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Chemical Physics 332 (2007) 10–16

Observations and analysis of the K2 41Rþg state using theinfrared–infrared double resonance spectroscopy

Dan Li a, Feng Xie a, Yizhuo Chu a, Li Li a,*, S. Magnier b, V.B. Sovkov c, V.S. Ivanov c

a Department of Physics and Key Laboratory of Atomic and Molecular Nanosciences, Tsinghua University, Beijing 100084, Chinab Laboratoire des Atomes, Lasers, Mole’cules et Surfaces (PALMS), CNRS et Universite’ Rennes I (UMR 6627), Campus de Beaulieu,

Bt 11B 35042 Rennes Cedex, Francec V.A. Fock Institute of Physics, St. Pertersburg State University, 1 Ulyanovskaya Street, Petrodvorets, St. Petersburg 198504, Russian Federation

Received 10 September 2006; accepted 9 November 2006Available online 22 November 2006

Abstract

Totally 1195 transitions into the K2 41Rþg v = 2 � 36, J = 1 � 85 ro-vibrational levels have been observed by infrared–infrared doubleresonance spectroscopy. Spin–orbit interaction between the 41Rþg state and the 23PgX = 0+ state has been observed. Molecular con-stants, RKR potential curve, and spin–orbit interaction matrix element have been determined from the analysis of the experimental data.� 2006 Elsevier B.V. All rights reserved.

Keywords: K2; Potassium dimer; K2 Rydberg states; Infrared–infrared double resonance; K2 41Rþg state

1. Introduction

Ab initio potential functions of ninety-eight electronicstates below the 4s + 5d atomic limit of K2, including the1–12 1Rþg states, have been calculated [1]. While many Ryd-berg gerade states have been observed by optical–opticaldouble resonance (OODR) spectroscopy and organizedinto Rydberg series [2–12], the 2–4 1Rþg states have not beenobserved till now, partially because two infrared lasers arerequired to access these lowest excited 1Rþg states from theground state by a two-step excitation. Recently [13,14] westudied the K223Pg state by perturbation facilitated infra-red–infrared (IR–IR) double resonance spectroscopy withsingle mode tunable diode lasers. The 41Rþg state is in thesame energy region as the 23Pg state and dissociates tothe same 4s + 3d atomic limit. In this paper, we reportthe first observation of the 41Rþg state and the analysisof the experimental results, including a deperturbation ofthe spin–orbit interaction with the 23PgX = 0+ state. The

0301-0104/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2006.11.018

* Corresponding author. Tel.: +86 10 6278 8938x155; fax: +86 10 62781598.

E-mail address: lili@mail.tsinghua.edu.cn (L. Li).

experimental term values, the molecular constants, andthe RKR potential function of the K2 41Rþg state arereported along with the perturbation matrix elementbetween this state and the 23PgX = 0+ state.

2. Experimental setup

The experimental setup was the same as in our previousexperiment of the 23Pg state [13,14]. Briefly, potassiumvapor was generated in a crossing heat pipe oven withabout 1 Torr Ar buffer gas. At equilibrium condition, thetemperature of the potassium vapor was about 500 K. AToptica DL 100 single mode tunable diode laser (centerwavelength 852 nm, �40 mW output) was used as the pump

laser; another Toptica DL 100 diode laser (a diode with980 nm central wavelength, �100 mW output, or a diodewith 935 nm central wavelength, �40 mW output, or adiode with 1050 nm central wavelength, �40 mW output)was used as the probe laser. The laser frequencies were mea-sured by Burleigh WA-1600 wavemeters with an accuracyof 0.003 cm�1. The pump laser was modulated with amechanical chopper and its wavelength was held fixed toexcite an A1Rþu intermediate level from the ground state.

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 360

10

20

30

40

50

60

70

80

J

v

Fig. 1. Data field of the vibrational rotational levels observed in thisexperiment.

