Infrared predissociation spectrum of HeNe+

PREDISSOCXATI&

m

SPE&RUM

OF HeNe* i

Alan CARRINGiON fipcvtmmx 4 m. Received

1 and Timothy P_ SOFTLEY Unicusiry of Soruhamp~on.Hempshire SO9 5NH. UK

17 July 19W

One hundred and sewn transitions of the H&c’ ion have bon obsn-03 using the technique of infzared predism&tim spcctrascopy. !scmlty-eight of the lines have been assigxd to rotational componam of Ibe A,‘rI,,-X’T’ sysceln our analysis kads to a modification of the assignment of the B’Z’ -X’Z’ bands of the optical &on spatrum_ The is unusual in that there as no potential cunc sxossins bcmccn the prcdisoa ‘at+ state and.& lifetimes ham been calculated for the im%GduaI Iwek and are compared ails those obmincd

1,Introduction High-resolution spectra of a number of molccular ions have been observed recently using the interaction of fast ion beams with infrared or visible lasers [l-3]. In some of these experiments transitions from bound states to predissociating states have been detected by monitoring the increased production of fragment ions at resonance_ This method is selective for transitions to states which p-ate with lifetimes within a range, typically 10-“-10-6 s, deFmed by the geometry and dimensions of the apparatus. In the case of infrared spectroscopy using a carbon dioxide laser, further selectivity is imposed by the requirement that the initial states in the observed transitionslie at most 1000 f 100 cm-’ below the predisxxiating states_ The selectivity, coupled with the very high sensitivity of the techmique, is advantageous in that it allows unique information to be obtained about molecular ions in levels close to or above dissociation limits_ A present disadvantage of infrared predusociation spectroscopy, however, is that the experimental data obtained may be frag-

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mentary; complete rotational branches or band heads are not generallyobsetible, making assignment difficult In two cases very accurate ab initio calculations have been used to assign the spectra [4,5]. However, very few molecules have been treated theoretically with sufficient accuracy for this method of assignment to be of general applicabiliq_ In this paper we report the observation of 107 transitions of the I-IeNe’ ion; 78 of thesetransitions may be assigned to individual. rotational components of the A2’II,~_-X’Z’ band system on the basis of energy Ievels derived from the optical emission spectrum of the ion [6]_ In our work the transitioti are observed by detecting Ne+ ions arising from the process: HeNe+(X’Z+

, u”, J”)

2 HeNe?(A,‘IIIlr_,

u’, -7’)

pZCd&UiGOQ _, Ne+ + He_ The weak pred&oGtion of the Az211ir- levels, which enables. the transitions CZIbe detected, was not observed in the Doppler-limited optical spectrum; in contrast, the high-resolutioninfmred predissmiation spectrum linewidths are dominated by the predissociationbroadening_Quantitativuinfor-

mationon

the variation of medkociation lifetime with rotationti quantum number is obtained for

The kinetic enew distxibution of the fragment ions formed in the interaction region may be mea-

the observed levels_ Moreover the experiment provides direct and unambiguous evidence for the electronic pred&ociation of a diatomic molecule in the absence of a potential curve crossing or avoided crossing

sured by monitoring the photofragment signal whilst scanning the ehxtrostatic analyser at a fixed acceleration potential_ If the laser and acceleration potential are tuned to a particular transition frequency of the parent ion, the fragment ions observed arise predominantly from a tigle predissociating state After a suitable transformation from the laboratory to the centre-of-mass fratn% the observed fragment kinetic energy yields the energy of the pred&ociating state relative to its dissociation charmeL

2. Eqxhnental The coaxial infrared laser-ion-beam apparatus used in this work has been descrii in detail elsewhere [2]; onIy those aspects specific to the recording of the HeNe’ spectrum are summar&ed here_ HeNei ions are produced by electron impact on a mixture of helium and neon in the ratio 5 to 1, at a total source pressure of IO-* Torr_ Ions are extracted from the source by applying accelerating potentials ranging from 15-10 kV and, following mass seiectiou, a total Hehe’ parent beam current of 4 x 10-t’ A is obtained_ The ion beam interacts colliuearly with singlefrequency radiation from a line-tunable carbon dia.ride laser chopped at 740 Hz Fragment Eie’ ions formed in the interaction region are separated from the parent ions using an dectrostatic ana.Iyser and the fragment current is amplified with an off-axis electron multiplier_ The multiplier output current is demodulated using a phase-sensitive detector referenced at the chopping frequency_ We use an Edinburgg Instruments PL3 or PL4 laser and 180 laser lines are obtainable in the rauge 880-1090 cm-’ using “CO, or r3Cq as the Iasing gas_ Singte Iines are selected by rotation of a diffraction grating, giving single-frequency powers of O-l-50 W cw_ The effective laser frequency observed by the ions depends on their velocity (X-) according to the relativistic Doppler shift formula,

3. Prediction of the transition fs-equencies The optied emission spectrum of the HeNe’ ion produced in a hollow cathode discharge through a mixture of helium and neon. was recorded under high resolution by Dabrowski and Herzherg [a]_ Two groups of bands near 4250 and 4100 A were assigned to the B’ZZ~-A22111/2 and B ‘2’-X ‘ZZtransitions respectively_ RKR potential curves were derived for the three states and are reproduozd in fig_ l_ The A,‘IT, state was xzot obsen=ed in the optical spectrum but its potential curve, however, can be estimated from the relative energizs of the other potential curves too,ether with the magnitude of the spin-orbit couphng as described in section 6_ 1n the B-X b;tnds fme structure due to spin splitting of the X ‘2+ rotation levels was resolved. Rotational and spin-splitting constants were derivedforu=6toz:=90fthegroundstate,X’ZC. using the following expressions:

F,(N)=B,N(Nsl)--=N’(N+l) fn,N3(N$_1)3f-L,N~(N~l)4 +-M#(N

where c is the vehxity of light and the upper and lower signs refer to parallel and antiparahel alignment of the laser and ion beams_ Transitions are Doppler tuned into resonance with single laser lines by scanning the acceleration potential of the ion beam_

for J = N F,,(N)

+

i)‘;

l/2 (e I&is)

= F,(N)

4-(1/2)N

x[r,+~~N(Ntl)+E,N’(N~l)*

(3-l)

A. Gzrringnm. T-P. Sofrley /

Infh

prdismcimian

IE

spmmtn: of HeNe +

201

forJ=N~1/2(flevels)

Ian-‘1

i 1) + c,N2(N

x [y+gqN

-I- 1)3 •J-‘l,N”(N

+r,lqiv

+ 1)2m-

_

-r l>“] _ (33)

In the&z expressions N &i the quantum number associated with the nuclear rotation, wbSst J represents the total angular mopxnt~ with-the electron spin coupled to the nuclear rota&Ott. The B state was assumed to have negligible spin splitting; consequently expJxssioIi (3-l) was used to describe the B-state energy levels. Dabrowski and HeAm-g assumed positive values of the spinsplitting constant yD for the four observed vibrational levels of the ground stat& We suggest, however- that the B-X bands can be equally well assigned on the assumption that yOis negative_ For example, fig_ 2 shows tbat the lines assigned to P, P&4.5) -r-Q&4-3, R,@-5) + Q&.5) ad R ff(4.5) assuming y, is positive can be reassigned to Pri(44.5)+ Q&4.5), P,(M), R,(4.5) and

(5.51,

I

Fig_ I. RKR

2

po~mtisl

-

L

3

for HcNe+

R&5.5)+ Q&J) respzctively taking yc to be negative_ This ambiguity arises because the spin splitting in the upper state is negligiik The probkm is resolved by the a.naIysis of the infrared .predism&tion spectrum as discussed later.

