _{u}$ state by using the argon-ion laser line at 457.9 nm, which in collisions with RG produced the excited KRG excimer and one free potassium atom. Photochemical formation of the LiRG 3$^{2}\Sigma ^{+}$ state has not been investigated so far. The 1$^{2}\Pi $ state of LiAr was photochemically formed in reactive collisions of the Li$_{2}$(1(A) $^{1}\Sigma _{u}^{+}$), excited by a HeNe laser at a wavelength of 632.8 nm, and Ar \cite{zha91}. The potential-energy curves of alkali-RG were calculated by Pascale and Vandenplaque using pseudopotential method \cite{pas74}. {\it Ab initio} calculations of the potential-energy curves for LiRG are available for LiHe \cite{jun88} and LiAr \cite{gu94,par97}. Ground state potentials were determined experimentally by Buck and Pauly \cite{buc68} and recently by Br\"{u}hl and Zimmermann \cite{bru95} for LiAr, and by Auerbach \cite{aue74} for LiKr and LiXe. The first excited 1$^{2}\Pi $ states of LiAr and LiKr were published by Scheps et al. \cite{sch75}. This paper is organized as follows. In section II we present the experiment. The experimental results (section III) are given separately for XeCl excimer laser excitation, where we give the cross section measurements for photochemical formation of LiRG relative to the collisional energy transfer of Li$_{2}^{*}$+Li system, and PTP dye laser excitation. In section IV we present results of the {\it ab initio} calculation of the LiKr potential-energy curves and transition dipole moments. In section V, the spectral simulation are performed using the {\it ab initio} potential-energy curves for LiAr (\cite{gu94,par97}) and LiKr (this paper). In Section VI we discuss the possibilities for photochemical formation of LiAr$^{*}$ and LiKr$% ^{*}$, compare the experimental results with the simulations and estimate uncertainties in theoretical potential-energy curves and experimental rate constants for photochemical reactions. Conclusions are given in section VII. \section{Experiment} The experimental arrangement is the same as in our previous paper \cite {mil92}. The mixture of lithium, lithium dimer and rare gas was prepared in a crossed heat-pipe oven. The lithium vapor pressure was varied in the range from 5 to 20 Torr and rare gas pressure in the range from 5 to 700 Torr. The temperature for the above mentioned range of lithium pressures was varied from 900 K to 1150 K. When lithium vapor pressure was equal to the rare gas pressure the heat-pipe oven was operating in the heat-pipe mode for lithium. In that case the mixing with rare gas in the central part of the heat-pipe oven was negligible and pure lithium and lithium dimer spectra were observed. For the observation of LiRG bands it was necessary to have the RG pressure higher than 30 Torr. The preparation of electronically excited Li$% _{2}$ molecules in specific rovibrational levels of the 2(C)$^{1}\Pi _{u}$ state is achieved by means of the pulsed XeCl excimer laser lines at 308 nm (LPX 105E) or using a pulsed dye laser (LPD 3002) working with PTP dye (range: 330-350 nm). The horizontal laser induced fluorescence was rotated by a Dove prism and focused to the vertical entrance slit of the monochromator. The resolution of the system was about 0.1 nm. The signal from the photomultiplier with S20 cathode was averaged by a boxcar averager (PARC M162 and M164). The analog output from the boxcar was digitized by an A/D converter and fed to a laboratory computer. The spectral response of the system was determined by means of a calibrated tungsten-ribbon lamp and was found constant in the region of interest (violet spectral region). \section{Results} \subsection{XeCl excimer laser excitation} The XeCl excimer laser lines at 308 nm excite simultaneously the v'=13, J'=6 and the v'=19, J'=24 rovibrational levels in the Li$_{2}$ 2(C)$^{1}\Pi _{u}$ state with the excitation energies of 24897.07 cm$^{-1}$ and 26260.72 cm$% ^{-1}$, respectively. The 308 nm laser line should also excite energy levels above the potential barrier of the double-minimum 2$^{1}\Sigma _{u}^{+}$ state, but they cannot be clearly identified since the spectroscopic constants for the rovibrational levels above the barrier are not well known. Identification of these transitions also requires a better spectral resolution. The 3$^{2}\Sigma ^{+}$ state of the lithium-rare gas excimer is populated in the photochemical process, given by \begin{equation} Li_{2}(2(C)^{1}\Pi _{u})+RG\rightarrow LiRG(3^{2}\Sigma ^{+})+Li \end{equation} Figures 1 a,b,c show the violet 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ bands of LiAr (414 nm), LiKr (420 nm) and LiXe (435 nm), for excitation at 308 nm. The temperature was T=1161 