The dissociation energy of the cesium dimer

Volume 88. number 4

14 May 1982

CHEMICAL PHYSICS LETTERS

THE DISSOCIATION ENERGY OF THE CESIUM DIMER

M. R&U%, H. WEICKENMEIER and W. DEMTRijDER Fnchbemcb Phyak. Unwersih% Kalsershutem. D~67.50Kaiserdaulem, FRG Received 10 March1982

Dye laser excitation of the recently discoveredD I Z’u - X ’ E; system of Cs, yields extended iluorescence progress~ono rangmgfrom dl = 0 to U”= 140. Analysis of the fluorescencespectra and application of the LeRoy-Bernstein method to determine (he dissociation limit results in a dlssociaGonenergy of De = 3648 * 8 cm-‘, more than one order of magmlude more accurate than pwiously known.

1. Introduction

De = 3 100 + 80 cm-t

Tbhedissociation energy D,(XlZd) of the Csl dimer ground state has been the subject of controversy in the literature for some rime. A precise detennina-

thermal dissociation of Cs,. Collins et al. [6] determmed a dissociation energy of De = 3480 f 50 cm-t from the measured onset of the photodissociatlon process

tion of De by extrapolation from measured vibrational levels far below the dissociation limit is often doubtful and may lead to incorrect results. One of the reasons for the uncertainty of the extrapolation is due to the part of the molecular potential V(R) whch is stdl at intermediate mtemuclear SeparationsR, but hes outside the range covered by spectroscopic observations. This part of Y(R) is important for an interpolatlon between the RKR potential obtained from spectroscopic data [I] at small values of R and the long-range van der Waals potential V(R) = De C6Rs6 at large internuclear separations. As early as 1934, Loomis and Kusch [2] deduced a dissociation energy ofDe = 3630 f 350 cm-t from the analysis of live nbrational band systems in rotationally unresolved absorption and magnetic rotation spectra. A detailed analysis of the 7667 and 6250 A band Systems by Kusch and Hessel [3] ylelded a dlssoclation energy of 3582 cm-t when extrapolating from vlbralonal levels Y”< 60, but a value of 3 197 f 80 cm-l when higher vibrational levels up to u” = 90 were included in the analysis. From the temperature dependence of the absorption coefficient of Cs2 at different wavelengths, Benedict et al. [4] obtained D, = 3420 * 200 cm-l ,wbile Glas and Weber [S] found 0 009-2614/82/0000-0000/.$02.75

0 1982 North-Holland

from the activation energy of

Cs2(XlZg+)+ CS(~~S) + Cs(5 2D5,2) and the vanishing of the photolysis cross section for the productlon of 6 2P312 atoms at 18055 cm-t with an atomic excitation energy of 14597 cm-l for the Cs (5 2D512) state. In a previous investigation of the Cs2 molecule [7], we obtained a value of De = 3550 f I50 cm-t from laser-induced fluorescence spectra of the E + X system using a Barge-Sponer extrapolation [S] from vibrational levels measured up to U” = 72. The relatively large error limits took mto account the uncertainties due to the wde extrapolation range. If it is possible to observe fluorescence from transitions to high-lying abrational levels of the X 1x9’ or the a 3 Z$ ground states, which both converge to the same dissocia(lon limit, the uncertainty in the dissociation energy could be substantially decreased. ln the case of heteronuclear molecules, such as the NaX molecule, fluorescence to the shallow triplet a 32 ground state could be excited by a laser tuned to transltions(X1X+D111,3fI)from the singlet ground state to a D 1Il state which is perturbed by a nearby 3ll state. From the measurement of the triplet tluorescence both dissociation energies D(X t X) and

