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Accidental predissociation in lithium dimer: A theoretical investigation
Volun~c 86. number 5.6
CHEMICAL
5 March 1982
PHYSICS LETTERS
ACCIDENTAL PREDISSOCIATION lN LITHIUM DlMER: A THEORETICAL
INVES’llGATlON
Davrd L. COOPER Hanard~Stttttltsotriott Cutter for Astroplt~sics, Catnbrtdge, hlassacltttsetts 02138,
USA
Jeremy M. HUTSON Deparrtttent ofC/tetttistry.
Untrerstty of Waterloo, Warerloo. Otttarto. Canado N-7L XI
and T. UZER * Dcpartmetrr of Tl~eorehcal
Recetved 7 December 198
Cltetmsrry. Oxford Utrtrwsrty, Oxford OXI
3TG. UK
1
The positions of acadcntally predissochted vibration-rotation levels tn Liz are predlctcd, usmg ab tnitto calculations of coupbng matrL\ elements together wtth recent potential energy curves and expertmental results The factorsaffectmg txedlssociation lifetimes are drscussed. and the most likely regions for cvpcrimentally observable predissociatlons are tdenkied.
1. Introduction
In a recent publication analyzmg the photodissociation of Liz, Uze: and DaIgarno [I ] drew attention to accidental predissociation as a possible drssociation mechanism and gave the quantal descnption of the process. The relative conf$uration of the potential energy curves involved is shown schematrcally in fig. 1. The process consists of particular rotation-vrbmtron levels of the A ‘?I: state mixing with levels of the b 3lIe state, which can dissociate into groundstate atoms because of its coupling with the repulsive a 32i state. The singlet levels acquire some triplet character and “borrow” predissociatron intensity from nearby triplet levels. An expression for the lifetime r,,, of a vibronic state predissociating by this mechanism has been given by Uzer and Dalgarno, r”J = WvJ
l0000 ;E Y w
5000
0
-5000
-10000
3
where
-15000 2
3
4
6
5 R/8
* Present address The Chemicd Laboratones. Cahforma institute of Technology, Pasadena, Cahfomia 91125, USA. 472
Fig. 1. Potential energy curves for Liz.
Volume 86. number 5.6
CHE~~ICAL PHYSICS LIYITCRS
kffJIL+J__ +L_J+Ibu’J)(bu’JIH,IAul) E(Aul) - E(bu’J)
2 I (0
and Iti./) is the continuum wavefunction in the a%& state, evaluated at the bound state energy E(Ad).-L+ and .I+ are the raising operators for the orbital and totai angular momenta respectively, and H, is the spmorbit coupling operator. Experimentally, accidental predissociation mamfests itself as a marked decrease in the lifetime of rotation-vibration leveis of the A state which are nearly degenerate with levels of the b state. So far, inaccuracies rn the exrsting potential curves and uncertainties in the coupbngs between them flave prevented any quantitative predmtions of positions and lifetunes of strongly predissociated levels. However such levels have recently been observed in the experiments of Johannsen et al. [2] at Freiburg. We have computed the coupbng matrix elements accurately and have used the potential curves of Davres and Jones [3] to predict positions and hfetimes of leveis that are depleted by accidental predissocration.