K, yielding a partial lithium vapor pressure of 9 Torr and a density of Li atoms of 7.5.10$^{16}$ cm$^{-3}$ and a Li$_{2}$ partial vapor pressure of 0.5 Torr and Li$_{2}$ density of 3.83.10$^{15}$ cm$% ^{-3}$, according to the Nesmeyanov tables \cite{nes63} and the ideal-gas law. Argon, krypton and xenon pressures were 150, 300 and 200 Torr, respectively. On all three spectra, lithium atomic lines were observed at 413.3 nm (5$^{2}$D-2$^{2}$P) and 460.3 nm (4$^{2}$D-2$^{2}$P) and their intensities decreased at higher rare gas pressure in the heat-pipe oven. We also observed the Li$_{2}$ diffuse band at 458 nm (2$^{3}\Pi _{g}$-1$% ^{3}\Sigma _{u}^{+}$) and the interference continuum at 452 nm (2$^{1}\Sigma _{u}^{+}$-1(X)$^{1}\Sigma _{g}^{+}$), as indicated by vertical bars \cite {li92}. Intensities of the LiRG, Li$_{2}$ diffuse band and Li$_{2}$ interference continuum show an interesting dependence on the rare gas pressure. These intensities are determined as areas under the observed bands. The Li$_{2}$ interference continuum at 452 nm and the diffuse band at 458 nm overlap and we first obtained the area under both bands together. The intensity of the Li% $_{2}$ diffuse band was estimated from the intensity at its maximum (458 nm) and its half width, which is about 8 nm and does not change with rare gas pressure \cite{li92}. The interference continuum intensity is then the total intensity minus the diffuse band intensity. As an example, Figures 2 a,b,c show the LiXe band behavior with increasing xenon pressure for 50, 100 and 246 Torr, respectively. Comparison of the relative intensities of LiXe and Li$_{2}$ continuum bands versus Xe densities is shown in Fig. 3. We compare the photochemical reaction of Li$% _{2}$ with Xe (see Eq. (1)) with the collisional transfer of population resulting in the Li$_{2}$ diffuse band at 458 nm: \begin{equation} Li_{2}(2(C)^{1}\Pi _{u})+RG\rightarrow Li_{2}(2^{2}\Pi )+Li \end{equation} By inspection of Fig. 3 we observe a slight decrease in the intensity at 452 nm, which indicates a small contribution of Li$_{2}$(2$^{1}\Sigma _{u}^{+}$% )+Xe $\rightarrow $ LiXe(3$^{2}\Sigma ^{+}$)+Li reaction. However, in all subsequent analysis we shall not take into account this reaction. The photochemical reaction rate constant $k_{LiRG}$ giving LiRG* can be evaluated from: \begin{equation} k_{LiRG}=\frac{\nu _{diff}}{\nu _{LiRG}}\frac{\alpha (\nu _{diff})}{\alpha (\nu _{LiRG})}\frac{I_{LiRG}}{I_{diff}}\frac{\gamma _{LiRG}}{\gamma _{diff}}% \frac{\Gamma _{diff}}{\Gamma _{LiRG}}\frac{[Li]}{[RG]}k_{diff} \end{equation} where $\nu _{diff}$, $\nu _{LiRG}$, $\alpha (\nu _{diff})$, $\alpha (\nu _{LiRG})$, $I_{LiRG}$, $I_{diff},\Gamma _{diff},$ $\Gamma _{LiRG}$ are frequencies, spectral responses, intensities at the band maxima and radiative transition rates for the given transitions as given in more details in Ref. \cite{azi96}. Note that in Ref. \cite{azi96} (Eq. 12) the similar expression is given for the corresponding cross section $\sigma $(cm$% ^{2}$). All these values can be taken from the observed spectrum. The values $\gamma _{LiRG}$ and $\gamma _{diff}$ are: \[ \gamma _{LiRG}=\Gamma _{3^{2}\Sigma ^{+}-1^{2}\Sigma ^{+}}+\Gamma _{3^{2}\Sigma ^{+}-2^{2}\Sigma ^{+}}+\Gamma _{3^{2}\Sigma ^{+}-1^{2}\Pi } \] \[ \gamma _{diff}=\Gamma _{2^{3}\Pi -1^{3}\Sigma _{u}^{+}}+\Gamma _{2^{3}\Pi -2^{3}\Sigma _{u}^{+}}+\Gamma _{2^{3}\Pi -3^{3}\Sigma _{u}^{+}}+\Gamma _{2^{3}\Pi -1^{3}\Pi } \] where $diff\equiv $ $2^{3}\Pi -1^{3}\Sigma _{u}^{+}$ and $LiRG\equiv 3^{2}\Sigma ^{+}-1^{2}\Sigma ^{+}$. The factor $\gamma _{LiRG}$/$\gamma _{diff}$ can be estimated from the values of transition dipole moments for transitions from the LiRG 3$^{2}\Sigma ^{+}$ state to all radiatively coupled lower states \cite{gu94} and the values of transition dipole moments for transitions from the Li$_{2}$ 2$^{3}\Pi _{g}$ state to all radiatively coupled lower states \cite{rat87}. For LiAr this factor is 8.6 and for LiKr and LiXe we could not find any calculated value. Therefore we assume in the first approximation the same value of 8.6 also for LiKr and LiXe. The factor [Li]/[RG] is the atom density ratio of lithium and rare gas. The rate constant for collisional energy transfer (2) giving the Li$_{2}$ diffuse band at 458 nm as obtained by Weyh et al. \cite{wey96} is: \begin{equation} k_{diff}=<\sigma _{diff}v(Li_{2},Li)>=(25\pm 7)10^{-16}(8kT/\pi \mu )^{1/2}=(5.7\pm 1.6)10^{-10}cm^{3}s^{-1} \end{equation} The intensities of the LiXe band and Li$_{2}$ diffuse band and atom densities of Li and Xe from the graph in Fig. 3 give k$_{LiXe}$=(19$\pm $9) 10$^{-10}$ cm$^{3}$s$^{-1}$, using the least square fit method. Using the same method