D. Li et al. / Chemical Physics 332 (2007) 10–16 11

The probe laser was scanned and transitions into the 41Rþgstate were detected by monitoring collision-induced yel-low–green fluorescence with filters and photomultiplier(PMT). When the pump and probe laser frequencies wereheld fixed to excite a 41Rþg level, resolved fluorescencewas recorded by scanning a Spex 1404 monochromator.

3. Observations

3.1. Excitation data and vibrational assignment

Accurate molecular constants of the X 1Rþg state areavailable [15]. The A1Rþu state is perturbed by theb3PuX ¼ 0þ state, and the term values of the A1Rþu levels,unperturbed as well as perturbed, can be calculated accu-rately from the deperturbed constants and perturbationparameters of these two states [16]. When the pump laserfrequency was held fixed to selectively excite an A1Rþu v0,J 0 level (or an A1Rþu � b3Pu mixed level), the probe laserfrequency was scanned and IR–IR double resonanceexcitation transitions were detected by monitoring colli-sion-induced 23Rþg =23Pg ! a3Rþu and 21Rþu ! X 1Rþg yel-low–green fluorescence. In order to confirm the excitationlines originated from the selected intermediate A1Rþu (v 0,J 0)level, we first set the pump frequency to the A1Rþu ðv0; J 0Þ X 1Rþg (v00,J00 = J 0 + 1) transition, scanned the probe laser,then changed the pump laser frequency to excite theA1Rþu ðv0; J 0Þ X 1Rþg (v00,J00 = J 0 � 1) transition andscanned the probe again. Only those signals whichappeared at the same frequencies with the same intensitiesin the two scans were confirmed to be via the selected A1Rþu(v 0,J 0) intermediate level.

Many of the observed levels were effectively populated viaperturbation-free levels of the A1Rþu state; hence, they belongto a singlet electronic state. The probe transition containstwo excitation lines into every vibrational level. These twolines were confirmed to be DJ = ±1 R and P lines by observ-ing the same upper J level from both J 0 = J + 1 andJ 0 = J � 1 intermediate levels. Thus the upper state mustbe a 1Rþg state. In the energy region of this experiment,21,200–24,000 cm�1, there are only two 1Rþg states, the31Rþg and 41Rþg states [1]. The Te value of the 31Rþg state is1062 cm�1 lower than the Te value of the 41Rþg state and itsxe is predicted to be only 33 cm�1 [1]. The vibrational sepa-rations of the lowest vibrational levels of this newly observedstate are �80 cm�1, thus it must be the 41Rþg state.

The vibrational numbering of the excited levels wasdetermined by the following two steps.

(1) Comparing the experimental molecular constantswith theoretical constants. Ref. [1] gives the theoreti-cal Re, Te, xe, and De of 98 electronic states. The dif-ferences of the Te values observed and calculated areall less than 120 cm�1. The 23Pg state is in the sameenergy region and the difference between the observedand ab initio Te values is �20 cm�1 [14]. The spacingof the two lowest vibrational levels of the newly

observed state is about 80 cm�1. If we assign the low-est vibrational level observed as v = 2, the empiricalTe differ from the ab initio [1] one of the 41Rþg stateby �10 cm�1.

(2) Comparing the calculated Franck–Condon factors(FCF) between the 41Rþg and A1Rþu states with theobserved line intensities of the probe transitions.We first assigned the lowest vibrational level asv = 2, fitted the Dunham constants, and calculatedthe RKR potential curve and Franck–Condon fac-tors. Although quantitative comparisons of the calcu-lated FCF with observed excitation line intensitieswere not possible for all lines due to day-to-day vari-ations of experimental conditions (diode laser intensi-ties, pressure variations, laser overlap conditions,etc.), all the transitions with nearly zero FCF werenot observed while all the transitions with largerFCF were observed. Then we changed the vibrationalquantum number of the lowest observed level to v = 1and v = 3, fitted the Dunham constants and calcu-lated the FCF again. This case the relative line inten-sities of the probe transitions completely disagreedwith the FCF. Thus we concluded that the lowestlevel is v = 2. The v = 0, 1 levels were not observeddue to small FCF from the intermediate levels inour experiment.