377

Volu~ne88. nunlber 4

CHCMCAL PHYSICS LETTERS

D(a3C) could be determined to within a few cm-l [9,10]. For homonuclear molecules the excltation-

lluorescence cycle from the X *EL ground state to the 32i ground state is parity fortndden and therefort cannot bc observed. However, another way to determine D(X t 2;) with comparable accuracy is based on optical excltahon of high vIbrationa levels m an ekclted electromc state which has Its potential minimum shifted to large internuclear dmmcesR. \Vhlle thecucatatlon Ins considerable Frank-Condon factors (FCFs) for transItIons to the repulsive hmb of the pofcntlal curve, the fluorescence will exhibit a brodd ranp of transitions with large FCFs from the outer attracttve potential hmb to high-lymg vlbratlonal levels in the electromc ground state, close to the dlssoclation limit. The present paper lcports such measurements

which arc based on fluorescence spectra emitted from tl~c D 1T?Zi state. This recently discovered state [ 1 l] hJs been analyzed with Doppler-free polanzatlon spectroscopy [l?), and can be excited with a rhodanune 6G dye laser from the bottom of the X 1x9’ state to the rcpulslve limb orits shallow potential curve (see fig. I). Fluorescence

transItions

which

start

from

the outer hmb of the D I C: potential termmate on high-lymg vlbrational levels of the X state up to the dissociation hmlt,and even on continuous energies

II 19 .-

14 May 1982

above

this limit. At the present resolution all vibrational levels up to u” = 140, representing more than 99% of the dissociation energy, have been resolved.

2. Experimental Cs, molecules were prepared m a purified, sealed, Pyrex

cell,

single-mode

operated

at = 700°C,

and excited by a

rhodanune 6C or rhodamine 110 dye

laser, depending on the excitation wavelength region. The fluorescence was focused onto the entrance silt (30-50 pm width) of a 3/4 m Spex 1702 monochromator and was detected by a C31034 RCA photomultipher. For wavelength caltbratlon, a thorium hollow cathode lamp provided reference lines which were recorded simultaneously with the Cs2 fluorescence. A detaIled description of this standard apparatus can be found in ref. [7]. For the measurements reported in the present paper, no attempt has been made to lmprove the spectral resolution of 03 A by using a Fabry-P&ot interferometer, since better methods are not at hand (see below). Smce the laser available for this exF,eriment was located in another room, the laser beam was guided through a 25 m long optical fiber to the fluorescence cell. The laser hght emergmg from the fiber end (X030 mw) was focused with a 100 mm lens into the cell. This arrangement drastIcally reduced spatial fluctuattons which were observed when the laser beam was sent through a mirror arrangement from one laboratory into the other. The laser wavelength was measured with a traveling Michelson mterferometer (wavemeter [ 13]),allowmg the laser frequency to be rapidly tuned to the transition of mterest. These transitions, which have been analyzed before by Doppler-free polarization spectroscopy [ 121, were selected so as to avoid any overlap between adJacent Doppler-broadened absorption lines excited m the fluorescence cell. Thus ensures a selective excMion of a single upper level (u’,J’) and results in a simple fluorescence progresSlon of P and R lines:

DtZ;(u’,J’)+Xt~(u”,J”=J’~I). 3

7

11

RIAI

Fy I. Scllcm.us diagram of the Csz potential m the X ISi gound

~1310, the excited D I S;

poWma (dashedCUNC), 378

sfafc md of the dtiference

The accurate wavelength measurements and the prevlous analysis by polarization spectroscopy guarantee the unambiguous assignment of the quantum numbers u’ and J’.

CHEMICALPHYSICS LETTERS

Volume 88. number 4 3. Results and discussion

Several fluorescence progressions resultmg from different excitation wavelengths have been recorded. Two of these progressrons can be followed up to the dissociation limit of the X state, where vibrational levels up to u” = 140 are still resolved. Fig. 2 shows a section of the fluorescence progression obtained by excitation of the transition (IJ’= 5O.J’ = 48) c (u” =