2. Electronic matrix elements
Off-dragonal matrix elements of the spur-orbit coupling operatortl, and the raisrng operator for the orbital angular momentum L+ have been calculated at three internuclear distances as shown III table I. Scpa. rate SCF procedures were carried out for the b3Bn and a 3 Cz states using the ALCHEMY programs of Bagus et al. [4]; the A 1r;i state suffered from severe convergence problems and so was constructed from the real and virtual orbitals of the a 32i state. The Slater-type orbital basis set was taken from the work of Olson and Konowalow [5] and off-diagonal matrix elements of
Table I Calcuktted values of the
R (~0)
couphng matrL\ elements
~b3t7,1H,,lA’X*,) (cm-‘)
4.0 5.0 6.0
0.364 0.266 0.186 0.217
1.241 1.268 1.287 1.414
H, and L, were computed using a program due to Hall et al. [6]. In view of the nature of the A 1Xi state used in Uus work, and smce Hartree-Fock wavefunctrons are unlikely to constitute a very good dcscnption of the b 311u and a 3ZL states, the error involved in usrng only tile one-electron part of H* is toierabie. The splitting between the lowest 2P1,2 and ZP,,r energy levels of Li [7] IS0.336 cm-t, so that the spinorblt coupling constant in the “P state is, by hndd’s rule, 0.224 cm-l. The calculated matrix elements for Li, thus seem reasonable but rt must be stressed that they are rather fess accurate than the vahxes obtamcd in calculations on motccules wrth larger spm-orbit coupling effects [S].
3. Nesrdegenencies Accidental predIssociation IS observed expeflrllentally only tf the lifettmc due to tlus mechanism IS shorter than that for radratrvc decay to the X state, tlus occurs only when there ISa near-degeneracy bctween the dissociatmg singlet level and a vrbrahonal level of the b 311u state with the same total angular momentum J. in LIZ, the levels must be degcner.rte to within a few ~vavenumbers for the effect to be obscrvable, as discussed below. The greatest uncertainty in predicting accidental predrssociations lies in the drfficuity of obhmmg accurate potentrai curves. The b 3 llu state of Liz has not been directly observed expenmentnliy, and ab mitio curves arc unlrkeiy to provide an absolute accuracy of 5 1 cm-t in the foreseeable future. However, two recent developments allow thus problem to be partially circumvented* (1) Davies and Jones [3] have performed manybody perturbatron theory (MBPT) calculations on all the relevant electronic states of LIZ; the potentials obtained are hkeiy to have very nearly correct shapes, ai~OU~I the absolute energtes may be more m error. Theu potentral curve for the A state ISIndeed srmilar to the RKR curve obtained by direct invcrsron of spectroscoprc data [9]. (2) Johannsen et al [2] have observed anomdousiy low lifetimes for the u=9,J= 16 and u= 14,5= 16 levels of the A t 2; state of 6 LIP. This allows the MBPT curves to be shifted bodily in order to give neardegeneracies at the correct places. The most plau473
CHEMICAL
Volume 86. number 5.6
PHYSICS
sable assignment of the near-degeneracy responsible for predlssociation of the u = 9,J = 16 level is with the u = 14,J= 16 level of the b state: thus requires the triplet states to be shifted down m energy by ~125 cm-t, which ISwell wlthin the accuracy of the ab initlo curves [3]. With the ab imtio curves modified m this way, Calculatrons of the vibration-rotation levels have been carried out, in order to predict further neardegeneracies. The levels obtained for the A and b states of 61, and 6 Li7 Li are shown m figs 2 and 3 as a function ofJ(J t 1). It may be seen that there are neardegeneracies corresponding to both the observed predissociations in 6L.i2 (to within k 2 III rotational quantum number J’). A further predissociation, for the u = 12,J = 37 level of 6 Li7 Li has also been observed [?I, and ths is also reproduced as shown in fig. 3. This protides support for the vibrational assignment used here, although it must still be regarded as tentative. Figs. 7- and 3 provide predlctions of the positrons of further predrssociahons in 6 Liz and 6 Li7 Li; these depend principally upon the differences III vibratlonal spacings and rotational constants in the two elec-
5 March 1982
LETTCRS so00
7
E ”
2
3000
2lKlo
IWO
0 0
500
low
lsw
2ooo
2sw
JlJ*ll Rg. 3. As for fig. 2, but for isotopic species 6 Li’Li.
tronic states. If further predissociation can be observed, it may be possible to obtain defmitive information on the potenttal curve of the b state.