Totally 1195 IR–IR double resonance transitions into 35vibrational levels of the 39K2 41Rþg state have been regis-tered. The data field of the observed K2 41Rþg state ro-vibrational levels is shown in Fig. 1. The IR-IR transitionsare listed in Appendix A.

3.2. Perturbation between the 23Pg and 41Rþg states

Perturbation between the 23Pg and 41Rþg states wasobserved. Besides the 41Rþg levels, many 23P0g levels and

555 560 565 570 575 580 585

-1000

-2000

-3000

-4000

-5000

-6000

-7000

-8000

-9000

0

1000

2000

3000

4000

5000

6000

23Π0g

v=12, J=36

λ, nm

41Σ+

gv=10, J=36

Inte

nsity

, Arb

itrar

y

Fig. 3. Resolved fluorescence spectra from the 23P0gv = 12, J = 36 level(lower) and 41Rþg v ¼ 10, J = 36 level (upper) to the a3Rþu state.

553.5 554.0 554.5 555.0 555.5 556.0 556.5 557.0 557.5-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

v'=8

v'=7v'=6

v'=5

v'=4

v'=3

v'=2

v'=1

v'=0

23Π0g

v=12, J=41

Inte

nsity

, A

rbitr

ary

λ, nm

41Σ+

gv=10, J=41

1 þ

12 D. Li et al. / Chemical Physics 332 (2007) 10–16

some 23P1g levels were also observed via perturbation-freeA1Rþu intermediate levels. Fluorescence from the perturbed41Rþg levels to the a3Rþu state was detected.

The energies of rotational levels of the 23P0gv = 12 andthe 41Rþg v = 10 vibrational levels cross. When probing the41Rþg v = 10, J = 19–69 levels, the 23P0gv = 12, J = 19–59levels were also observed via perturbed as well as unper-turbed A1Rþu levels (>99.4% singlet character) by detectingthe yellow–green fluorescence. Fig. 2 shows the energy dif-ferences between the observed and calculated term valuesof these two vibrational levels. The crossing is betweenJ = 40 and J = 41. Fig. 3 gives the resolved fluorescencespectra into the a3Rþu state from the 23Pgv = 12, J = 36level and the 41Rþg v = 10, J = 36 level, both excited fromthe A1Rþu v0 ¼ 13, J 0 = 37 (83.03% 1R+ character) intermedi-ate level. Both spectra have bound–bound lines into theshallow well and a bound–free diffuse band into the repul-sive wall of the a3Rþu state as do other 23Pg levels [13,14].Fig. 4 shows the bound–bound lines into thea3Rþu v0 ¼ 0� 8 levels from the strongly mixed 41Rþg v = 10,J = 41 and 23Pgv = 12, J = 41 levels. The fluorescence intoeach a3Rþu v0 level consists of four lines: two stronger linesand two weaker lines. In the 41Rþg v ¼ 10, J ¼ 41! a3Rþuspectrum (upper), the two stronger lines are from the IR–IR double resonance excited upper 41Rþg v ¼ 10, J = 41level and the two weaker lines are from the collisionallypopulated 23P0gv = 12, J = 41 level. The lower spectrumis the vice versa. This kind of effective DJ = 0 collisionenergy transfer between a singlet–triplet mixed pair hadbeen observed in Na2 and Li2 [17,18]. Fig. 5 gives thebound–bound lines from mutually perturbed 23P0gv = 9,J = 21 (lower) and 41Rþg v ¼ 8, J = 21 (upper) levels to thea3Rþu levels. While the 23Pgv = 9, J = 21 fluorescence hastwo lines, the 41Rþg v = 8, J = 21 fluorescence has four lines:two stronger lines from the 41Rþg v ¼ 8, J = 21 level, twoweaker lines from the collisionally populated 23Pgv = 9,

20 30 40 50 60 70-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Tob

s−

Tca

l, cm

−1

J

23Π0g

41Σ+

g

Fig. 2. The energy differences between observed and calculated termvalues of the 23P0gv = 12 and 41Rþg v ¼ 10 levels. The 23P1gv = 12 and41Rþg v ¼ 10 terms cross at J=66 � 67.