Rlit

_

J-

Nl

6-

f

~
6L

L-

4.5 f -

Fff

p

(W

f

Ree

R

5.-

positive

35

BY’

e

==

*

N-

t (XW)

<55t

(CS

Qef


I

I

5s

5+

Y (XT

t

V

1

Jf 5.5 c

L-5

X=X.’

1 negative

Fis 2 (a) Ftotationalbramhcs of the B’Z+-X’ZZ* transition as assigned by Dabrowki ad Hazbag of the B’Z+-X =Z+ transitionwith y(x’E+) ncgativt.

[S]. (b) Aitanati~~ ass&man

The A,2fl,r_ state exhibits a I--e a-type doubling and is well separated from the A,‘II, state. Under these circumstances the rotational structure of a %I ,r_ state is indistinguishable from that of a ‘S state with a large spin splitting_ The rotational/fme structure IeveIs of the Al’ff,r_ state were therefore assigned au effective quantum number N and totaI angular momentum quantum number J_ In this particuIar case the AZ state behaves like a ‘2- state and therefore expressions (32) and (33) were used to obtain molxular constants from the B-A, bands but with the “e” and “T designations reversed. There is no ambtguity concerning the sigu of y, for the Az’firy_ state_ Only transitions to _A121&fl u =O and 1 were assigned by Dabrowski and Herzbergg On the basis of the assignment of Dabrowski and Herzbergg transitions between the A,‘flrr_ and X’E+ states are predicted to lie in the infrared_ In particular the O-6, O-7. l-7 and 1-S vibrational bands of the AZ-X system should have a number of rotational components in the CC& laser reggon SSO-1090 cm-‘_ Such transitions would be observable w&h the apparatus described in section 2 provided that: N’

1’

7-

7.5 65

t e

L.5

55

f c

L-5 3-5 35 25

t t t e

4

I 1

‘1

!

!

T

4

A

!

!

_ e

vibration-rotation states pre(a) The A2’flI,, dissociate with lifetimes in the range 10s610-l’ s. (b) The transition frequencies lie within the limited Doppier-tuning range of one or more laser lines_ For example, using the “CQ laser line at 983212 cm-’ the ranges 98232-98289 and 983_61-984-M cm-’ may be scanned for parallel and antiparallel atignment respectively. (c) There is =FFicient transition intensity and population of the u= 6, 7 and 8 levels of the ground state_ ‘fitr_-‘Zitransitions are expected to have six branches assuming that the “ff,, state is intermediate between Hund’s cases (a) and (b) [i]; the selection rules applying are &J= 0, &l and -I-H -_ Fig 3a ilhtstrates the six branches for a particular vibration-rotation level of the ground state with spin splitting such that ye is positive_ For comparison fig 3b shows the predicted branches assuming y, to be nw&tive_ The branches Qrc_ R,, P, and Qd in fig 3a become relabelled R,. Q,. Q& and P, respectively in fig_ 3b: taking all 4 branches together there is no difference in the predicted transition frequencies_ The branches R,

N’

J’

J-

N,

5-

(4

Y (X*E’)

5.5 LS

l

t

positive

Fig 3_ PrediccrdA,‘TI,,-X*x*

Y (X*X3

0) transitionswith (a) y(X’Y)

positk

nrpatire

(b) y(X’E*)

ncgativ~

-1203..

and P,, however, are predicted to Iie ar‘different transition frequencies for the two cases, the difference being equal to the spin spIitt& in the ground state. It may be anticipated that the observation of the R, and Prr branches in the infrared spectrum would reveal the true sign of yO_ The most satisfactory procedure for predicting infrared transition frequencies from the optical spectrum was found to be as follows: (a) A series of vibration-rotation energy IeveIs for the B’Z+ state were calculated from the molecular constants given in ref. [6]_ (b) The optical transition energies for the B-X and B-A, bands were subtracted from the B’x+ energy levels to obtain vibration-rotation energy Ievels for the X and A, states. Each X or A, state vibration-rotation IeveI is connected to more than one B-state IeveI; thus several estimates for each energg IeveI may be obtained_ In general the mean of these estimates is assumed to give the best prediction_ (c) Infrared transition frequencies arc caIculated direct@ from the A,- and X-state energy levels_ Two sets of predictions were thus obtained, one for each possible sign of y,_ The predictions were considered to be accurate to better than 0.1 cm-‘_ 4. Results We have conducted a systematic search for infrared predissociation transitions of HeNe* through the range 880-1090 cm-‘. ApproximateIy 50% of that range is accesst_ble for this ion using the method of Doppler tuning in conjunction with

.

a CO2 laser_ For each laser frequency and for both parallel and sntiparallel aIignm& of ion_ beam and laser beam, the source potential was Scanned from 2-10 kV in 1 V steps with a 1 s integration time (1 V = 2 MHz). A total of 107 resonances in the Ne’ photofragment signal were observed- ekin transitions may .be Doppler tuned into rcso_ nance with more than one laser line enabling appropriate corrections to bemade for earth-&Id penetration into the source: the transition wavenumbers of the resonances may therefore be measured to within an absolute error of 0.002 cm-‘_ The majority of *-he A,‘II,E-X’Zc transitions predicted to Lie in the Ca_ Iaser region belong to the O-7 vibrational band_ Table 1 shows the numbers of lines within each rotational branch of this band predicted to Iie witbin the Doppiertuning range of the available laser frequencies_ For comparison the numbers of transitions observed within 0.1 cm-’ of these predictions are shown. The comparison is made for the two sets of predictions separately (yr positive and negative); fig 4 i!Iustratcs the comparison graphicahy. Table 1 shows that no resonances are detected close to de predicted transition frequencies for the R, and Prr branches assuming y, to be positive_ By contrast the R, and Pfl branches are succxssfuhy predicted assuming y, to be negative_ From the discussion of section 3 it is quite clear that the spin splitting constant y, must be negative, not positive as suggested by Dabrowski and H_+zberg_ The remainder of the results presented in this section are based on this conclusion. In considering ah four possible vibrational bands, O-7, 1-7, l-8 and O-6, a total of 78

Numbers oz‘A,‘rt,,-XLZ’ (O-7) tmndtionspraiictcdto lie -i&in the &ppIcr runiag rzns_~of CO, laser frequenda and numbers of obs&ed transitionswithin 0.1 cm- ’ of the praiiuio~~ T-.a~sas of predictions ue considered based on the CUDpossible aE&gnmacs of the optical acssion spcctnun R,

Qk

Rff

P+

Qd

Pff

Total

pndiCliO0 obsavatifm

10 0

12 12

13 0

10 7

11 10

6 0

62 2s

7 negative pdiCtiOa obxncaknl

11 II

13 0

12 12

11 10

10 7

6 6

63 46

y positive

I : : 1: . : .:. : III c

Prediction

Experiment

..