4. Predkociation
lifetimes
The calculations described in the previous section were concerned only with prelcting which vlbrationrotation levels would be depopulated by predissociation. However, usmg the electronic matrix elements from section 2, it is possible to perform more quantitative calculations of the predissociation hfetimes. The expression for the predissociation lifetime, eq. (I), involves a summation over all bound and continuum levels of the intermediate electronic state @ state), but in practice good accuracy can be obtained by including only the nearest level of the triplet state. The expression for the lifetime then reduces to r,,, = q,,A$/J(J
0 0
500
IO00
1500
2ooo
2500
JlJ*ll rig. 2. Czkulalcd viintlon-rotation level energes for 6Li2. The sohd hnes show the levels of the A I Xi state, and the
dashed bnes those of the b 3t&, state. The solid circles indicate observed predlssochtcd levels, and the shaded area indlrites B region in which obscrvablc prcdissociatlons are unhkely to occur (see text). -414
t 1) ,
where ‘yvJ = (tr/2n)((aEJI~+Ibu’J)(bv’JIH,IAun)-2 and A”J is the difference in energy between the singlet level and the nearest triplet level. The precise lifetime for any particular level is strongly dependent on A,, but the coefficient 9 may be calculated accurately.
CHEMICAL PHYSICS LCTTCRS
Volume 86. number 5,6
Neardegeneraaes with low values of avJ are most likely to be experimentally observable as accidental predissociations. The coefficient depends on two essentially independent quantities: it is proportlonal to the lifetime of the directly predissociating triplet level, and inversely proportional to the square of the bound-bound matrix element (bu’JIH,IAul). The more important of these effects arises from the hfetime of the trIplet levels; the corresponding width is plotted as a function of u’ for J = 10 and J = 30 in fig. 4. This shows the beginnings of the usual oscillatory structure, due to alternate constructive and destructive interference between the vibrational parts of the bound and continuum wavefunctions [IO]. Neardegeneraaes lying close to the shaded bands in figs. 2 and 3 are thus unhkely to rcsuit in observable accIdental predlssoclatlons, as the triplet levels themselves are only weakly predlssociated In ths region. We have calculated CY~for several of the nearde-
5 March 1982
Table 2 Uctimc cocKic~cn~~ for accidcntsl predrssocntion ”
J
v’
tivJ
2.31
\’
I
I
1
I
bLI*
24
20
16
3
9
5
IO
6 7 8 9 II IZ I3 I4 15
II I?
12
034 TRIPLET
068 LEVEL
I 02
I36
I 70
WIDTH /cm-’
Trg. 4. Widths of directly predwocnted levels of the bsfl, state of 6L~z as a function of vibrational quantum number. The lifctlmes (in ps) of the triplet levels are given by 7 = 5.309/r. where the width r LSin cm-‘.
47; (cm
75 68 121 7400 II2 II 5 29000 I08 I5 0 7.5 81
31 81 17 07I2 73 0.1 16 3.5 35 0.7
)
generacies predlcted by fig. 1 for 6Lil, and the results are given in table 2. The ehperimcntal radlatlve lifetimes of the smglet levels are typIcally I9 ns 131, and a level is detectably anomalous if Its lifetlmc IS more than 1 ns below this. The criterion for an expernnentally observable accIdental predissociation is thus that the predissociation lifetlme should be less than ~300 ns. Also given in table 2 IS the largest value of A, which satisfies this criterion. The magnitude of A”:/“‘ is generally a few wavenumbers, except where the nearby triplet level IS Itself relatively stable 3s dlscussed above. The change in A, for successive values ofJ IS given by
PP:
00
13 14 I5 I6 I7 I8 19
%I (~1s (cm-‘)-‘)
--
‘uJ
Y
IS 38 34 78 22 I4 35 30 ‘4 17 3
in 6~1~
- A~J- 1 =
Y(B” - B;) ,
where B, and BL are the rotational constants of the appropriate singlet and triplet levels respecllvcly. IINS quantity is in most cases comparable with A?, so that vibration-rotalion levels with anomalously short lifetimes WIUarise for most of the crossmgs shown in figs. 2 and 3. However, A:,&’ 1snever large enough to encompass more than one rotational quantum number, so that predissociations wtuch are found will be entirely restricted to one vibration-rotation level. Note: After completion of this work, we received details of more extensive experimental measurements
of accidental predissoclatlon m Liz from the Frelburg group [ 111. The new expenmental results appear to be m good agreement with our predlctlons for all three isotopic species. We are very grateful for having been informed of these results in advance of pubhwtion.