we obtain rate constants for photochemical formation of LiAr and LiKr in the 3$^{2}\Sigma ^{+}$ state, which are k$_{LiAr}$=(2.3$% \pm $1.1) 10$^{-10}$ cm$^{3}$s$^{-1}$ and k$_{LiKr}$=(6.9$\pm $3.2) 10$% ^{-10} $cm$^{3}$s$^{-1}$. The ratios of the rate constants for LiRG (3$% ^{2}\Sigma ^{+}$) and Li$_{2}$(2$^{3}\Pi _{g}$) formation are k$_{LiAr}$ / k$% _{diff}$=0.4, k$_{LiKr}$ / k$_{diff}$=1.21 and k$_{LiXe}$ / k$_{diff}$=3.33. The k$_{LiRG}$ values from LiAr to LiXe increase by a factor of about 8, which implies that, for the heavier rare gas atom with deeper potential well of the relevant 3$^{2}\Sigma ^{+}$ state, i.e. larger energy difference between the Li$_{2}^{*}$ energy level and the minimum of the 3$^{2}\Sigma ^{+}$ state potential, the probability of the photochemical reaction (1) rapidly increases, as compared to competitive collisional transfer processes between the excited states of alkali dimers (2). \subsection{Dye laser excitation} The PTP dye laser covers the range from 330 nm to 350 nm. This wavelength range enabled us to excite the Li$_{2}($2(C)$^{1}\Pi _{u})$ levels up to v'=6, which has the energy of 23660 cm$^{-1}$. There is no evidence in the spectrum around the laser line that we have excited any level in the inner well of the double minimum Li$_{2}$ 2$^{1}\Sigma _{u}^{+}$ state, below the potential barrier \cite{li93}. In order to study the dependence of the LiKr band intensity on the exciting laser wavelength we measured the selected wavelength excitation spectrum. Figure 4 presents the selected wavelength spectrum taken at the LiKr band maximum (420 nm). The laser wavelength was scanned from 335.2 to 335.4 nm. For large Franck-Condon factors in the Li$% _{2}$ 1(X)$^{1}\Sigma _{g}^{+}\rightarrow $2(C)$^{1}\Pi _{u}$ rovibrational excitation, identified in Fig. 4, we get maxima in the LiKr band intensity, which proves the validity of the photochemical reaction (1). \section{Potential-energy curves: The LiKr excimer} We calculated LiKr potential-energy curves for the four lowest states of the $^{2}\Sigma ^{+}$ symmetry and three of the $^{2}\Pi $ symmetry by using the MOLCAS2 package \cite{mol91}. The basis set for Li (6s4p3d) was used as in Ref. \cite{mil92}. For Kr we used primitive functions (21s16p10d) Ref. \cite {par89}. We added additional exponents to this: 0.08 and 0.03 for s type, 0.04 and 0.0165 for p type, 0.229 and 0.0916 for d type functions. This additional exponents were obtained from extrapolation of the s and p exponents in a log plot. For d type functions the exponents were taken from Ref. \cite{ric91}. As in Ref. \cite{ric91} even-tempered 4f type exponents were added. With this basis set almost the complete Hartree-Fock total energy was obtained at -2752.051 Hartree \cite{sch92}. Spherical coordinates were used giving with the above basis set 210 primitives and 81 contracted basis functions. The calculation was performed in the C$_{2v}$ symmetry. In MRCI 28 electrons were frozen (7,3,3,1) in a1, b1, b2, a2 irreducible representations and 22 virtual orbitals were deleted (12,5,5,0). In MRCI calculations 11 electrons were correlated (1s and 2s of Li and 4s and 4p of Kr). Nine main references were used defining a real space of 51709 configurations. Preceding to the MRCI either a SCF or a CASSCF calculations were performed. First order relativistic corrections (mass-velocity and Darwin term) were included as well \cite{mol91}. Table \ref{tab1} presents the {\it ab initio} potential-energies for the LiKr 1$^{2}\Sigma ^{+}$, 2$^{2}\Sigma ^{+}$, 3$^{2}\Sigma ^{+}$, 4$% ^{2}\Sigma ^{+}$, 1$^{2}\Pi $, 2$^{2}\Pi $ and 3$^{2}\Pi $ states. In Table \ref{tab2} we give dipole moment for the ground state and transition dipole moments for the LiKr $\Sigma $-$\Sigma $ transitions. Note that values and dependence on R obtained for LiKr molecule are similar to those of LiAr \cite {gu94,par97} which supports our assumptions in Sec. 3.1. Table \ref{tab3} presents the spectroscopic constants for the LiKr 1$^{2}\Sigma ^{+}$, 1$% ^{2}\Pi $, 2$^{2}\Sigma ^{+}$, 3$^{2}\Sigma ^{+}$ and 2$^{2}\Pi $ states. Table \ref{tab4} presents a comparison of the R$_{e}$ and T$_{e}$ taken from the LiKr 1$^{2}\Sigma ^{+}$ and 1$^{2}\Pi $ {\it ab initio} potentials with the values calculated by Pascale and Vandenplaque \cite{pas74} and with the experimental values given by Auerbach \cite{aue74} and Scheps et al. \cite {sch75}. From these data, we may conclude that the {\it ab initio} calculation of the ground state gives too deep minimum, because the experimental value is about 70 cm$^{-1}$. We believe that this is mainly due to the basis set superposition error. However, the difference potentials relevant