OJ” = 49). The rotational spacings for u’< 100are partlyresolved(seefig.Z), but they decrease beyond the resolution of the monochromator (50 pm shts) for higher vibrational levels. However, separate runs with smaller slit wdth allowed rotational resolution up to u” = 134 but with a sacrificed ngnal-to-noise ratlo. The structured continuum in the fluorescence spectrum beyond the dissociation limrt and the unusual intensity behaviour of the fluorescence Linesshortly before the dissociation hrmt are due to Condon Internal diffraction bands [ 14-161. These features will be discussed below. The measured hne positions are complied m table 1 for two of the observed fluorescence progressIons. In the last column the rotation-free vtbratlonal term values C(u”) are listed. They are taken from the measured line positlons by subtractmg the rotational energy. The rotational constants,necessary for this procedure, are obtained for vibrational levels u” G 134, where the rotational lines were resolved, from a weighted

ii

-*AL%

___~&__d-__L’d-L

--___

7000

7050

’ 6950

I

A

WAVELENGTH

Fig. 2. Long-wavelength

sectron of the

fluorescenceprogres-

sion emted at A = 5702 A on the transition X ’ X&I” = 0, J” = 49) - D

I &(u = 50. I’ = 48). Assortedreferencelines are markedwith theu wavelengrhs m air.

I4 May 1982

Table 1 Observed tine positions for u” > 60 of two fluorescence progressaonsexcitcd byq = 17576 821 cm-’ and us = 17531.749 cm” and rotation-free vIbratIonat term values C(u”) Progression

63 64 65 66 67 68 69 7’; 72 73 74 75 76 77 78 79 80 81 82 a3 84 85

1

R(47) 53-u”

N49) 53-u”

15361.2

15359 3

Progression 2 R(47) 50 -u”

W”)

P(49) 50 -“I’ 2243.1

15330.6 15329.5

2213.4

15301.4

15299.5

.;303

15241.B

15240.2

2362.7

15 184 6 15 156.5 15127.6 151000 150718 15043 a 15016.3 14990.4

15 183.1 15 154.8 15126 2 150986

2420 I 2448.4 2477.3 2505 .O 2533.5 2561.5 2589.2 2615.3 -

150700 15042.3 15014.7 14988 6

1

14937 1

14935.2 -

2668.9

:;

14884.9 14859.3 14833.9 14809.6 14784.4 14760.3 14736.2 14712.1 146892 14665.6

2721.1 2746.8 2772.4 2796 8 2822 2 2846.5 2870.6 2894.8 2918.1 2941.7

tf

14883.4 14857.9 t4832.3 14808.2 14782.8 14758.6 14734.7 I4710 B 14687 4 14664.2 -

14620 0

14618.2

2987.7

14575.9

14574 5

3031.9

14533.2 14512.1 14491.8 14471.6 14451.4 14431.9 14412.7 14393.5 14375.2 14357.5 14340.1 14322.5 -

145318 14510 4 14490 4 14469.9 14449.7 14430.4 14411.3 14392.0 14374.0 14356.1 14338.6 14321.2

14289.2 142373

14287 8 14272.0

3075.0 3096.4 3116.8 3137.3 3157.7 3177.4 3197 0 3215.9 3234.5 3252.2 3270 2 3281.6 3304.4 3321.3 3337.6

90 91 92 93 94 95 96 97 98 99 100 101 102 to3 104 105 106 107

14446 5

14445.1

14406.0 14386.3 14366 7

14404.5 14384.9 14365 0

14329.7

14328.3

14294 4

14293.1

14260.8 14244.2 14228 0

14259.4 14242.8 14226.6

379

Volume 88, number4

CHEMICALPHYSICSLETTERS

Table 1 (Conunued) Progression1

Progrewon 2

R(47) 53--u”

P(49) 53--v”

R(47) 50 -“)I

P(49) 50 -“I*

108

14257.2

14255

14212.2

14211.0

109

14241 9 14226.9 14212 4 14198.1 14184.4 14171.3 14158.7 14146.4 14123 1

14240.7 14225.7 14211.1 14196.8 14183.2 14170 2 14157.6 14145 3

V’I

110 111 112 113 114 115 116 117 118 119 120 121 122 I23 124 1%

126 127 128 129

130 131 132 133 134 135 136 137 138 139

8

14112.0

14121.9 141109

14072 9

14072.0

l4OK2 14047.3 14040.3 14033.2 14026.9 14020.9

140542 14046 5 14039.6 14032 4 14025.9 14020.1

14009.8 14009.2 14005.1 14004.3 14000 8 14000.1

140

14182 3 14181.0 14167.7 14166 4 14153 8 14152 6 14140.3 14139 2 14127.1 14125 8

duced from this fit represent an extension of earlier data and are therefore compiled in table 2. Since the Dunham potential expansion converges only for internuclear separations R < 2R,, the relation between the Dunham coefficients Yik and meaningful molecular constants may become doubtful outside this range. Nevertheless extrapolated valuesof