Fig. 4. Bound–bound transitions from the 4 Rg v ¼ 10, J = 41 (upper)and 23P0gv = 12, J = 41 (lower) levels to the a3Rþu v0 ¼ 0� 8 levels.

558.3 558.6 558.9 559.2 559.5 559.8 560.1 560.4 560.7

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

v'=3

v'=2

v'=1

v'=0

23Π0g

v=9, J=21

41Σ+

gv=8, J=21

Inte

nsity

, Arb

itrar

y

λ, nm

Fig. 5. Bound–bound transitions from the 23P0gv = 9, J = 21 (lower) and41Rþg v ¼ 8, J = 21 (upper) levels to the a3Rþu v0 ¼ 0� 3 levels.

D. Li et al. / Chemical Physics 332 (2007) 10–16 13

J = 21 level. The 23Pgv = 9, J = 21 and 41Rþg v ¼ 8, J = 21levels are only weakly mixed. The radiation rate of the23Pgv = 9, J = 21 level to the a3Rþu state was much biggerthan collisionally energy transfer rate under our experi-mental conditions, while the 41Rþg v ¼ 8, J = 21! 23Pgv =9, J = 21 collisionally transfer rate is comparable with theradiation rate of the 41Rþg v ¼ 8, J ¼ 21! a3Rþu transition.

Obviously, the 23P0g � 41Rþg perturbation comes fromthe spin–orbit interaction.

4. Analysis

In Ref. [14] we separated perturbed levels of the K2 23Pg

state from the unperturbed ones. The majority of thembelonged to the X = 0 component and exhibited a charac-teristic resonance-like behavior. As is discussed both inRef. [14] and in the current work, the reason for the mutualperturbation of the 23Pg and 41Rþg levels is the spin–orbitinteraction. Many of the newly observed 41Rþg levels areperturbed via this mechanism, so their reasonable analysisis impossible without at least a partial deperturbation.

To simplify further analysis, we started by constructingthe zeroth order approximation for the 41Rþg state. Withthe aim to damp down as much as possible of the perturba-tion effect we used all the available a-priori information.

1. Besides the experimental term values, we included intothe data set to be fitted the ab initio potential values[1] within the range of the energy observed; they werecompared with the RKR potential function values cal-culated from the current set of the molecular constantsat every step of the fitting procedure.

2. We did not fit the Y02 molecular constant but computedit iteratively from the well known semi-classical equa-tion [19] Y 02 ¼ �4Y 3

01=Y 210.

Table 1The molecular constants of the K2 41Rþg state and the spin–orbit 41Rþg �23P0

This work zeroth appoximation

Y00 21417.437(159)Y10 85.54083(6365)Y20 �0.715549(6921)Y30 8.07458(27956) · 10�3

Y40 �6.5452(3764) · 10�5

Y50

Y01 0.0383329(342)Y11 �1.2521(496) · 10�4

Y21 �1.1569(1356) · 10�6

Y02 �3.079119 · 10�8

Y12

f0

f1

Re (A) 4.751Y00 �0.1319

Measurement units are cm�1 and A.Y02 values were not fitted but calculated from Y 02 ¼ �4Y 3

01=Y 210.

a [1].

3. Believing that the lower levels are less perturbed due togeometry and energy reasons (see Fig. 8 below) werather arbitrary increased their weights relative thehigher ones.