to spectroscopy should be more accurate. \section{Spectral simulation of the LiAr and LiKr 3$^{2}\Sigma ^{+}$-1$% ^{2}\Sigma ^{+}$ bands} {\it Ab initio} potential-energy curves, transition dipole moments and spectroscopic constants for LiAr are published by Gu et al. \cite{gu94} and Park et al. \cite{par97}. The {\it ab initio} LiAr ground-state potential given in Ref. \cite{gu94} is completely repulsive whereas calculation of Ref. \cite{par97} shows shallow minimum at about 10 Bohr, closer to the experimental values \cite{buc68,bru95}. The 3$^{2}\Sigma ^{+}$ state has a shallow minimum and contains only 10 bound vibrational levels for J'=25.5. Note that shallow outer well of the 3$^{2}\Sigma ^{+}$ potential, which is obtained in calculation of Ref. \cite{par97}, does not affect spectral formation of the considered LiAr diffuse band. We performed the quantum mechanical simulation using the standard Numerov-Cooley method for the bound-free transitions \cite{num33}. Rotational averaging was performed over J'=0.5-40.5, assuming a Boltzmann distribution. The rovibrationally averaged LiAr spectral simulations for the effective temperature of 800 K are given in Fig. 5a. The calculated peak position is at 416.4 nm using potentials from Ref. \cite{gu94} and 413.1 nm using potentials from Ref. \cite{par97}, which is in a good agreement with the measured peak position at 414 nm. Prior to this simulations we performed another spectral simulations of the LiAr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transition using a different set of the {\it ab initio} potential energy curves and transition dipole moments as reported in Ref. \cite{azi94}. The calculated maximum of the LiAr band was at 405 nm. The shape of the simulated LiAr band was similarly asymmetric as in Fig. 5a but without the quantum oscillations on the blue wing of the band. Using the potential-energy curves given in Table \ref{tab1}, transition dipole moments given in Table \ref{tab2} and spectroscopic constants given in Table \ref{tab3} we performed quantum-mechanical spectral simulations of the LiKr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ band. The emission profiles for the range of rotational numbers from 0.5 to 150.5 and vibrational numbers from 0 to 10 were obtained in which the rotational averaging assuming the Boltzmann distribution for an effective temperature of 1000 K was assumed. The rotationally averaged spectra are vibrationally averaged assuming the Boltzmann distribution among 11 vibrational levels which give a significant contribution to the spectrum. Figure 5b shows simulation of the LiKr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ band with the maximum at 433 nm, which is shifted by 710 cm$^{-1}$ from the experimental position at 420 nm. Table \ref{tab5} gives the experimental positions of LiAr, LiKr and LiXe bands observed in this work and in the work of Wang and Havey, as well as the calculated positions of the LiAr and LiKr excimer bands. \section{Discussion} First we present the systematization of the possible photochemical reactions populating LiAr and LiKr in their excited states. Table \ref{tab6} presents a list of possible photochemical reactions populating the LiAr (upper part) and LiKr (lower part) excited states. We give the energy defect, and the positions of extrema in the difference potentials of the excited LiAr (LiKr) product of the reaction, and the spectral position of the observed bands. Because of the shallow minima of the LiAr excited states, usually we have to excite very high rovibrational levels in the Li$_{2}$ excited states. The other way of LiAr* formation is through the three-body recombination. These reactions are presented as collisions of Li atom in the excited state with two Ar atoms, giving LiAr in the excited state and the other argon atom in the ground state. Such collisions were studied in several papers. Excitation of the LiAr 1$^{2}\Pi $ state by exciting the lithium atomic 2$^{2}$P state was studied by Scheps et al. \cite{sch75}. The formation of the LiAr 3$% ^{2}\Sigma ^{+}$ and 2$^{2}\Pi $ states by exciting lithium to 3$^{2}$P and 3% $^{2}$D levels was studied by Wang and Havey \cite{wan84}. In the work of Zhang and Ma, the lithium dimer was excited by a He-Ne laser to the high rovibrational levels of the Li$_{2}$ 1(A)$^{1}\Sigma _{u}^{+}$ state and they observed the photochemical reaction leading to the LiAr 1$^{2}\Pi $ state \cite{zha91}. Other photochemical reactions listed in Table \ref{tab6} were not studied up to now. Collisions of one lithium atom in an excited atomic state with two Kr atoms are the only three-body recombinations observed so far. Excitation