G(v”)

3353 6

3369.2 3384.2 3399.0

3413.2 3427.0 3440.4 3453.7 3466.2 3490.0 3501.4

14037 3 14035.9 14027.9 14026.8 14019.3 14018.1

14010.4 14009.7 14002 7 14002.0 13995.5 13988.4

13994.7 13987.7

13969.8 13964.9 13960 3

13952.1 13948.8 13945.7 13943.1 13940.7 139385

14 May 1982

3531.9 3541.3 3550.3 35595 3567.4 3574.8 3582.2 3589.1 3595.3 3601.2 3606.7 3611.7 3616 6 3620.1 3623.8 3627.2 3630.2 3632.9 3635.4

the rotational energy were

used for vibrational levels

with u” >

134 where the rotational spacings could not be resolved. The uncertainty of this extrapolation does not represent a major contnbution to the total uncertainty of the dtssociation energy of the rotationless potential. A Birge-Sponer plot of the vibrational spacings AC@ + $) = G(u” + 1) - C(u”) versus the vibrational quantum number u” 1sshown m fig. 3. Note that the plot exhrbits a positive curvature for the last few levels below the dissociation limit. If the outer part of the attractive potential limb can be described by the function V(R)=D,

-C&R-” n

)

such a positive curvature 1s to be expected, as has been shown by LeRoy [ 171. Since the X 1“9 state drssociates into two 2S,R atoms, the lowest exponent in eq. (2) is n = 6 and the dominant term will be the van der Waals potentral C6Rm6. A LeRoy-Bernstein plot [ 181, where [AG(u”)]~“R’~‘~) with AC@“) = [G(u” t 1) G (u” - 1)]/2 is plotted versus G(u”) according to the relation AG(u”) = K,, [D, - G(~I”)]“‘+~‘/~ , for R = 6. the straight hne gives the constant

expansion: u=T’(u’,J’)-,~Y,k(“~~t~~[J”(J”+L)]~.

K6 = (2nh2/~C;‘3)1’2

(1)

All line positrons measured in this work and from earlier investigationspf the Cs2 molecule [7,1 I] are included in this fit. The experimental data are weighted according to the widely different accuracy of line positions taken from fluorescence spectra and those

taken from Doppler-free polaruation spectroscopy. The molecularconstants Y,g of the X t ~g’state de380

(3)

should yield a straight line if the correct value of n is chosen. Fig. 4 shows this plot

least-squares fit of the line positions Y to a Dunham

(2)

[6l$)/r($)],

The

slope of

(4)

which depends on the reduced mass JL,the values of the gamma function and on the van der Waals coefficient C6. The intercept De = G(G) yields the dissociation energy De. Since the accuracy of vibrational spacings AG(u”) taken from measured lure positions is always less than that of each line position, it is advantageous to take the term values G(u”) directly from a non-lmear leastsquares fit to the equation

Volume 68, number 4 Table 2 Dunham eoefficiente the two fluorescence

~~[~A~

PHYSICS LETTERS

of the X * ~6 ground state of Csa and the two term values of the (6.J’) progressions in table 1 start Dunbam referents

Standard

0.4201941275D+O2 -0,8191024094D-01 -03640401160D-04 -0.3291162492D-06 -0.5817263633D-118 OAS83170906D-11 O.l174344740D-01 -0.2214971663D-04 -0.8244811979D-07 -0.5875085579D-09 -0.3039065309D-11 -O.l816143892D-13 -0.3729995089[3-08 -O.l260802404D-10 -0.927040809lD-12 0.979X6685021)-14 0.26308505 1 lD-14 -0.3764814230D-15 0.4094462999D-16