v0hmc i-46.numbfr 5.6
CtlCbllChL
PHYSICS LEI-IXRS
References [ 11 7. Uzcr .~nd A. Dallgarno. Chcm. Phys 5 1 (19801271. j $1 Johannscn, pnv~cc communx~lron (1981). ,I D W D~vrts .md G J.R. Jones, Chen. Phys Letters 81 (1991) 279, C J R. Jones. Pit. D. Thcris. Bummgham University (19SO).
1 PS Uagus, m
Proccedmgs of the Scmmdr Sclcctcd Top~csm Slolccular Phyncs(lBX1 Germany, Ludwgsburg, 1969) I] \I L Olson and D.D. ~ono\v3io~~‘,Chem. Phys Lcttcrs 39 (1976) 18 I
476
5 March 1982
16) J A. Hz& 3. Schamps, JM Robbe and H. Lefsbvre-Brian, J. Chem. Phvs 59 (1973) 3271. [71 1. Johans&, Ark,; Fysik IS (1959) 169. [Sl W G Richads. HP. Tnvedi xnd D.L. Cooper,Spmorbit coupling in molecules, internetional senes of mono~phs on chern~~ (C~~~don Press, Oxford, 1981). (91 P. Rusch and h1.M. Hcssel, J.Chcm. Phys. 67 (1977) 586. [ 101 M S. Child, Speciabst Per:odwl Reports, blolecular Spectroscopy. Vol. 2 (Chem. Sot., London, 1974) p. 466. {llj W. Pxeuss. private ~rnmuni~t~on.
CHEMICAL
5 March 1982
PHYSICS LETTERS
ACCIDENTAL PREDISSOCIATION lN LITHIUM DlMER: A THEORETICAL
INVES’llGATlON
Davrd L. COOPER Hanard~Stttttltsotriott Cutter for Astroplt~sics, Catnbrtdge, hlassacltttsetts 02138,
USA
Jeremy M. HUTSON Deparrtttent ofC/tetttistry.
Untrerstty of Waterloo, Warerloo. Otttarto. Canado N-7L XI
and T. UZER * Dcpartmetrr of Tl~eorehcal
Recetved 7 December 198
Cltetmsrry. Oxford Utrtrwsrty, Oxford OXI
3TG. UK
1
The positions of acadcntally predissochted vibration-rotation levels tn Liz are predlctcd, usmg ab tnitto calculations of coupbng matrL\ elements together wtth recent potential energy curves and expertmental results The factorsaffectmg txedlssociation lifetimes are drscussed. and the most likely regions for cvpcrimentally observable predissociatlons are tdenkied.
1. Introduction
In a recent publication analyzmg the photodissociation of Liz, Uze: and DaIgarno [I ] drew attention to accidental predissociation as a possible drssociation mechanism and gave the quantal descnption of the process. The relative conf$uration of the potential energy curves involved is shown schematrcally in fig. 1. The process consists of particular rotation-vrbmtron levels of the A ‘?I: state mixing with levels of the b 3lIe state, which can dissociate into groundstate atoms because of its coupling with the repulsive a 32i state. The singlet levels acquire some triplet character and “borrow” predissociatron intensity from nearby triplet levels. An expression for the lifetime r,,, of a vibronic state predissociating by this mechanism has been given by Uzer and Dalgarno, r”J = WvJ
l0000 ;E Y w
5000
0
-5000
-10000
3
where
-15000 2
3
4
6
5 R/8
* Present address The Chemicd Laboratones. Cahforma institute of Technology, Pasadena, Cahfomia 91125, USA. 472
Fig. 1. Potential energy curves for Liz.