The molecular constants determined in this procedureare presented in Table 1. The energy differences betweenthe term values observed and calculated with these molec-ular constants are shown in Fig. 6 along with the analogousvalues of the 23P0g state determined in Ref. [14]. Fig. 6clearly exhibits 9 pairs of the resonantly perturbed vibra-tional bands (vP and vR are used for the vibrational quan-tum numbers of the 23P0g and 41Rþg states, respectively):(vP,vR) = (9, 8), (12, 10), (16, 13), (19, 15), (31, 24), (32,25), (36, 28), (37, 29), and (42, 33). We have not used thezeroth order approximations for other purposes than fordetecting those band pairs.

The second step was to perform 2 · 2 deperturbationsfor the mixing pairs of the nine combination bands, sup-posing that the perturbations are purely resonant. If T P

obs

and T Robs are the experimentally measured term values of

the 23P0g and 41Rþg states, and T Pcal is the theoretically pre-

dicted [14] ‘‘unperturbed’’ term value of the 23P0g state,then the deperturbed term value T R

cal of the 41Rþg state is

T Rcal ¼ T P

obs þ T Robs � T P

cal

and the absolute value of the perturbation matrix elementW between these two levels is

jW j ¼ 1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðT P

obs � T RobsÞ

2 � ðT Pcal � T R

calÞ2

q:

We computed the T Rcal and jWj values for all mixing couples

having the same J within the bands listed above.The next step was to replace the observed perturbed

term values with their corresponding ‘‘deperturbed’’ T Rcal

g interaction matrix element f(R) = f0 + f1(R � 5)

This work final Ab initioa

21416.6763(1194) 2141086.050225(44963) 84.00�0.8033429(59715)0.01428188(35460)�2.525726(96211) · 10�4

2.01949(9705) · 10�6

0.03799930(3096) 0.0383�1.04431(3198) · 10�4

�1.7318(770) · 10�6

�2.964031 · 10�8

�6.976(796) ·10�10

7.003(51)�5.423(118)4.772 4.75�0.1614

21500 22000 22500 23000 23500 24000

-3

-2

-1

0

1

2

3

v=

42, v

=33

v=

36, v

=28

v=3

7, v

=29

v=

31, v

=24

v=

32, v

=25

v=

19, v

=15

v=

16, v

=13

v=1

2, v

=10

Tob

s−Tca

l, cm

−1

Tobs

, cm−1

41Σ+g

23Π0g

v=

9, v

=8

Fig. 6. The energy differences between observed and calculated termvalues of the 23Pg (only ‘‘perturbed’’ terms of the X = 0 component fromRef. [14] are shown) and 41Rþg (zeroth approximation) levels. Nineresonantly perturbed band couples are clearly observed. Vibrationalquantum numbers of the 23P0g and 41Rþg state states are designated as vP

and vR.

21500 22000 22500 23000 23500 24000-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tob

s−Tca

l, cm

–1

Tobs

, cm−1

Fig. 7. The energy differences between empirical and final calculated termvalues of the 41Rþg levels. Empirical term values included the experimentalones not belonging to the detected resonantly perturbed series (Fig. 6) andthe ones obtained from the resonantly perturbed series using a 2 · 2deperturbation.

14 D. Li et al. / Chemical Physics 332 (2007) 10–16

values in the data set. However, the resulting data set stillcould not be considered totally ‘‘unperturbed’’: relativelyweak perturbations from the 23P1g levels and other nearbystates (23Rþg and 31Rþg Þ are not included, and the non-reso-nant effect in the 41Rþg � 23P0g interaction is also signifi-cant, especially for high vibrational levels (see Fig. 9 andthe section ‘‘Discussion’’ below).

Thus we decided to apply a procedure similar to the zer-oth order one to this final set of data as well. However, thistime we weighted equally all the term values and decreasedthe weights of the ab initio data.

The final molecular constants of this procedure are listedin Table 1 along with the zeroth order and ab initio con-stants. The agreement with the ab initio values is quite rea-sonable. The energy differences between the term valuesincluded into the final set of the data and the ones calcu-lated with the final set of the molecular constants areshown in Fig. 7. The standard deviation of these differencesis �0.11 cm�1.