0.6349786534E-04 0.1030368253L-O4 0.73140421078106 0.2221568381E-07 0.2753l~OSE~9 O.l118350386E-11 0.2564533064E-06 0.17944446178-07 0.1703177543E-08 0_4990481888E-IO 0_8890929867E-~2 0.612431987OE-14 O.B815245822E-11 011762367188-11 O.l133873057E-12 0_298401~799E-X4 0_91357t926SE-I6 0_258393432OE-I6 0.32093790756-17

YX(3.31 YX(O.4) Y-W PI

-05164498487D-18 -O.l331452308D-19

~~(24) YX(3,4)

~~16665073OD-21 0.6153205394D-23 O.l762668565D+BS O.l758182907D+OS

0.10388226398-18 0.42363533838-21 0 26062698938-21 OA064664898E-22 0.12775448788-23 0.8715318638E-01 O.l387810813E+OO

Y-W.01

f-X(2,0) YX(3.0) YX(4P) YX(S *O) =X6,0) Y.x(O,l) Y-W .l) YX(2,l) YX(3.1) YX(4,U Y-W*0 YX(O.2) YX(l.2) YX(2.2) YXf3,2) YX(O,3) YX(l,3) Yx(2,31

0.4868896196D-20

Y(l) Y(2)

14 May 1982

deacon

levels in the D t EC state from which

Standard

dentin

(56)

0.0001511155 0.0125792360 0.8090395522 6.7501023924 4.7327937636 24.4012368154 0.0021837992 0.0810143374 2.0657566804 8.4943135234 29.2554748366 33.7215564074 0.2363339793 9.3292709028 12.2311018700 30.4750084~8 3.4725345382 6.8633780101 7.8383394249 20.1146857105 3.1817537576 5.3528968127 7.8671176173 20.7622661078 0.0004944389 00007893438

AG I.--OS) I

AGd 20t

I

OO

Fig. 3. Bkge-Spotter

50

lob

w

3&o

3& G&Y

156UC

plot of vibrational spacings AG(u” + 1[2) = G(e” + I) - G(~“)wrsus vibrational quantum number u”. The crosses refer to the accurate measurements of ref. [7].

Ftg. 4. f&Roy-Bernstein plot of AG3R$“) versus the nbrational term value C(u”) for the last observed viiational levels. The two points in brackets are basd OR a very we& fhorssance line and are therefore ksr accurate.

381

CHEMICAL PHYSICS LETTERS

Volume 88. number 1

C(u”)=D,-

[(v;-lY)H#

(5)

)

whsh represents the integrated form of eq. (3) for R = 6 where Hg = f Kg and I$ IS the (m general nonInteger) vrbratlonal index at the chssociatlon limit. From this fit we obtain De = 3648 f 3 cm-1 for a rot;ll~onless potential. The error limits represent one srandard deviation of the fit. A possible systematic er-

ror induced by the uncertamties of the extrapolated rotatIonal energes will Increase the error lirmts to less

than +4 cm-l. Under the assumption that eq. (3) is valid (which rmphcs that the potential IScorrectly described by V = - C6/R5 within the range R of outer turnmg points used for the plot of fig. 4), we obtain for the rotationless potentral D,=3648?6cm-’

and

6=156*5.

For Ihe rotating molecule the number of vIbratIonal levels below the dissociation energy decreases from u;;(O) to&J”). In case of a R-6-laded potential, $(J”) becomes [ 171 I$#“)

= l&(O) - 0.25 [Y(.J” + l)] ‘12 ,

which yields $(49)

(6)

= 144 + 5 for the progression

This shows that nearly all vibrational levels u” < 6 except the very last few are resolved in the speclnmi of fig. I _ The value of the coefficient C6, taken from the slope of the LeRoy-Bernstem plot [ 181 m fig. 4 is shown in fig 1.