Volume 86. number 5.6
CHE~~ICAL PHYSICS LIYITCRS
kffJIL+J__ +L_J+Ibu’J)(bu’JIH,IAul) E(Aul) - E(bu’J)
2 I (0
and Iti./) is the continuum wavefunction in the a%& state, evaluated at the bound state energy E(Ad).-L+ and .I+ are the raising operators for the orbital and totai angular momenta respectively, and H, is the spmorbit coupling operator. Experimentally, accidental predissociation mamfests itself as a marked decrease in the lifetime of rotation-vibration leveis of the A state which are nearly degenerate with levels of the b state. So far, inaccuracies rn the exrsting potential curves and uncertainties in the coupbngs between them flave prevented any quantitative predmtions of positions and lifetunes of strongly predissociated levels. However such levels have recently been observed in the experiments of Johannsen et al. [2] at Freiburg. We have computed the coupbng matrix elements accurately and have used the potential curves of Davres and Jones [3] to predict positions and hfetimes of leveis that are depleted by accidental predissocration.
2. Electronic matrix elements
Off-dragonal matrix elements of the spur-orbit coupling operatortl, and the raisrng operator for the orbital angular momentum L+ have been calculated at three internuclear distances as shown III table I. Scpa. rate SCF procedures were carried out for the b3Bn and a 3 Cz states using the ALCHEMY programs of Bagus et al. [4]; the A 1r;i state suffered from severe convergence problems and so was constructed from the real and virtual orbitals of the a 32i state. The Slater-type orbital basis set was taken from the work of Olson and Konowalow [5] and off-diagonal matrix elements of
Table I Calcuktted values of the
R (~0)
couphng matrL\ elements
~b3t7,1H,,lA’X*,) (cm-‘)
4.0 5.0 6.0
0.364 0.266 0.186 0.217
1.241 1.268 1.287 1.414
H, and L, were computed using a program due to Hall et al. [6]. In view of the nature of the A 1Xi state used in Uus work, and smce Hartree-Fock wavefunctrons are unlikely to constitute a very good dcscnption of the b 311u and a 3ZL states, the error involved in usrng only tile one-electron part of H* is toierabie. The splitting between the lowest 2P1,2 and ZP,,r energy levels of Li [7] IS0.336 cm-t, so that the spinorblt coupling constant in the “P state is, by hndd’s rule, 0.224 cm-l. The calculated matrix elements for Li, thus seem reasonable but rt must be stressed that they are rather fess accurate than the vahxes obtamcd in calculations on motccules wrth larger spm-orbit coupling effects [S].
3. Nesrdegenencies Accidental predIssociation IS observed expeflrllentally only tf the lifettmc due to tlus mechanism IS shorter than that for radratrvc decay to the X state, tlus occurs only when there ISa near-degeneracy bctween the dissociatmg singlet level and a vrbrahonal level of the b 311u state with the same total angular momentum J. in LIZ, the levels must be degcner.rte to within a few ~vavenumbers for the effect to be obscrvable, as discussed below. The greatest uncertainty in predicting accidental predrssociations lies in the drfficuity of obhmmg accurate potentrai curves. The b 3 llu state of Liz has not been directly observed expenmentnliy, and ab mitio curves arc unlrkeiy to provide an absolute accuracy of 5 1 cm-t in the foreseeable future. However, two recent developments allow thus problem to be partially circumvented* (1) Davies and Jones [3] have performed manybody perturbatron theory (MBPT) calculations on all the relevant electronic states of LIZ; the potentials obtained are hkeiy to have very nearly correct shapes, ai~OU~I the absolute energtes may be more m error. Theu potentral curve for the A state ISIndeed srmilar to the RKR curve obtained by direct invcrsron of spectroscoprc data [9]. (2) Johannsen et al [2] have observed anomdousiy low lifetimes for the u=9,J= 16 and u= 14,5= 16 levels of the A t 2; state of 6 LIP. This allows the MBPT curves to be shifted bodily in order to give neardegeneracies at the correct places. The most plau473