of the lithium resonance line gives the LiKr band at 801 nm \cite{sch75}. Wang and Havey studied the excitation of lithium 3$^{2}$P and 3$^{2}$D atomic states, populating the LiKr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ states [6]. Photochemical reactions from the lithium dimer molecular states, as the input channel, to the LiKr excited states, as the output channel, have not been observed to date. The observation of the relatively intensive LiRG 3$^{2}\Sigma ^{+}$-1$% ^{2}\Sigma ^{+}$ bands can be explained by analyzing the shape of the potential-energy curves of Li$_{2}$ and LiRG, which are presented in Figs. 6a and 6b, respectively. The 2$^{2}\Sigma ^{+}$ state is repulsive, with a shallow van der Waals well at large internuclear separations. Such a repulsive 2$^{2}\Sigma ^{+}$ state has an avoided crossing with an energetically higher 3$^{2}\Sigma ^{+}$ state, which has the same symmetry. This avoided crossing is responsible for the increase of the transition dipole moment of the 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transition (intensity borrowing). The 2$^{2}\Pi $ states in alkali-rare gas excimers does not overlap with the 3$^{2}\Sigma ^{+}$ state and the transition dipole moment for the 2$^{2}\Pi $-1$^{2}\Sigma ^{+}$ transition is about 3 times lower than that for the 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transition. Photochemical population of the 3$^{2}\Sigma ^{+}$ state is preferred here, since for the photochemical population of the 2$^{2}\Pi $ state more energy is needed for excited alkali dimers in the input channel of the reaction. The 2$^{2}\Pi $ state can be achieved in three atom collisions, including the alkali atom in the second excited P state or the first excited D state with two rare gas atoms. Because of the shallow 3$^{2}\Sigma ^{+}$ states in LiRG excimers, the higher laser photon energies are more probable to populate the LiRG 3$^{2}\Sigma ^{+}$ state in reaction (1). Therefore the excimer laser line at 308 nm gives more intensive LiRG bands than the dye laser excitation at photon energies of 335 nm. The smallest excitation energy in the Li$_{2}$ 2(C)$^{1}\Pi _{u}$ state which will enable photochemical formation of the 3$^{2}\Sigma ^{+}$ state is 25544 cm$^{-1}$ and 24395 cm$^{-1}$ for LiAr and LiKr, respectively. According to Table \ref {tab5} the calculated LiKr excited states are too deep by about 500 cm$^{-1}$% , which moves T$_{e}$(LiKr) to 24900 cm$^{-1}$. The excimer laser line at 308 nm which populates Li$_{2}$(2(C)$^{1}\Pi _{u}$) with E=26260.7 cm$^{-1}$ provides for all LiGR molecules enough energy to start reaction (1). In the case of dye laser excitation at 335 nm, E=23660 cm$^{-1}$ does not reach the threshold for the reaction (1) for LiAr and LiKr. However, we observe the reaction at high temperature and rare gas pressure because the collisional energies give an additional 1000 cm$^{-1}$. The positions of maxima of the LiRG bands at 414, 420 and 435 nm correspond to energies of 24154, 23809 and 22988 cm$^{-1}$ for LiAr, LiKr and LiXe, respectively. Spectral simulations give maxima in the LiAr and LiKr bands at 416 and 433 nm, which correspond to energies of 24038 and 23095 cm$^{-1}$, respectively. Using all these values we can roughly estimate the error of the 3$^{2}\Sigma ^{+}$-1$% ^{2}\Sigma ^{+}$ difference potential, which is about 120 cm$^{-1}$ for LiAr and 700 cm$^{-1}$ for LiKr. The large uncertainties in the determination of the rate constants k$_{LiRG}$% , which are about 50 \%, are mainly due to the uncertainty of the collisional energy transfer cross section $\sigma _{diff}$ \cite{wey96}, which is 28 \%. The second large contribution is the uncertainty in the intensity measurements of the Li$_{2}$ diffuse band at 458 nm, which is about 15 \% because of the overlap with the Li$_{2}$ interference continuum at 452 nm. The LiRG bands are not disturbed by other molecular transitions and the error in the intensity determination is not higher than 5 \%. The errors in the atom density ratios [RG]/[Li], frequencies and spectral responses are not larger than few \%. The accuracy of factor $\gamma _{LiRG}$% /$\gamma _{diff}$ for LiAr depends on the uncertainties of transition dipole moments. For LiKr and LiXe we took the same value as for LiAr and, in these cases, rate constants may be underestimated since the transition dipole moments for LiKr and LiXe are slightly larger than for LiAr. \section{Conclusion} We investigated photochemical formation of the lithium-rare gas 3$^{2}\Sigma ^{+}$ states in the reaction given by relation (1). We worked with all rare gases, from He to Xe, but we observed no LiHe and LiNe 3$^{2}\Sigma ^{+}$-1$% ^{2}\Sigma ^{+}$ bands in the spectrum. The LiAr, LiKr and LiXe 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transitions were observed at 414, 420 and 435 nm, respectively. We found that the rare gas pressure had to be at least about 2 times larger than the lithium vapor pressure if we want to observe the LiRG band as a result of the above reaction. We estimated rate constants for this photochemical reaction at T = 1160 K as (2.3$\pm $1.1) 10$^{-10}$ cm$^{3}$s$% ^{-1}$, (6.9$\pm $3.2) 10$^{-10}$ cm$^{3}$s$^{-1}$ and (19$\pm $9) 10$^{-10}$ cm$^{3}$s$^{-1}$ for LiAr, LiKr and LiXe, respectively, measured relatively to the collisional energy transfer \cite{wey96}. The photochemical reaction can populate only the 3$^{2}\Sigma ^{+}$ state of the Li-rare gas excimer because the 2$^{2}\Pi $ state is energetically too high. Spectral simulations of the LiAr and LiKr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transitions were calculated using the recently calculated ab initio potential-energy curves. Using potentials of Ref. \cite{par97} spectral simulation of the LiAr band gives peak at 413.1 nm, in better agreement with experimental position at 414 nm, compared to the case when using potentials of Ref. \cite{gu94}. The simulated position of the LiKr band is at 433 nm. It is shifted by about 13 nm to the red, as compared with the experimental value of 420 nm. The LiKr ground state {\it ab initio} potential is about 200 cm$^{-1}$ too deep when compared with the experimental potential. To reproduce the experimental position of the LiKr band, we have to add about 800 cm$^{-1}$ to the 3$^{2}\Sigma ^{+}$ {\it ab initio} potential. \section{Acknowledgments} This work was financially supported by the Ministry of Science and Technology of the Republic of Croatia. We also gratefully acknowledge partial support from the Alexander von Humboldt Stiftung, Germany. One of us (S.M.) is grateful to the Max-Planck-Institute f\"{u}r Str\"{o}mungsforschung for the hospitality during his stay in G\"{o}ttingen. \begin{references} \bibitem{ros82} F. Rostas, Alkali-rare gas excimers, in Spectral line shapes, Vol. II, p. 767 (1982). \bibitem{tam75} A. C. Tam, G. Moe, W. Park and W. Happer, Phys. Rev. Lett. {\bf 35}, 85 (1975). \bibitem{tam76a} A. C. Tam, G. Moe, B. R. Bulos and W. Happer, Optics Comm. {\bf 16}, 376 (1976). \bibitem{tam76b} A. C. Tam and G. Moe, Phys. Rev. A {\bf 14}, 528 (1976). \bibitem{web78} Ch. R. Webster and F. Rostas, Chem. Phys. Lett. {\bf 59}, 57 (1978). \bibitem{wan84} W. J. Wang and M. D. Havey, Phys. Rev. A {\bf 29}, 3184 (1984). \bibitem{mil92} S. Milo\v {s}evi\'{c}, X. Li, D. Azinovi\'{c}, G. Pichler, M. C. van Hemert, A. Stehouwer and R. D\"{u}ren, J. Chem. Phys. {\bf 96}, 7364 (1992). \bibitem{hem92} M. C. van Hemert, D. 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Azinovi\'{c}, Ph.D. Thesis: Photochemical formation of lithium-IIB and lithium-rare gas excimers, Institute of Physics, Zagreb, Croatia, 1994. \end{references} \newpage \begin{figure}[tbp] \caption{a) The LiAr excimer band at 414 nm. Argon pressure is 150 Torr and the temperature 1161 K. b) The LiKr excimer band is at 420 nm. Krypton pressure is 300 Torr and T=1161 K c) The LiXe excimer band is at 435 nm. Xenon pressure is 200 Torr and T=1161 K. The Li-rare gas bands, lithium dimer diffuse band at 458 nm and the interference continuum at 452 nm are indicated by bars. * - the lithium atomic 4$^{2}$D-2$^{2}$P line is out of scale.} \label{fig1} \end{figure} \begin{figure}[tbp] \caption{Dependence of the LiXe band and Li$_{2}$ band shapes and intensities on the xenon pressure: a) P$_{Xe}$=50 Torr, b) P$_{Xe}$=100 Torr, and c) P$_{Xe}$=246 Torr. Temperature is 1161 K. Bars indicate the positions of the LiXe band and Li$_{2}$ bands.* - line out of scale.} \label{fig2} \end{figure} \begin{figure}[tbp] \caption{Intensities of the LiXe band, Li$_{2}$ diffuse band and Li$_{2}$ interference continuum versus the atom density of xenon. The intensities are the areas under the bands and the errors of intensities are up to 20 \% for Li$_{2}$ bands and up to 10 \% for the LiXe band.} \label{fig3} \end{figure} \begin{figure}[tbp] \caption{Selective absorption spectrum on the LiKr excimer band maximum at 420 nm. The maxima correspond to the Li$_{2}$ 2$^{1}\Pi _{u}$-1$^{1}\Sigma _{g}^{+}$ rovibrational transitions (v',v'',J'), identified using spectroscopic constants for the Li$_{2}$ 2$^{1}\Pi _{u}$ and 1$^{1}\Sigma _{g}^{+}$ states \protect\cite{kon84,ish91,sch85}.