C6 = 2.0 X lo7 cm-l R6 E 3.9 X 1O-57 ergcm6. This should be compared with a value C, = 3.3 X lO-57 erg cm6 obtained by Buck and Pauly [19] from elastic scattermg data, and with a theoretical value C6 = 6.4 X 1O-57 erg cm6 calculated by Dalgarno and Davrson [20] from the polaruabdity of Cs atoms which can be derived from experimental oscillator strengths. The contrrbution of higher-order terms with tt = 8 and n = 10 in the expansion (3) of the potential may be estimated from approximate calculations of the ratios C8/C6 = 28 A2 by Davlson 12l] or C8/C6 = 18A* and Cl,& = 400 A4 by Fontana 1221. At internuclear separations of R = IO ii this implies that the term C8/@ is = 20%~of C6/R6 while ClO/~Lo contnbutes

only ~4% to the potcntid

energy.

difficult to give realistic error limits for our spectroscoprc value of the coefficient C6 because It is

382

14 May 1982

they depend only partly on the scatter of the experimental points in fig. 4. The major uncertamty comes from the questionable validity of the poiential expansion (2) over the whole range R (U~in) < R SZR(I& ofintemuclearseparationsR usedin the plot.The LeRoy criterion 1171R>4(&)1/2 gives(with the rrns ra&usof{&)l/2

~2.6~ofthecesiumatom)avalid~ty

range R > 10.4 A. However, for rhe lowestenergy levels in fig. 4 with D, - C(u”) = 70 cm-l, a potenteal Y(R)= De - CgRB6 would yield an outer tummgpoint ofR ~8.1 Aif the vahreofC6 = 2 X IO7 cm-l A6 is used. This would indicate that, although all the experimental points of !ig. 4 can be well fitted by a straight line, only Ihe lower part of the plot with De - G(u”)< 20 cm-l fulfdls the LeRoy criterion and can be therefore safely represented by eq. (2). If we use only the last six points in fig. 4 the extrapolated dissociation energy becomes 3650 cm-l which is only 2 cm-l more than obtained from the fit to aLl points m fig. 4. Including all these possible errors into the error hmits, the dlssoclatlon energy can be safely stated as De = 3648 f. 8 cm-l

_

A possrble explanation why Colons et al. [6] found a smaller value from photolytic

spectroscopy

of Cs2 may be as follows: Becauseof the relative position of the two X 1IZi and D 1q potential curves (fig. 3 of ref. [6] and fig. 8 of ref. [ 111) the FranckCondon factors for photodissociation are very small for transitions starting from u” = 0 but become larger for higher vibrational levels u”. Because of the small FCFs, photodissociation from levels u” < 5 has apparently not been seen by these authors. A much more accurate method of determining the dissociation energy is based on opbcal-optical double-resonance polarization spectroscopy. This technique replaces the laser-induced fluorescence by stimulated emission mduced by a weak probe laser which is coupled via a common excited level with a strong pump laser. This method offers, besldes its Doppler-free spectral resolution an accuracy of wavelength measurements of better than 10B3 cm-l_ Such experiments, which are currently prepared in our laboratory w1I1give detailed information on the potential curve around the LeRoy distance R and on effects of rotational predissociation. The results of these investigationswill be reported in a forthcommg paper.

Volume 88. number 4

Finally,

we briefly

CHEMICAL

discuss the structure

PHYSICS LETTERS

in the

fluorescence continuum beyond the dissociation hm~t shown in fig. 2. This interference structure [ 15,161 is due to bound-free transitions from the excited bound level (u’,J’) in the D 1Z: state to contmuous states above the dissociation limit of the X lq state. The form of the intensity modulations is determmed by the difference potentlalX(R) =E(u’,J’) + Y”(R) V'(R)depicted in fig. I by the dashed curve. For terminatmg pointsX(R) above the dissociation limit, there are always two values of R which lead to boundfrze fluorescence transitions with the same wavelength X which can Interfere with each other. From this interference structure the difference potential X(R) can be obtained [7_3]. Since the X t II; potential curve is known, this allows the construction of the D 1YEi potentral, which is quahtatively deptcted m fig. 1. The ongin of the continuum at 7 130A in fig. 2 underlymg the discrete lmes has not yet been clarified. More detailed future investigations. based on Dopplerfree polarization double resonance spectroscopy wdl hopefully clear up this point.