CHEMICAL
Volume 86. number 5.6
PHYSICS
sable assignment of the near-degeneracy responsible for predlssociation of the u = 9,J = 16 level is with the u = 14,J= 16 level of the b state: thus requires the triplet states to be shifted down m energy by ~125 cm-t, which ISwell wlthin the accuracy of the ab initlo curves [3]. With the ab imtio curves modified m this way, Calculatrons of the vibration-rotation levels have been carried out, in order to predict further neardegeneracies. The levels obtained for the A and b states of 61, and 6 Li7 Li are shown m figs 2 and 3 as a function ofJ(J t 1). It may be seen that there are neardegeneracies corresponding to both the observed predissociations in 6L.i2 (to within k 2 III rotational quantum number J’). A further predissociation, for the u = 12,J = 37 level of 6 Li7 Li has also been observed [?I, and ths is also reproduced as shown in fig. 3. This protides support for the vibrational assignment used here, although it must still be regarded as tentative. Figs. 7- and 3 provide predlctions of the positrons of further predrssociahons in 6 Liz and 6 Li7 Li; these depend principally upon the differences III vibratlonal spacings and rotational constants in the two elec-
5 March 1982
LETTCRS so00
7
E ”
2
3000
2lKlo
IWO
0 0
500
low
lsw
2ooo
2sw
JlJ*ll Rg. 3. As for fig. 2, but for isotopic species 6 Li’Li.
tronic states. If further predissociation can be observed, it may be possible to obtain defmitive information on the potenttal curve of the b state.
4. Predkociation
lifetimes
The calculations described in the previous section were concerned only with prelcting which vlbrationrotation levels would be depopulated by predissociation. However, usmg the electronic matrix elements from section 2, it is possible to perform more quantitative calculations of the predissociation hfetimes. The expression for the predissociation lifetime, eq. (I), involves a summation over all bound and continuum levels of the intermediate electronic state @ state), but in practice good accuracy can be obtained by including only the nearest level of the triplet state. The expression for the lifetime then reduces to r,,, = q,,A$/J(J
0 0
500
IO00
1500
2ooo
2500
JlJ*ll rig. 2. Czkulalcd viintlon-rotation level energes for 6Li2. The sohd hnes show the levels of the A I Xi state, and the
dashed bnes those of the b 3t&, state. The solid circles indicate observed predlssochtcd levels, and the shaded area indlrites B region in which obscrvablc prcdissociatlons are unhkely to occur (see text). -414
t 1) ,
where ‘yvJ = (tr/2n)((aEJI~+Ibu’J)(bv’JIH,IAun)-2 and A”J is the difference in energy between the singlet level and the nearest triplet level. The precise lifetime for any particular level is strongly dependent on A,, but the coefficient 9 may be calculated accurately.
CHEMICAL PHYSICS LCTTCRS
Volume 86. number 5,6
Neardegeneraaes with low values of avJ are most likely to be experimentally observable as accidental predissociations. The coefficient depends on two essentially independent quantities: it is proportlonal to the lifetime of the directly predissociating triplet level, and inversely proportional to the square of the bound-bound matrix element (bu’JIH,IAul). The more important of these effects arises from the hfetime of the trIplet levels; the corresponding width is plotted as a function of u’ for J = 10 and J = 30 in fig. 4. This shows the beginnings of the usual oscillatory structure, due to alternate constructive and destructive interference between the vibrational parts of the bound and continuum wavefunctions [IO]. Neardegeneraaes lying close to the shaded bands in figs. 2 and 3 are thus unhkely to rcsuit in observable accIdental predlssoclatlons, as the triplet levels themselves are only weakly predlssociated In ths region. We have calculated CY~for several of the nearde-
5 March 1982
Table 2 Uctimc cocKic~cn~~ for accidcntsl predrssocntion ”
J
v’
tivJ
2.31
\’
I
I
1
I
bLI*
24
20
16
3
9
5
IO
6 7 8 9 II IZ I3 I4 15
II I?