} \label{fig4} \end{figure} \begin{figure}[tbp] \caption{a) Spectral simulation of the LiAr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transition using the {\it ab initio} potential-energy curves from Ref. \protect\cite{gu94} (dashed line) and Ref. \protect\cite{par97} (full line). b) Spectral simulation of the LiKr 3$^{2}\Sigma ^{+}$-1$^{2}\Sigma ^{+}$ transition using the {\it ab initio} potential-energy curves from Sec. IV.} \label{fig5} \end{figure} \begin{figure}[tbp] \caption{a) The Li$_{2}$ 1$^{1}\Sigma _{g}^{+}$, 1$^{1}\Sigma _{u}^{+}$, 1$% ^{1}\Pi _{u}$, 2$^{1}\Sigma _{u}^{+}$ and 2$^{1}\Pi _{u}$ potentials \protect\cite{kon84,ish91,sch85}. b) {\it Ab initio} potential-energy curves of the LiKr excimer.} \label{fig6} \end{figure} \newpage \begin{table}[tbp] \caption{Potential energies for LiKr molecule in hartree, interatomic separation R is in Bohr.} \label{tab1} \begin{tabular}{llllllll} R & 1$^{2}\Sigma ^{+}$ & 2$^{2}\Sigma ^{+}$ & 3$^{2}\Sigma ^{+}$ & 4$% ^{2}\Sigma ^{+}$ & 1$^{2}\Pi $ & 2$^{2}\Pi $ & 3$^{2}\Pi $ \\ \hline 3.25 & -0.4005085 & -0.3234644 & -0.2961731 & -0.2876754 & -0.3380897 & -0.2920849 & -0.2772029 \\ 3.5 & -0.4375632 & -0.3612275 & -0.3339143 & -0.3248739 & -0.3780887 & -0.3292013 & -0.3156819 \\ 3.75 & -0.4596559 & -0.3832798 & -0.3561417 & -0.3465490 & -0.4021021 & -0.3505374 & -0.3382916 \\ 4. & -0.4726528 & -0.3956805 & -0.3688309 & -0.3585256 & -0.4161919 & -0.3621480 & -0.3510792 \\ 4.25 & -0.4801896 & -0.4022790 & -0.3757338 & -0.3645550 & & & \\ 4.5 & -0.4844912 & -0.4055250 & -0.3791750 & -0.3670242 & -0.4283643 & -0.3697614 & -0.3611132 \\ 5. & -0.4883810 & -0.4080389 & -0.3809768 & -03667541 & -0.4310826 & -0.3689544 & -0.3618997 \\ 5.5 & -0.4897088 & -0.4095498 & -0.3796883 & -0.3641447 & -0.4303854 & -0.3653886 & -0.3595355 \\ 6. & -0.4903606 & -0.4121060 & -0.3774106 & -0.3602489 & -04289024 & -0.3617274 & -0.3567152 \\ 7. & -0.4911732 & -0.4165793 & -0.3728927 & -0.3552986 & -0.4263529 & -0.3564139 & -0.3523502 \\ 8. & & & & & -0.4251961 & -0.3541763 & -0.3507252 \\ 8.5 & -0.4920470 & -0.4216463 & -0.3701660 & -0.3536025 & & & \\ 9.5 & & & & & -0.4248510 & -0.3532627 & -0.3505684 \\ 10. & -0.4923555 & -0.4237854 & -0.3696169 & -0.3531456 & & & \\ 11. & -0.4921555 & -0.4240683 & -0.3693427 & -0.3526411 & -0.4244894 & -0.3527058 & -0.3505085 \\ 12.5 & -0.4919990 & -0.4239981 & -0.3693398 & -0.3523484 & & & \\ 15. & -0.4920005 & -0.4240205 & -0.3696144 & -0.3522318 & -0.4242991 & -0.3524386 & -0.3505300 \\ 18. & -0.4918726 & -0.4238290 & -0.3695808 & -0.3522761 & -0.4241580 & -0.3522776 & -0.3504068 \end{tabular} \end{table} \newpage \begin{table}[tbp] \caption{Dipole moment for the ground state and transition dipole moments for LiKr in atomic units.} \label{tab2} \begin{tabular}{lllll} R & 1$^{2}\Sigma ^{+}$ & 2$^{2}\Sigma ^{+}-1^{2}\Sigma ^{+}$ & 3$^{2}\Sigma ^{+}-1^{2}\Sigma ^{+}$ & 4$^{2}\Sigma ^{+} -1^{2}\Sigma ^{+}$ \\ \hline 3.25 & 1.77776874 & 1.86186478 & 0.92245651 & 0.38236908 \\ 3.5 & 1.79671425 & 1.90200787 & 0.91466456 & 0.36047910 \\ 3.75 & 1.79152689 & 1.93262393 & 0.90494948 & 0.33517901 \\ 4 & 1.76002886 & 1.96183103 & 0.89052320 & 0.30862715 \\ 4.25 & 1.70208274 & 1.99678065 & 0.86668951 & 0.28140826 \\ 4.5 & 1.61937599 & 2.04227469 & 0.82738405 & 0.25065849 \\ 5 & 1.40927266 & 2.12598452 & 0.69529641 & 0.24336991 \\ 5.5 & 1.14072158 & 2.25505190 & 0.50135385 & 0.23199599 \\ 6 & 0.87099314 & 2.33929207 & 0.29932825 & 0.17813524 \\ 7 & 0.42212540 & 2.38938202 & 0.06776487 & 0.03502065 \\ 8.5 & 0.12787435 & 2.41388895 & 0.00413534 & 0.03975754 \\ 10 & 0.03951016 & 2.41989614 & 0.00830578 & 0.06651151 \\ 11 & 0.02049474 & 2.41730242 & 0.00368579 & 0.06967306 \\ 12.5 & 0.01641412 & 2.41121085 & 0.00348032 & 0.06437032 \\ 15 & 0.01526793 & 2.39976461 & 0.00479587 & 0.07530521 \\ 18 & 0.01638541 & 2.39239426 & 0.00267635 & 0.08321014 \end{tabular} \end{table} \newpage \begin{table}[tbp] \caption{Calculated spectroscopic constants of LiKr (in cm$^{-1}$.)} \label{tab3} \begin{tabular}{llllllllll} State & R$_{e}$(Bohr) & D$_{e}$ & T$_{e}$ & B$_{e}$ & $\omega _{e}$ & $% \omega _{e}x_{e}$ & $\alpha _{e}$ & v$_{max}$ & E$_{exp}$($\infty )$ \\ \hline 1$^{2}\Sigma ^{+}$ & 9.36 & 273 & -273 & 0.105 & 9.9 & 0.85 & 0.012 & 5 & 0 \\ 1$^{2}\Pi $ & 5.06 & 1411 & 13444 & 0.362 & 218.4 & 9.1 & 0.003 & 11 & 14855 \\ 2$^{2}\Sigma ^{+}$ & 11.71 & 88 & 14767 & 0.068 & 4212 & 4.3 & 0.005 & 4 & 14855 \\ 3$^{2}\Sigma ^{+}$ & 4.95 & 2509 & 24395 & 0.373 & 229.1 & 5.1 & 0.005 & 22 & 26904 \\ 2$^{2}\Pi $ & 4.64 & 3806 & 26849 & 0.431 & 313.7 & 6.7 & 0.011 & 22 & 30655 \end{tabular} \end{table} \newpage \begin{table}[tbp] \caption{Comparison of the LiKr 1$^{2}\Sigma ^{+}$ and 1$^{2}\Pi $ excited states with the previously published experimental \protect\cite{sch75}, \protect\cite{aue74} and calculated potentials \protect\cite{pas74}.