4. tonclusion Tha work puts an end to an old discusslonabout the correct value of the Cs, dissociation energy-The different previous results m the hterature with often non-overlapping error limits stated by the authors, show how difficult a reahstic estimate of extrapolated values is to obtain. Although the present results stti leave open questions about the accurate rotational constants close to the dissociation limit and about the exact form of the potential around the LeRoy internuclear distance R, this does not significantly influence the value of the dissociation energy.

I4 Mdy

References

[I] R.N. Zare..A.L. Schmeltekopf,

WJ. Harrop and D L.

Albntton, J. Mol. Spectry. 46 (1973) 37. [Z] F.W. Loomts and P. Kusch,Phys. Rev. 46 (1934) 292. [3] P. Kusch and M M. Hesscl, J. Mol. Spectry. 32 (1969) 181. (4) R.P. Benedict, D.L. Drommond and L.A. Schhr. J. Chcm.

Phys. 66 (1977)

4600.

[S] H J. Glas and H.G. Weber,Chem. Phys. Letters 44 (1976) 574. [6] C B. CoUuts. F.W. Lee, J A Anderson. P.A. Vtcharclh. D. Popescu and I. Popescu. J. Chcm. Phys. 74 (1981) 1067. 171 G. H&nng. M. Czajkowskl. M Stock and W Demtradcr. J. Chem. Phys. 7 1 (1979) 2138. [8] A C Caydon, Dlssociatlon energies and spectra of dtatomic molecules (Chapman and Hall, London, 1968). [9] EJ. Breford and F. Engclke. J. Chem Phys. 71 (1979) [IO]

1994. D Eisel,

D. Zcvgobs and W. Dcmtrader. J. Chem. Phyr.

71(1979)

2005. [ 111M. Raab, G Hanmg, W. DcmtrGdcr and C.R. Vtdal, J. Chcm. Phys. (IS Aprd 1982), to be published.

[ 12)

H.Wexkenmeier.hL Raab, U. Dlemer and W. Demtradcr. tobepubbshed. [ 131 K. Wicket&Diplomthess, FachbcrelchPhyslk, Umvcrsit8t Kacrslautem (1979). F.V. Kowalslci, RE, Texts, W. Demrrt5de.r end AL.

Schawlow.J. Opt. Sot. Am. 68 (1978) 161I. [ 141 J. Tellmghuaen and hl B. Moeller,Chem. Phys. 50 (1980) 301. [IS] J. Tellmghutsen,G. Pichler,\V L Snow, M.E. Htllard and RJ Exton,Chem. Phys. 50 (1980) 313. [ 161 H. Kato, Intern. J. Quantum Chem 18 (1980) 287 [ I?] R J. LeRoy, Molecular Spectroscopy, Vol. 1. Chem. Sot. Spcctit PerlodtcalReport @he ChentlealSociely. [IS]

London, 1973) pp. 113-176. RJ. LeRoy and R B. Bernstern, (1970)

[ 191

J. Chem. Phys. 52

3869.

U. Buck and H. Pauly. Z Phystk 185 (1965) 15.5. Dalgamo and W.D. Damon, III. Advances m atomic and molecular physics, Vol 2, ed. D. Bates (Academic

[ZO] A.

[Zll

Press, New York. 1966) pp. l-81. W.D Dwison, J. Phys. Bl(l968)

139.

[22] P.R. Fontana, Phys. Rev. 123 (1961)

Acknowledgement

1982

1865.

1231 J. Telhnghutsen,Phys. Rev. Letters 34 (1975) 1137.

This work was supported by the Deutsche Forschungsgemeinschaft within the Sonderforschungsberech 91 “Energy transfer in atomic and molecular colllslons”.

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