12
034 TRIPLET
068 LEVEL
I 02
I36
I 70
WIDTH /cm-’
Trg. 4. Widths of directly predwocnted levels of the bsfl, state of 6L~z as a function of vibrational quantum number. The lifctlmes (in ps) of the triplet levels are given by 7 = 5.309/r. where the width r LSin cm-‘.
47; (cm
75 68 121 7400 II2 II 5 29000 I08 I5 0 7.5 81
31 81 17 07I2 73 0.1 16 3.5 35 0.7
)
generacies predlcted by fig. 1 for 6Lil, and the results are given in table 2. The ehperimcntal radlatlve lifetimes of the smglet levels are typIcally I9 ns 131, and a level is detectably anomalous if Its lifetlmc IS more than 1 ns below this. The criterion for an expernnentally observable accIdental predissociation is thus that the predissociation lifetlme should be less than ~300 ns. Also given in table 2 IS the largest value of A, which satisfies this criterion. The magnitude of A”:/“‘ is generally a few wavenumbers, except where the nearby triplet level IS Itself relatively stable 3s dlscussed above. The change in A, for successive values ofJ IS given by
PP:
00
13 14 I5 I6 I7 I8 19
%I (~1s (cm-‘)-‘)
--
‘uJ
Y
IS 38 34 78 22 I4 35 30 ‘4 17 3
in 6~1~
- A~J- 1 =
Y(B” - B;) ,
where B, and BL are the rotational constants of the appropriate singlet and triplet levels respecllvcly. IINS quantity is in most cases comparable with A?, so that vibration-rotalion levels with anomalously short lifetimes WIUarise for most of the crossmgs shown in figs. 2 and 3. However, A:,&’ 1snever large enough to encompass more than one rotational quantum number, so that predissociations wtuch are found will be entirely restricted to one vibration-rotation level. Note: After completion of this work, we received details of more extensive experimental measurements
of accidental predissoclatlon m Liz from the Frelburg group [ 111. The new expenmental results appear to be m good agreement with our predlctlons for all three isotopic species. We are very grateful for having been informed of these results in advance of pubhwtion.
v0hmc i-46.numbfr 5.6
CtlCbllChL
PHYSICS LEI-IXRS
References [ 11 7. Uzcr .~nd A. Dallgarno. Chcm. Phys 5 1 (19801271. j $1 Johannscn, pnv~cc communx~lron (1981). ,I D W D~vrts .md G J.R. Jones, Chen. Phys Letters 81 (1991) 279, C J R. Jones. Pit. D. Thcris. Bummgham University (19SO).
1 PS Uagus, m
Proccedmgs of the Scmmdr Sclcctcd Top~csm Slolccular Phyncs(lBX1 Germany, Ludwgsburg, 1969) I] \I L Olson and D.D. ~ono\v3io~~‘,Chem. Phys Lcttcrs 39 (1976) 18 I
476
5 March 1982
16) J A. Hz& 3. Schamps, JM Robbe and H. Lefsbvre-Brian, J. Chem. Phvs 59 (1973) 3271. [71 1. Johans&, Ark,; Fysik IS (1959) 169. [Sl W G Richads. HP. Tnvedi xnd D.L. Cooper,Spmorbit coupling in molecules, internetional senes of mono~phs on chern~~ (C~~~don Press, Oxford, 1981). (91 P. Rusch and h1.M. Hcssel, J.Chcm. Phys. 67 (1977) 586. [ 101 M S. Child, Speciabst Per:odwl Reports, blolecular Spectroscopy. Vol. 2 (Chem. Sot., London, 1974) p. 466. {llj W. Pxeuss. private ~rnmuni~t~on.