} \label{tab4} \begin{tabular}{llll} State & Reference & R$_{e}$(Bohr) & T$_{e}$(cm$^{-1}$) \\ \hline 1$^{2}\Sigma ^{+}$ & This work & 9.36 & -273 \\ & Auerbach \cite{aue74} & 9.04 & -67.9 \\ & Pascale et al. \cite{pas74} & 9.45 & -65.7 \\ 1$^{2}\Pi $ & This work & 5.06 & 13444 \\ & Scheps et al. \cite{sch75} & 6.01 & 13800 \\ & Pascale et al. \cite{pas74} & 6.0 & 14300 \end{tabular} \end{table} \newpage \begin{table}[tbp] \caption{Maxima ($\protect\lambda $) of the LiAr, LiKr and LiXe excimer bands compared with the observations ($\protect\lambda ^{*}$) of Wang and Havey \protect\cite{wan84} and the calculations ($\protect\lambda ^{c}$). $% ^{a}$ using Ref. \protect\cite{gu94}, $^{b}$ using Ref. \protect\cite{par97}% . } \label{tab5} \begin{tabular}{llll} & LiAr & LiKr & LiXe \\ \hline $\lambda $(nm) & 414 & 420 & 435 \\ $\lambda ^{*}$(nm) & 411 & 416 & 431 \\ $\lambda ^{c}$(nm) & 416.4 $^{a}$ & 433 & \\ & 413.1 $^{b}$ & & \end{tabular} \end{table} \newpage \begin{table}[tbp] \caption{A list of photochemical reactions producing the excited LiAr and LiKr excimers. We give the energy defect of the reaction, the spectral positions of the listed transitions calculated from the extrema in difference potentials and observed values (in nm), where available.} \label{tab6} \begin{tabular}{lrll} Reaction & $\Delta $E(cm$^{-1}$) & Transition & Calculated position in nm, comments \\ \hline Li(2$^{2}$P)+Ar+Ar$\rightarrow $LiAr(1$^{2}\Pi $)+Ar & 79 & 1$^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 674, min at 4.2 Bohr, obs. at 790 \cite {sch75} \\ Li$_{2}$(1$^{1}\Sigma _{u}^{+}$)+Ar$\rightarrow $LiAr(1$^{2}\Pi $)+Li & -9270 & 1$^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 674, min at 4.2 Bohr, obs. at 740 \cite{zha91} \\ Li$_{2}$(1$^{1}\Pi _{u}$)+Ar$\rightarrow $LiAr(1$^{2}\Pi $)+Li & -2902 & & \\ Li(3$^{2}$P)+Ar+Ar$\rightarrow $LiAr(3$^{2}\Sigma $)+Ar & 4807 & 3$% ^{2}\Sigma ^{+}\rightarrow 1^{2}\Sigma ^{+}$ & 416, min at 3.5 Bohr, obs. at 411 \cite{wan84} \\ Li(3$^{2}$D)+Ar+Ar$\rightarrow $LiAr(3$^{2}\Sigma $)+Ar & 5166 & & \\ Li(3$^{2}$P)+Ar+Ar$\rightarrow $LiAr(2$^{2}\Pi $)+Ar & 1837 & 2$^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 394, min at 3.5 Bohr, obs. at 380 \cite {wan84} \\ Li(3$^{2}$D)+Ar+Ar$\rightarrow $LiAr(2$^{2}\Pi $)+Ar & 2196 & & \\ Li$_{2}$(2$^{1}\Pi _{u}$)+Ar$\rightarrow $LiAr(3$^{2}\Sigma $)+Li & -4064 & 3% $^{2}\Sigma ^{+}\rightarrow 1^{2}\Sigma ^{+}$ & 416, min at 3.5 Bohr \\ Li$_{2}$(2$^{1}\Sigma _{u}^{+}$)+Ar$\rightarrow $LiAr(3$^{2}\Sigma $)+Li & -4315 & 3$^{2}\Sigma ^{+}\rightarrow 1^{2}\Pi $ & 825, max at 5.2 Bohr \\ & & 3$^{2}\Sigma ^{+}\rightarrow 2^{2}\Sigma ^{+}$ & 1674, min at 4 Bohr \\ Li$_{2}$(2$^{1}\Pi _{u}$)+Ar$\rightarrow $LiAr(2$^{2}\Pi $)+Li & -7034 & 2$% ^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 394, min at 3.5 Bohr \\ Li$_{2}$(2$^{1}\Sigma _{u}^{+}$)+Ar$\rightarrow $LiAr(2$^{2}\Pi $)+Li & -7285 & 2$^{2}\Pi \rightarrow 1^{2}\Pi $ & no extrema \\ & & 2$^{2}\Pi \rightarrow 2^{2}\Sigma ^{+}$ & 631, max at 14 Bohr \\ \hline Li(2$^{2}$P)+Kr+Kr$\rightarrow $LiKr(1$^{2}\Pi $)+Kr & 1559 & 1$^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 744, min. at 4.5 Bohr, obs. at 802\cite {sch75} \\ Li$_{2}$(1$^{1}\Sigma _{u}^{+}$)+Kr$\rightarrow $LiKr(1$^{2}\Pi $)+Li & -7876 & 1$^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 744, min. at 4.5 Bohr \\ Li$_{2}$(1$^{1}\Pi _{u}$)+Kr$\rightarrow $LiKr(1$^{2}\Pi $)+Li & -1508 & & \\ Li(3$^{2}$P)+Kr+Kr$\rightarrow $LiKr(3$^{2}\Sigma $)+Kr & 6539 & 3$% ^{2}\Sigma ^{+}\rightarrow 1^{2}\Sigma ^{+}$ & 433, min. at 3.5 Bohr , obs. at 416 \cite{wan84} \\ Li(3$^{2}$D)+Kr+Kr$\rightarrow $LiKr(3$^{2}\Sigma $)+Kr & 6898 & & \\ Li(3$^{2}$P)+Kr+Kr$\rightarrow $LiKr(2$^{2}\Pi $)+Kr & 4085 & 2$^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 401, min at 3.5 Bohr, obs. at 392 \cite {wan84} \\ Li(3$^{2}$D)+Kr+Kr$\rightarrow $LiKr(2$^{2}\Pi $)+Kr & 4444 & & \\ Li$_{2}$(2$^{1}\Pi _{u}$)+Kr$\rightarrow $LiKr(3$^{2}\Sigma $)+Li & -2332 & 3% $^{2}\Sigma ^{+}\rightarrow 1^{2}\Sigma ^{+}$ & 433, min. at 3.5 Bohr \\ Li$_{2}$(2$^{1}\Sigma _{u}^{+}$)+Kr$\rightarrow $LiKr(3$^{2}\Sigma $)+Li & -2583 & 3$^{2}\Sigma ^{+}\rightarrow 1^{2}\Pi $ & 1053, min at 4 Bohr \\ & & 3$^{2}\Sigma ^{+}\rightarrow 2^{2}\Sigma ^{+}$ & 1904, min. at 4.7 Bohr \\ Li$_{2}$(2$^{1}\Pi _{u}$)+Kr$\rightarrow $LiKr(2$^{2}\Pi $)+Li & -4786 & 2$% ^{2}\Pi \rightarrow 1^{2}\Sigma ^{+}$ & 401, min at 3.5 Bohr \\ Li$_{2}$(2$^{1}\Sigma _{u}^{+}$)+Kr$\rightarrow $LiKr(2$^{2}\Pi $)+Li & -5037 & 2$^{2}\Pi \rightarrow 1^{2}\Pi $ & no extrema \\ & & 2$^{2}\Pi \rightarrow 2^{2}\Sigma ^{+}$ & 1324, min. at 4.5 Bohr \end{tabular} \end{table} \end{document}