: : :

_

.

. Y__ L

.

.

:

:* :. :.

m :

925

900

. .. ;

975

950

I

Prediction

7

Negatirc

1000

km-‘)

o-=0-c”= 7 band I>+ing in the region WeWOO cm-’ with y(X’E’) Fi& 4. (a) Ruiic~cd -aansitions of the AZ-X. Expmimenralry observed ttitions in the region WO-ICOO an-‘_ (c) Predicted tmnsitions cI‘ the AI-X, LI’= O-o”= uningclllgeof ca_ Iasef lines are not shown Y(X 2x* ) ncgacive Transitions predicted to lie oufside the Doppler

resonances are found to lie close to predicted wavenumbers-Table 2 summar&s the number of observed and predicted lines in the region 580-1090 cm-’ for the four bands while table 3 presents details of the 78 transitions_The deviations shown in column 4 of table 3 are, with only 2 exceptions, positive and of the order 0.05 cm-‘. Weareuncertain of the origin of this consistent deviatioo Column 5 lists the excess exrgies of the

AtzZrfl predksociating states obtained by measuring the photofragment kinetic energy distribution for each transition_For comparison column 6 gives the energies of the states relative_to the He(%) + Ne+(‘P,,,) dissociation limit calculated from the energ) laqzls and dissociation energies of ref. [6]_ The experimental error for the former values is of the order 50 cm-‘; the two columns are therefore in reasonable agreement and providp good support for the assignment made

Table 2 tlansitions of four r?%rafionaI bands predicted to lie within the Doppler Numkrr of AZ’II,,-X2~+ transitions freqlIen&s compared to ntlmbers of obsned

0-e o_o”=

o’=l-o”= pndicrion obsemation

o’=O-0”=6 pKCd.iCtioEl obsa%aLion

Liming rage

of a_

RC.Z

Qk

RU

P,

Qd

Pa

TomI

11 11

13 0

12 l2

11 10

10 ?

6 6

63 46

1 1

4 0

4 4

S 5

2 0

6 5

22 1s

10 9

9 0

8 4

7 2

8 0

3 2

45 17

0 0

0 0

2 0

1 0

2 0

3 0

8 0

7

plUiiCthn

posithr. (b) 7 band with

7

laser

A.

cnrringron. 7-_P.Softky / Infka+p _aiw_m;fH&

_;

_... -rabk3 Assigd~z'n,fl-X'Z+

infrardpl.uEwaa _ tiontransitionsofHcNe~

Assignment

Obsawed

iV'.J'-N".J"

wamun;ber

_wava-I~

Obs-prcd (cm-')

-.

.ry;-

.. _. _-.

.___-.. ..

.~ _Exasemr&

Wjdlh.

obs(cm-t)

(MHZ).

1

prca(clK’)

:

0'=o.t?-=7

R-branch 215-0.0.5 5.45-335

1095-8.85 11.105-9.95 12.115-10.105 17.165-15.155 19.185-17.175 20.195-18.18.5 212OL19.195

lCM42% 1049816 1049.715 1043.674 1039802 1035.037 1029.411 989510 968_731 957.359 !?45_090

R,brancb 1.1_5-1.05 2.2X-215 3.x-3J.5 4.45-435 55Ai-5.4-5 6.65-6.55 7.7_5-7.65 9.9-C9.85 10.105-10.95 13.135-13.125 14.145-14.135 15.155-15.145

1037591 1035232 1031.891 1027582 1022311 1016.G96 1008_958 992009 982261 948.426 935.795 922.595

i-O.08 G-0.07 iO.07 i-o.06 to_07 +0_03 -s-o_05 to_06 to.01 r0.03

zo35.17 1031.82 102754 102225 1016.08 1008.88 991.92 9822 94837 935.74

to.06 +0_07 i-o_@4 +0_06 +0.02 iO.08 -FOB9 -l-O_06 co_06 +osM t0.06

935.443 919590 905s63 891997

1034Ao 102621 1006X2 94538 91954 90591 891.94

i-O.08 +0_05 +0_05 +0_06 to-05 -I-o_05 +0_06

P'brancb l.OS-1.15 3.25-3.35 5.45-52.5 7.65-7.7.5 985-995 1095-10.105 15.145-15.155 16.155-16.16.5 18.175-ls.las 19.18s-19.195

1038163 1034658 ls26_741 1015.164 lOC0_l37 991.418 937Aso 92534c899.693 a86564

1038-73 1036.60 1026.iO 1015.09 lOCNKJ7 991.40 937x2 92530 599-67 88655

Pnbranch O,ozi-215. 3.35-5.4s 555-7.65 6.6-5-8.75 8.85-10.95 10,105-12JlS

1029_765 loo&603 986558 975234 95O_l65 922182

1029.74 100655 986-47 97520 950.11 92217

6.55-4.45 9.65-7.75

3p6

502

X49-74 1049.65 1043Ao 1039.74 1034.97 102938 989-46 968.67 957.35 945.06

-254

523 533 573 590 607 627 748

.186 157 124 104 81 184 -236 221 >lam

e-03 832

862/82 500 504 SOS 515 524 534 547 576 592 652 675 699

358 278 198 ma 197 133 120 =. 101 25.5 341 42s 272 234~

690

502 514 545 649 695 721 748

216 81 113 146 164

10.03 +0_06 i-o_04 io.07 to.07 +0_02 +0_06 iO.04 -CO_02 +0_01

MO 520 a0 590 610 670 650 820 810

500 507 523 545 573 590 695 721 775 803

320 267 220 200 129 132 98 151 180 193

i-o.03 +0_05 +0_09 +0_03 +0_06 i-o.01

520 640 530 570 640

498509 524 534 561 592

540 500 500 520 590 570 600 670 640

Qd brada US-215 435-4.3s 7.65-7.65 13.125-13.12.5 15.145~15.145 16.155-16.155 17.165-17.165