The K2 41Rþg RKR potential function computed fromthe final set of the molecular constants is presented in Table2. Fig. 8 shows this potential function and the RKR poten-tial function [14] of the 23P0g state along with the ab initio

[1] potential functions. The lowest intersection point of theRKR potential functions is at RX = 5.10 A.

The absolute values of the perturbation matrix elementsW = hvP, JjnjvR, Ji determined above were used to fit theelectronic matrix element n = h1R+jHj3P0i as a functionof the internuclear distance R. The accuracies of thesejWj values depend on the relative positions of the mutuallyperturbed levels and on the strength of the perturbation.Supposing that the uncertainties D of all the observedand calculated [14] term values are equal, an uncertaintyof the W value results

dW ¼ oWoT P

obs

D

� �2

þ oWoT R

obs

D

� �2

þ oWoT P

cal

D

� �2" #1=2

¼ D2W

�������� T P

obs � T Pcal

� �2 þ T Robs � T P

cal

� �2h

þ T Pobs þ T R

obs � 2T Pcal

� �2i1=2

:

The weights of the jWj values in the fit were based onthese uncertainty estimates. An actual value of D doesnot influence the result of the least-square fitting. Thevibrational wavefunctions for calculating the matrix ele-ments were computed using the RKR potential functionsof the states involved with the ordinary Numerov–Cooleyprocedure [20]. The resulting parameters f0, f1 of the linearapproximation f = f0 + f1(R � 5) of the 23P0g � 41Rþginteraction electronic matrix element are also included intoTable 1.

As a final check of the quality of the results, we com-pared the empirical energy differences between the per-turbed and unperturbed term values in thevP = 32 � vR = 25 band with the corresponding theoretical

differences. The empirical differences are the differencesbetween the observed term values (perturbed) and the cal-culated term values with the final Dunham constants(unperturbed). The theoretical differences are the differ-ences between the term values calculated using the fullquantum mechanical two-channel (the interacting 23P0g

and 41Rþg states) split-operator [21–23] technique(perturbed) and the term values calculated from the non-interacting RKR potential functions using the Numerov–

Table 2The RKR potential curve of the K2 41Rþg state

Rleft Rright Te + Gv v Rleft Rright Te + Gv v

4.63417 4.91836 21459.50231 0 3.98684 5.98323 22864.25734 194.53681 5.03340 21543.99102 1 3.96963 6.02717 22928.84591 204.47121 5.11717 21626.99442 2 3.95303 6.07100 22992.65861 214.41859 5.18845 21708.58660 3 3.93701 6.11475 23055.70731 224.37358 5.25261 21788.83618 4 3.92152 6.15847 23118.00301 234.33372 5.31211 21867.80657 5 3.90655 6.20219 23179.55612 244.29765 5.36828 21945.55622 6 3.89206 6.24595 23240.37666 254.26456 5.42196 22022.13885 7 3.87805 6.28975 23300.47455 264.23386 5.47371 22097.60367 8 3.86449 6.33364 23359.85981 274.20518 5.52392 22171.99568 9 3.85136 6.37762 23418.54284 284.17821 5.57288 22245.35584 10 3.83866 6.42172 23476.53461 294.15272 5.62081 22317.72139 11 3.82638 6.46593 23533.84696 304.12856 5.66790 22389.12602 12 3.81451 6.51027 23590.49282 314.10556 5.71428 22459.60017 13 3.80305 6.55474 23646.48643 324.08362 5.76007 22529.17123 14 3.79199 6.59933 23701.84363 334.06264 5.80537 22597.86380 15 3.78134 6.64404 23756.58204 344.04254 5.85027 22665.69996 16 3.77111 6.68885 23810.72137 354.02324 5.89484 22732.69944 17 3.76131 6.73374 23864.28360 364.00470 5.93914 22798.87995 18 3.75194 6.77867 23917.29326 37

Measurement units are cm�1 and A.Re = 4.77196 A, Te = 21416.83767 cm�1, vmin = �0.49812.