1034Asl 1026.260 1006.874

570

331 242 .gE 152 73 101 f_

_.

ampnge)

,-

A. Civrin@a

206

7: P- Sofrky / b#nmf

predissociafion specmm

0J HeIUe+

-rabk 3 (cu.rlrinued) Assgmac N..J*-N"J" II’= Lo”=

ob5en-cd uavammkr

lacsellumba

ohs-prcd (cm-9

Exassamgy *C=-'>

P=d (==-‘)

Width (LUIW

7

R-branch

16.155-14.145

1aSo.139

-

45

165

Rnbranch

lO.l05-lo.95 lI.IlJ-ll.lC.5 14.14~14.135 16.165-16.155

1093.981 1079598 iOZS.%S 985.424

1093_95 107951

P, branch 11.105-11.115 lL115-12.125 14.135-14.145 15.145-15.155 16.155-16.165

1090.%3 1076531 XOU.182 1014*19f loo6547

109090

+ 0.06

1076.67

-0.09

1os3.804

lam.74 106822 IO5156 1033.57

+0_03 -r-O_09

7Oa 719 &03/23

120 1% 178 522

703 716 766 784 802f22

97 69 106 90 140

658 667 677 688 803/u

76 92 85 125 540

645

652 660 670 680 692 703 733 766

195 209 117 175 120 83 115 % 128

634 638 659 688

240 169 81 100

721 733

SS 133

638 643

180 162

766

740 830 750 SOo/32

Pm branch

7.75-9.85 s.ss-IO.95 995-11.105 10.105-12.11.5 16.165-18.175

iO68168 1051.524 1033.901 906.169

i.o.06 io_os io.06 io_03

690 710 720 ioo/60

c'=l.o"=S R,

branch 945334 945595

wL23 94554

i-o.10 i 0_06

945.086 913.817 941.791 939-019 935510 926286 920548

945.05 943.77 941.73 938.98 93551 926.23

+0_04 + o_os i- 0.06 f om 0.0 +0.06

9292al 925.778

92.926 925.71

-I-

91l.029 890553

9LlMl 89055

to.03 0.0

P, bm 12115-12.125 13.125-13.135

886.830 518.892

886.90

878.83

-0.07 HMJ6

P,btandl 4.45-655 5.55-7.65

901.053 89x95

901.03 S92.n

co.02 +0.03

5.4.5-3.3.5 655-4.45 7.6.5-555 8.75-6.65 9.85-7.75 10.95-8.85 11.105-9.95 13.12.5-11.115 14.135-12.125 R,bd 335-3.x 4.45-4.3.5 7.75-7.65 10.105-10.95

-

om

+0.07

The_linewidths listed in column 7 of table 3 vary from 56 to > 1000 MHz The contribution to the linewidths from power broadening has been

780 710

eliminated as far as possible by reducing the&sex power until no furthe! decrease in linewidth is obsesved_ In. tie case of lines with low s&al to

noise it may not have been possible to eliminate this contribution entirely_-Doppler. broadening is likely to be ikgnificant as the velocity spread of the ions is considerably~re&tced on acceleration [8]; the DoppIer width, is probably = ‘, MHr We conclude that the linewidth variations are predominantly due to predkociation broadening The linewidth (fwhm), P, and predkociation lifetime, r. are related by the expression. P(MHz) = (l/217)

-.

922.59

925.33

922.60

925.3.t

922.61 ZIG

925_35

I 9.9/s-9.6.5

FWWY=SSM=

992.GO

0-7>1-7>1-8=-O-6 and within each vibrational band

x lo+,

so that a linewidth of 100 MHz cotres+onds to an

I’

upper state lifethne- of l-59 X- 10m9. s_ The. .lir+ wid,thvariations are illustratedby the -thrgk&i& tions shown in f&s_ ‘-. : --: -_ y -~-_:_T_:.,_;A comparison of-.& sig&l-tonoise ratios ~o;b-’ ‘served for the various transitionssuggestthe order of relative intknsities

992.01

992.02

~czn-l

F~5.Expaka1taRy0bsawdlixsforrbnx 0-?bandmansitions_lluhorizoIltalscaItistisameill~&~illunrating rh~mriaionsiniincwidfi~

Typical signal-tonoise ratios of 10 : 1 to 100 : 1 are obtained -for R,-branch transitions of the O-7 band using 10 W of laser power. .compared to 2 : 1 for the 017 Qcrbranch lines and 2 : 1 for the 1-8 band R,-branch lines_ No O-6 band lines were observed, nor any Q-branch lines in the 1-7 or l-8 bands, prcsumaply. due to the low ~hncnsityof time transitions. The O-7 and 1-7 band transitionwavenumbets were used simultaneously in a Ieast-square%fitting procedure to obtain iotation and spin-splitting constants for AzzHir_(u = 0 and 1) and X’Z’(o = 7); the expressions (32) and (33) were used for. the energy levels The absence of low rotationaI quantum number components of the l-7 band leads to poor definition of the Al’Htfl(v = 1) molecular constants_To correct for this instability, transition wavenumberspredicted from the opticai spectrum for the low-J lines of the l-7 band were included in the fit The constants thus obtained are shown in table 4 and compared with those obtained by Dabrowski and Her&erg for these states, Seven of ~the obseked 1-7 band transitions shown m table 3 are seen to have nc predicted wavenumber in cohunn 3; the upper states of these transitions wer¬ observed in the op.tical spectrum. Assignment of the resonancesis based on an iterativeextrapolation and refitting procedure.The iast en& Ievel observed in the optical spectrum for A,2HII/2(o = 1) is N = 13, J = 13.5. The energy levels for (u = l), N = 14 were predicted by extrapolation us-mg the molecular constants. o-bmined in the least-squares fit. Assignment-of the transitions 14,14_5-14,135 -and 14,13.5-14,145 enables an improvement in the mokcukr constants to be made; thus a better estimate-for the

Tab!cS RomhaIandspiSspIittingconwanufofHcIue* CoiuIaxlr~

B D x10-* HXIO-' Lxlo-'* M x10-" Y tx10-4 rx10-' CXlO-9 qx10-'2

x'x*

X~~'(u=7)and_4z'n,,(c=0.1) A2'l-Ily_(c=O)

(I=?)

lhisaurk

=f-PI

Ihisarork

ref.161

thislmrk

135545 2822 O-619 -x13 035 -la895 -158 -2_28 S-73 -8_98

135755 2%1 O-649 -3-15

0.86210 1.161 -0506 0547 -029 03072.9 -6.012 1.14 -243

OS6571 1592 1.41 -3.17 030470 -4-629

0.71169 l-978 0_600 -8.73

1.08720 278 0_844 -0.0249

Bi = 15 energy levels is obtained

and so on_ The observation of alI Four transitions to the N = 16 enables a direct kvelsintheinfrarecspectrum comparison of the combination differences X’Z’(

u = 7) 16,15J-X’Z+(

X’Z+(a=7)