4 5 6 7 8 9 10 11 12 13 14

21500

22000

22500

23000

23500

24000

24500

25000

25500

U(R

), c

m−1

R, Angstrom

RKR potentials (dots)ab initio potentials (solid lines)

41Σ+

g

23Π0g

Fig. 8. The RKR and ab initio potential functions of the K2 41Rþg and23P0g states.

23250 23300 23350 23400 23450-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Tpe

rt−T

unpe

rt, c

m−1

Tobs

, cm−1

23Πg (v=32) empirical

41Σ+g (v=25) empirical

23Πg (v=32) theoretical

41Σ+g (v=25) theoretical

Fig. 9. Empirical and theoretical energy differences between the perturbedand deperturbed levels of the K223Pg (v = 32) and 41Rþg (v = 25) bands.The change of sign and the intersection of the both types of the curves athigh energies indicate a significance of the non-resonant effect in theinteraction of the states.

D. Li et al. / Chemical Physics 332 (2007) 10–16 15

Cooley method [20] (unperturbed). The former method(split-operator) involves the non-resonant effects of theinteraction as well. This comparison is shown in Fig. 9.The overall resemblance between the theoretical and empir-

ical curves is reasonable.

5. Discussion

The model, which was used in the current paper, is def-initely not complete. There are many physical effects whichwere not included into the model while they could influencethe observations.

1. Interaction of the K223PgX = 0+ component with othercomponents of the triplet as the rotational quantumnumber increases. This interaction was studied in Ref.[14] but was not included into the current model. Thisinteraction can influence the term values of the 23Pg

state directly and of the 41Rþg state indirectly. In ourexperiment many 23P1g � 41Rþg perturbations have beenobserved;

16 D. Li et al. / Chemical Physics 332 (2007) 10–16

2. Interactions of the K223Pg and 41Rþg states with otherelectronic states. We have already observed23Pg � 23Rþg and 23Pg � 13Dg perturbations;

3. Non-resonant effects in the interaction between the K2

23Pg and 41Rþg states (see Figs. 2 and 9).

To include those effects into the model, the full quantummechanical computations of the term values are needed.This can be based on the multi-channel split-operatormethod [21–23] similar to the one implemented in the cur-rent work to calculate the values presented in Fig. 9, theDVR method [16], or some other modern technique. How-ever, this kind of research is beyond the scope of the currentarticle. The primary purpose of this work was to present theexperimental results and the model of the major effects influ-encing the values observed. This model can play the role ofthe zeroth approximation in a more advanced analysis.

6. Conclusions

The first observation of the K2 41Rþg state is reported.The observed levels span the range of v = 2 � 36 andJ = 1 � 85 vibrational and rotational quantum numbers.Many of the newly observed terms are perturbed by thespin–orbit interaction with the 23Pg state. The molecularconstants and the RKR potential of the K2 41Rþg state aswell as the electronic matrix element of the 41Rþg � 23Pg

interaction are determined from the analysis of the experi-mental data. Further improvement of the data descriptioncan be achieved via full multi-channel quantum mechanicalcomputations.

Acknowledgements

We thank Prof. T. Bergeman for calculating the termvalues of the intermediate levels. Support from the NSFC(20473042), KGPCME (NO.306020), and SRFDP of Chi-na as well as from the RFBR (05-03-39012) of Russia isgratefully acknowledged.

Appendix A. Supplementary data

Supplementary data of the K2 41Rþg state by infrared–infrared double resonance: Intermediate levels, probe

transition frequencies, the v, J assignments and term val-ues of the 41Rþg state. All quantities are in cm�1. Supple-mentary data associated with this article can be found, inthe online version, at doi:10.1016/j.chemphys.2006.11.018.

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