A2'I-Ily_(o=l)

c = 7) 18,175

16, ‘16%X’2*(0=7)

14,145

to be made with- the optical spectrum; the comparison serves to confii the assignment Insufficient transitions were observed for the

rcT.WI O-n658 2388

010243 -4_243 0.058 -o_m

ozO35 -492

1-8 band to enable reliable constants for the X’Z*(o = 8) state to be obtained In addition to the 78 assigned transitions a futher 29 resonances were observed which couId not be assigned on the basis of predicted transition frequencies for the O-7, l-7, l-8 and O-6 bands_ ‘?-he transitions apparently fall into two groups and are collected in table 5 Group A transitions have excess energies in the range 600-800 cm-‘, hewidths mostly in the range 33-100 MHz, and are of relatively low signal-t-noise ratio_ Group B

TabIc5 lhass@&infxaredp~ticm~tio~ofHclNe' GroupB

GroupA ua>ul* (an-')

width @II-w

excessalagy (cm_')

wa\mumber (a-')

aid& (MI-U

IOn_ la66_766 1054509 lM1.865 1oG5.068 991377 991379 989383 986212 958346 95OsJ41 937585 937.424 931.674 918-118 888688

790 76 84 55 so 33 75 n3 157 805 74 92 45 60 60 95

720 n0 i70 75!? 780 780 630 710 no 650 600 7rm 700 no 780 m

1078_023 10579R 1O47mO 1021_857 1020328 10~152 968.737 964.034 939.039 921.404 318.183 895.810 88s_m

12 301 94 22% 537 43 8 W loccl 1920 21 28 4aoo

ex-al(a-') 400 loo 440 12 88 W i2 170 49 35 200 73 265

transitions have excess energies in *e range 12-440 Iinewidthsvarying from S-4&)0 MHz and -. are of higher signal to noise_ Further discussion of the nature of these transitions is presented in section 5.

cm-‘,

5_ DiscusGon The transitions we- have assigned involve 33 different rotational levels of the A22H,r_(u = 0) state and 22 different rotational levels of the Aa211,,&u = 1) state The fact that these transitions are observed in our experiments demonstrates directIy and conclusively that aII 55 levels are weakIy pmdissociating; measurem ems of the transition linewidths show that the lifetimes range from 1.5 x lo-” to 2.8 x lo-’ s. state correlates with the The Az211tyNe+(‘P& -C He@) dissociation limit (see fig 1). The work of Dabrowski and Herzberg [6] has shown that 30 of the 33 (u = 0) levels and 19 of the 22 (D = 1) levels he below this dissociation limit. It is apparent; therefore, that predissociation of these levels can only occur via a non-radiative transition to one of the states correlating with the only lower-lying dissociation limit, Ne+(‘P,r_) •? He(%)_ The excess energy measurements conFirm that predissociation occurs via the lower-lying limit and hence that the mechanism is electronic For the 6 vibration-rotation states lying above the Ne’(‘P& + He(%) dissociation Iimit there is likely to be competition between electronic predissociation and rotational predissociation The latter type of predissociation occurs via the upper dissociation limit and wiII give rise to a small excess energy_Thetransitionsto(u=O~N=19,J=18~~, (0.20.19.5) and (1. 15, 14.5) have large excess energies; thus it would appear that electronic prediisociation dominates for these levels_ The transition to (0,21,20_5) shows a smaI.I excess energy and is considerably broader than other members of the same branch In this case rotational predissociation is dominant The pruiissociation of the states (1.16,1&S) and (1.16,15.5) gives rise to fragment ions with both large and smah kinetic energy reIeases_ suggesting that rotational and electronic predissociation occur at comparable rates for these levels.

Fig 1 shows that there is no. curve- crossing. between the Aa2.Htfl state and either. of the two states correhuing with the Iowest dissociation I&it Never&e&s* continuum 1eveIs of the -A,‘II& and X’Z* states-are degenerate tith the bound state and provided there is a levels of the A2’lI,,o coupling between the bound and continuutn states, pred&ociation may stih occur- This example corresponds to the case c, of M&I&en’s &ssification of electronic pred issociation [9]. The nature of the couphng between the states is discussed further in section 6. Very little experimental informtition exists on the electronic pr&issociation of diatomic molecules in the absence of a potential crossing or avoided crossing. Et-man and his colleagues proposed that such a mechanism operates in the predissociation of the A26 states of CH, SiH and GeH [10,11,12]_ In each case they measured radiative lifetimes for individual rotational levels of the -4% state and observed a sudden drop for Ieveh. above the dissociation Iimit of the 211 ground state. The drop was ascribed to predissociation via rotational and spin-orbit couphng -to continuum levels of the ground state There is DO potential curve crossing between the A b and X ‘II states in any of the three molecules. For each molecule, predissociation Iifetimes were derived for several rotational levels and found to be of the order lo-’ s, considerably longer than the lifetimes observed in this work for the HeNe’ ‘)Hrr_ state. A number of lines observed in the infrared -and visible predissociation spectra of CH+ may also involve an electronic predissociation in the absence-of curve crossing [13,14]. No assignment has yet been made, however, to contirm the nature of the predissodation. Apart from the experiments mentioned above we are aware of no other examples from which quantitative information on the Lifetimes for predissociation in the absence of potential crossings can be extracted Because of its simpiicity the HeNe+ ion is particuIarly attractive as a model system for comparison of experimental and calculated Lifetimes The molectde has 0nIy 11 electrons so that ab initio &&ration of the matrix eIements coupling the various states should be reasonably -_ accurate_ The calculation of pred+octation Iife-

times should be straightfcxward as the situation may be reduced to the in:eraction of one bound state with two continua- Under these circumstances

the

separate contributiom to the liuewidth

the coupling to the two perturbing states are additive to a good Ievel of approximation [15]_ In section 6 wx present a preliminary calculation of &e peation lifetimes for the Al’Ill/z t‘ = 0 from

and u = 1 rotational levels. The experimental observation that the spinsplitting constanl5 y, for the X’Z* state are negative is in agreement with theoretical e?cpectations_ Cooper has cakulated the magnitude but not the sign of the spin-splitting constants using secondorder perturbation theory from the expression 116)

zn;

@I-I:.

‘2,)

Only the AI’II state is sufficiently close in energy to the ground state to merit consideration in the summation_ The matrk elements in the exp_xssion have been calculated ab initio by Cooper and have the vaIues at 4-5 bohrz (X’2*[t’~_A’n)
= 1_171, = -337.4%

- E(%) is always posiAs &l:r ‘xc )= E(‘n) tive. y, musf certainly be neggtive assuming the man-ix ekments do nof change sign with change in internuclear distance Further evidence for the sign of y comes from a consideration of the refative intensities of the rotational branches_ Cooper has cakulated values for the transition dipole moment (‘S*lp, f ip$n) as a function of internuclear distance and fimds the

The appro.ximate hamikxian

term to be very smaLl[17J. Another contribution to intensity results tiom the spin-orbit mixing of

the

the ‘Xi

and

zlII,/,

states;

this leads

to the intro-

duction of terms including the permanent dipole moments, {‘Z+/p$S+ ) and (‘I-&L~II) into the intensity expression_ If these terms are dominant, as suggested by tke ab initio calculations of Cooper, the P and R branch transitions should be at least an order of magnitude more intense than

the Q branch tranSitions. The experimental observations are in axord with these theoretical predictions provided that a negative value is taken for y,(‘Z’)_ The relative intensities of the four vibrational bands are as expected on the basis of caicuIated Fran&-Condon factors; the vibrational overlap integsats can be catcsulatexi numerically frcm the RKR potential curves by solving the one-dimensional S&r&linger equation to obtain the vibrational =avefunctions. The f& questim of this section concerns the identity of the 29 unassigned lines_ It would seem likely on the basis af the excess energy measurements that the group A transitions are -4, %r_ -X ‘S* transitions involving vibrational levels not obxzxxi by Dabrowski and H-bergThe state is expected to support at least fwo AZ2Q/L? more vibrational leuek (u = 33); the calculated Fran&-Gmdon factors for the (Z-7) and (2-S) bands are comparable to that for the (l-8) band_ The transitions in group B are most probably vibration-rotation transitions of the ground state for which the upper states are rotationally quasibound- Unfortunately the lower vibrational states of these transitions must be u = 2-5, which were not observed in the optical spectrum- We are currently testing out methods of extrapolating the existing data in order to assign these transitions_

for a rotating diatomic molecule may be u-ritten in the form: (6.1)

p and m are the reduced mass of the molecule and the tiassof the electron respectively_n labels the. electrons and V(r; R) is the electrostaticpotential- *so is the spin-orbit operator while the third and fourth terms in (6.1) represent the nuckar kinetic energy and the rotational motion of the nuclei respectively_ We defme relativisticadiabatic electronicwavefunctions, +zd(r; R), as those which diagonalise

the first two terms in eq_ (6.1): XqB~(r;

R) = U,“d(R)QZ(r;

R),

.S”=X~+S&-p

1 (6-2) (6-W

The relativistic adiabatic potential curvesI U,“s(R), are thus obtained by solving eq. (62) over a range of values for the intemudear distance R. The Born-Oppenheimer separation may be used to express the total wavefunction, *=,,, as the product: (63) x,&R) is the vibrational wzwefunction and +,%(a) is the rotational wavefunction wh+h is a function Of the Euler angles a, 8, y, represented by o_ Substitution of the product (63) and the hamiltonian (6.1) into the Schr&iinger equatiou, multiplication by &“(r; R)* I/,&O)* Ia and integgation over the ekctronic and rotational coordinates leads to the following equation for the vibrational wavefunction, U,,,(R)

U,,,AR)=

1

x&R)

Q?‘(R) +4,(R)

= Czc,x,c~(~)-

- C,,wn(Rh

(6-4)

(6-5) (6.5a)

(6Sb) The diagonal matrirc eiement of the rotational operator, C, ,a-,e( expression

R), may usually be approximated by the

(6-54 whilst the term A,, is often ignored. For each electronic state a discrete series of vibration-rotation energy levels, &,z, together with an infinite set of continuum levels lying above the dissociation asymptote are obtained in the solution of the one-dimensional ScbrTkkger equation (6.4) for all values of J_ Off-diagonal matrix elements of the nuclear kinetic energy operator, -(ti2/2p)(d2/dR2), and the rotational operator (h2/2pR2)(J - I. - S)* may still be non-zero between different relativistic adiabatic states which have the same rotational quantum number J. Thes matrix elements lead to a breakdown of the Born-Oppenheimer approximation (63). In tbe c&e where bound Ievels of one adiabatic state are degenerate with continuum levels of another state (or states), non-zero off-diagonal matrix elements give rise to non-adiabatic transitions from bound to continuum levels and hence predissociation_ Tiie-dependent perturbation theory may be used to calculate the probabibty of the non-adiabatic transitions; the fimrd

A. Camkgrron. T-P. Softiq- /

ZlZ

InJkredpre&sociation

specmmz

of .He.Ve+

resuh is the familiar Fermi goIden rule expression I-=2=x

m [j

x,,,(R~~-,(R)x,,(R)dR

Z I

-

-~ (6-6) (6.6a)

7 = h/l-_

I’ is the praation Iinewidth and 1 the predissociation lifetime xnr, is tha vibrational wavefunction for the bound state n, J while xmU is the continuum wavefunction for the unbound state m, J evaluated at the energy E of the bound state and normahsed to a delta function of energy_ Tbe remainingterms in (6.6) are given by 3

dSLmJLt-

=

A no1 +

4,(WdR)

-

qJSmJi?-.

(6.6b)

with

clnm and q,,,, are given by (6Ja) and (6Jb), and the summa tion in eq_ (6-6) is performed over all the continuum states which are deggenerate with the bound state_ For an alternative time-independent viewpoint it may be considered that the effect of the non-adiabatic coupling is to mix a part of the continuum wavefunction into the bound vibrational wavefunction- There is therefore a non-zero probabihty of the nucIei appearing a? infinite intcmuckar separation_ Using the scattering formahsm of Child 1151 we consider the system prepared in the predkociating state and cakuiate the outgoing Ilux along the open channel. ix_ the rate at which the nuciei are separating Such a treatment leads to precisely the same resuk (66) but is more easiIy genera&cd to cover such cases as the interaction of two bound states with one continuum_ 62

Caku~arkms for Heive +

The aim of the cakulations performed in this work was to evaluate the expression (6.6) for all the rotational ieveIs of the Ar’l’ltr_( o=O) and (u= 1) states of HeNet_ Tbe RKR potential curves for the and ‘XL states were taken to be a good rep resentation of the relativistic adiabatic potentials_ The Qlt, curves were calculated using an RKR program of LeRoy 1181 in which the vibrational energies and rotational constants are entered as near-dissociation limit expansions. The potentiab were extrapolated to Iarggeintemuctear distance using the form U(R)=

D,-

CJR9,

where C, = 11901.8 cm-’ = r’e’a_ a is the pohuisability of the helium atom calculated to be 0.204956 X lo-‘* cm3 [19]_ The inner wahs of the potentii3Is were fitted to the cxprcssion lJ(R)=Aexp(-BR)-+C and estrapolated to short internuckar distance using this form_ The A, zlX3rL potential curve was derived from the A,%llE and X’Z+ curves as descrii beIow_ Each of de three states. X, A, and AZ. is doubly degenerate in the non-rotating molecule due to the two possible vahres of 0 It is convenient to divide the total six states into two sets of three, by using linear combinations of defined parity, such that there is no interaction between the two sets_ We therefore defme:

._.

._._ 1

T-P_ Softky

A. Gvringtat.

Infh

/

pre&oriaion

spectrum of HeNe *

-.

_.

--:.

ilusr

elevelsareodypred issociated by coupling to the e levels of the X*x+ -and A, ‘n,h &ite.s:Thus the ‘n,, From this point on we consider only the predissociation of the e levels; the treatment for the f levels is directly analogous_ the matrix element of the radial and rotational operators over theIn order to cakulate &!&A,,~. electronic and rotational coordinates, it is useful to express the eigenfunctions of Z&, in terms of a diabatic basis set +,$ which are eigenfunctions of sd only_ The chosen parity-defined Hund’s case (a) basis set, &=

(I/Gj[p,s,z,s) i p-n.s-~,-a)]

wasrestricted

(6-7)

to the electronic states correlating with the Ne*(*P)

+ Ee(*S)

dissociation limit Thus we

write,

a? = (C,,(R)/~)[10,1/2,i/2,1/2)

+ W/2,-

+ (Cz,(R)/fi)1lL1/2,-

l/2,1/2)

;(C,,(R)/~)fl1.1/2,1/2,3/2)

l/L,-

+ I+I-

l/2)1

1,1/2,1/2,-

l/2)]

&l/2,-l/2,-

3/2)]-

(6.8j

The R-dependent coefficients C,,(R), the diabatic potent.% curves U&(R) (the eigenenergies of sd), the relativistic adiabatic potentials, U,“d(R), and the matrix elements of the spin-orbit operator between the diabatic basis functions, are related at a given value of R by the matrix equation @s,x i

v,”

ODSO

0

x&o

0

Cl,

Z.&,-&“-;A

0

c 28 = 0,

0

c&,

-

u,“” -I- $A

II

c,,

(6-9)

1

where 3powo= (‘II~Jf&,fZ)_ Values for the spin-orbit coupling constant A and the off-diagonal spin-orbit matrix element souse have heen calculated by Cooper [16]_ The former quantity was evaluated for a range of internuclear distances and found to be fairly constant_ The off-diagonal matrix element was evaluated only at 4.5 bohr and is considered in this calculation to be constant also_ Substitution of these quantities and the relativistic adiabatic potentials for the ‘Ii,, and *2* states into eq- (6-g), enables the coefficients C,,(R) and the diabatic potential tunes e(R) to be evahtatd The matrix equation is solved for a fine grid of R vahes. Once Tn, is obtained, the ‘lIsr- relativisticadiabatic eigenenergy is given by ucGdn,,= U
R) =J&(r;

R)S”(r;

R)+z(r;

(6_1Oa)

R)dr

may then be expressed in terms of a sum of matrix elements between the diabatic basis functions_ ~~~(R)=C/~,(R)~~(r;-R)~(r; 1y

R)C&(R)#(r;

R)dr.

(6SOb)

Ma-u-ix elements of the rotationaf operator between the diabatic. basis functions have been tabulated by Kovacs [20]- The% evaluation requik a value for (*fflL.*~z’) which has been calculated at one internuclear distance by Cooper [16] and is assumed to be constant_

A_ Cirnhgtw~

214

TX

Sofw / Infrrnmdprrdirrodnrion

.rpcryrmr o/ ISaVe*

iMat.ri~ ekments of d/a R and d2/a R’ were calculated using the procedure adopted by Graff et al [21]Cl~,fR)~i(d/dR~~~(R)~d~=CIC,,(R)~~[O,(dC*~(R)/dR) 12 B

+ &(R)(dgi/dR)]dr

(6_11b)

=~Cmi(R)(d2/dR2)Cmi(R)_ i

The omission of the second term in the square bracket of eq_ (631a) is exact while the omission of the analogous term in eq_ (6.11b) is an approximation of uncertain validity_ To catcuiate the radial wavefunctions, xnrl (R) and x==(R), the diagonal matrix element of the rotational opcmtor for a particular value of J was added to the appropriate relativisticadiabatic potential curve and then the one-dimensional Schr&iinger equation (6-4) was solved. For the bound radial wavefunctions the solution was obtained by a Numerov-Cc&ey method [22] using a program of LeRoy_ For the continuum wavefunctions a uniform Airy approximation 1231was made to obtain the solution using a program of Hutson- In this appro_ximation the solution of (6-4) is expressed in terms of two known independent solutions of the Airy equation (612). d’O/do”

(6-12)

- go = O_

The mapping relation between the sohrtion of (6-4) and the two independent solutions of (6.12), Ai Bi(a), is given at energy E by

x,,JR)=

u(R)

[a(R)/[E-

= (3/2(2p/h2)1nLR[

V,,,(R)]]“~[~(a(R))~BBi(u(R))I-

E -

0;,& R)]

and

(6-13)

rr-d R)2/3-

The requirement for the solution to be non-divero,entat the origin gives /3 = O_

6-R Resuk The results of the IinevZdth calculations for the Az’ff,,ju=O,l) revels of HeNe’ are shown in table 6_ Cohmms 2 and 3 show the. cahxrlated contributions from rotationa.I coupling to the X’E’ and A,=l-& states respectiveLy. assuming radial coup*hng to be zero_ Column 4 gives the

contribution to the linewidth from radial coupling to the X*x* state, including both first and second derivative terms, assuming rotational coupling to be zero_ The total calculated linewidths are shown in cohmm 5 and compared with the experimental hneaidths in colunrn 6; the comparison is also madeinfigs_6and7foro.=Oandu=lrespectively.

05

15 25

35 45 55 65 7.5 85 95

105 115 125 135 145 15.5 16.5 17.5

185 195 v= 0(f1cw&) 05 15 25 35 45 55 65 75 85 95 105 115 125 135 145 I55 163 175 ~-~ 185 195 o=l(ekw?k) 05 .I5

25 35 45 55 65

0.05

O-17 0.35 058 O-85 l-13 1.40 1.67 213 1.97 1.97 1.84 159 0.23 0.80 038 O-08 O-01 025 o-13 030

0.54 0.83 1.15 1.47

1.13 2.00

213 212 136 1.64 1.19 0.67 023 0.01

OS8

l-80 4.72 8.70 13.6 193 25.6

324 395 429

53.6 60-l 66.0 71.1 88.0 775 78.4 77-l 73.6 665

1.83 4-85 9.01 14.2 203 256 34.9

429 513 595 67.6 753 821 880

924

OS1 2-14 3.81

953 96.0 942 89-l

O_OlYM 0.015 0-M 0.13~ 013 033 .0.44

0.0 214 559 102 15.6 218 28.3

2270 2280 2260 2200 2100 1970 1800 1600 1420

1180 935 681 441 231 78.6 3.6 30.7 176 443 n4

2140 2020 1870 1690 1470 l2lO 993 731 4x2 262 952 739 23-9

167 4.53 876 1410 2010 - 2510 2860 160 162 156

144 128 -110 : 883

2270 2220 2230 2150

320 306 267 234

2050

220

1910 1740 1540 1370 1140 w2 668 458 266 135 785 116 261 512 814

186 200

2lSO 2080 1940 1770 1560 1320

1100 844 590 362 184 83.6 89.7 229 520 965 1540 22co‘ 2760 3160 161 1643 -155 145 133 119 .-

106

:

129 124 104 81 81 9s 146 164 180 193 221 33i 358 278 198 204 185 133 120 73 56 101 -. 255 341 428 -

19-j -209. -.117. :-

... -. __.

kvnhuedonnexrpagcl

SJ

a64

95

0.X

X05

O-77

115 125 135 145 155

OS0

c=l(flc\rls) 05 13 25 35 45 55 65 7-5 SJ 95 105 115 IL5 135 145 155

o_so 0.75 0.6% 055

4023 462 505 53-4 54-3 533 49.8 429

0113

0.17

21s

029 0.43 058 O-74 OSS 0.99 1.06 I-13

5.73

I_11 1.w

O-91 O-72 O-49 O-26

105 16.4 G-0 302 375 44-7 51_3 563 613 63-S a-4 62-4 575

The cakuiared iinewidthsfor o = 0 are. on average_ an order of magnitude too Iaro,ee;by contrast

for c = 1. the average caIcuIated Iinewidtb is in good agreement Gth experiment_Rotational coupling to the %Z+ state is apparently negggible for all vibration-rotation states as shown in column 2 Rotational coupling to the ‘rISr state is reIativeIy insi_ticant at low rotationai quantum number J where the Iinewidthsare determined essentiallyby the radial coupI& For the highest rotational quantum numbers. rotationalcoupling to the zI13r state makes a comparable contriiutiott ‘_o radial coupling_particularlyfor the (u = 1) state_ The cakuIated variations in Iinewidth with J, are deter&n ed almost entirely by the radial coupling_The clear md in the experimental Iinewidths for u = 0 shown in fig 6 is weII matched by the caIcuIations_The radial contribution to the coupling fimction, S=‘-(R) is independent of J_ Thepositionsofthe minimaandmaximaofthe _ vtbrattonaI wavefunchons xnzJ(R) and x,.&R)

53-6 38-9 31.8 24-7 20-6 18.8 IS.4 115

141 120 97.6 73.1 SO_2 30.7 142 4-3 O-05 0.80 5.13 11.9 202

285 3x0 513

s3.4 75.6 733 iO.1 e7_7 c53 Cl.8 s5-3

120 83 97 69 % 106 90 140

145

I51 II4 95.7 XL1

631 s-4 ZS 463 513 58.4 673 76.1 s45 924 101

240 -

180 162

-

76 92 85 100 156

17s

vary slowly with JI ir is the change in overlap between the rapidIy osciikting _wntinuum wavefunction xmEI(R) and the coupling function wbicb causes the variations with rotational quantum number_ In addition interferencebetween the first and second derivative terms is of some importance The caIcuIationssuggest a similar trend in Iinewidths should be observed for D= 1_ The experimental results do not show any clear trend howeverWhile the success in expIainingthe variations in Iinewidtb for u = 0 is satisfying, the t&agreement in order of magnitude between experiment and theory is rather disappointing_The caIcuIated results are sen.+tive to the exact form of the potentials used as the energy differences between the ‘Xi and ‘I&, states determine the variations 05 the coefficients C,(R) with R_ The ‘I&. state potential is not weII defked by the RKR procedure as onIy two vibrational IeveLs have been observed experimentaIIy_We have been unable to

*. : i : : :

d :: ;

E ; : i

0 :

Fig 6. Expaimaxal and theoreticallinewidths for A,‘I-ftn,. vsticxl wales M diff-t 10 ilhaate the similar trend%

modify the potential curves, however, so as to produce an improvement in the linewidth magnitudes whife stih giving the correct vibration-rotation energies_Another possible source of error is in the values used for the off-diagonal spin-orbit coupling matrix element. Only further ab initio calculations will show whether the matrix element is indeed constant with intemuelear distance An ab initio calculation of the neglected term, (~i,,.P2/dR2J~j), in eq (d.llb) is also required to determine whether the approximation-made there is valid The importance of the spin-orbit coupling in the ~radial coupling should be emphasised. The effect of spin-orbit coupling is to decouple the electron spin from the internuclear axis as R increases and keouple it to the orbital angular momentum of the Ne+ fragment_73te radial cou-

D= 0 as a function of rotational quvtum

number J_ Note that the

pling operator represents the vibration of the molecule; this gives rise to a periodic decoupling and recouphng of the angular momenta leading to pmdisso&tion_ The predkociation of HeNei At2f&,& D= 0) falls into the “non-adiabatic” category whereas the p_mdisso&tion of CH. SiH and GeH would be eksified as “nondiabatic” [24]_ In the hypothetical absence of spin-orbit coup&g in HeNec, the ‘Z* and ‘II states both c&relate with the same dksociation limit, so that degeneracy between bound IeveIsof *II and contiuuutnIeveIsof ?IZt is not possible (except for rotationally quasibound levels). In CH, SiH and GeH the X% and-Ah states correlate with different dissocktion limits even in the absence of spin-orbit couphug The spin-orbit coupling tiy therefore.be treated explicitly in the~caktdation of predissociation line-

Theorylr=l)

OS

widths; these wouId be evaluated from eq. (6.6) but the viirational wavefunctions would be cakuIated from the diabatic patentiak and the ampling matrix ekmeznt*A,,, would include the spin-orbit operatorX&.

55

Research Gmnd

LOS

15.5

J

for grants towards the purchase

of equipment References [I] RJ. SayIcanyand KC wood% Ana Rev_ Phys- .acm F (1981) 403.

We are indebted to Dr.G_ XiFXS. for his interestand axrespondence We wish to thank Dr_ RA_ Kennedy for drawing our attention to the posiiility of an infrared predissodation-Spectrtmxof HeNe* and for his contisued interest in this work AC thanks the Royal Society for a Reseanb Professorship,Tps thanks the University of Southzmpton for a Researce Studentship, and we are indebted to the Science and Engineering

Kajlf& CJpi co mmnn

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