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Reorientation of Na2 by He under multiple-collision conditions
Volume 130, number 6
CHEMICAL PHYSICS LETTERS
24 October1986
REORIENTATION OF Na, BY He UNDER MULTIPLE-COLLISION CONDITIONS M. KOLWAS and J. SZONERT Institute of Physics of the Polish Academy of Sciences, Al. Lotnikbw 32/44
02-668 Warsaw, Poland
Received 17 June 1986; in final form 18 August 1986
Collisional depolarisation of molecular fluorescence is studied under multiple-collision conditions. Simple theoretical considerations suggest that the observed effective cross section for reorientation can be lower than in the single-collision limit. As an example we consider Naz(B ‘II,) interacting with He in a heat-pipe.
1. Introduction Transfer of molecular angular momentum is a fundamental effect occurring in the course of atom-diatom or diatom-diatom collisions [ 11. A technique frequently used to study such collisions is laser-induced fluorescence. Intensity and/or polarisation measurements have been carried out for various diatomics such as, e.g., Na2 [l-3], Liz [4], NaK [5,6], I2 [7-g], CO [lo], CdH [ 111, NaH and KH [ 121 interacting with gases like He, Ne, Ar, Xe or Hz. As a result of such studies rate constants (or cross sections) for different transfer processes, scaling laws [6] and propensity rules [2] have been determined. While most of the data come from experiments in the bulk, where thermal and orientational averaging is inevitable, there is a growing number of beam experiments which yield more detailed information on collision dynamics [3]. On the theoretical side, several attempts have been made to clear up experimental observations (see refs. [2,10,13], and references therein). The significant experimental outcome is that in both elastic and inelastic collisions reorientation of the molecular angular momentum is an inefficient process. In this work we studied the depolarisation of molecular fluorescence by perturbing gas of such density that multiple-collision conditions were met, i.e. a molecule underwent several encounters during its excited-state lifetime. The system under study was laser-aligned Na, (B 1Ilu) molecules interacting with He atoms. The aim was to determine the effect of secondary transfer between levels on the resultant reorientation of the molecular angular momenta.
2. Theory We consider a system consisting of diatomic molecules diluted in a bath of inert gas perturbers being selectively excited by resonant laser radiation. By expansion of the rotational density matrix for the ith level in terms of irreducible tensor operators one gets components iPf which are known as kth order multipoles. In practice, if the excitation is weak, the only multipoles created are those with k = 0, 1, 2 which are called population, orientation and alignment, respectively. In the isotropic collisions regime (i.e. an isotropic velocity distribution of perturbers) components of different multipoles remain uncoupled and each multipole relaxes according to its own rate [4,10]. This allows a set of rate equations to be written describing a time evolution of the excited states density matrix components:
498
0 009-2614/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
$k = 4
ir iPi
24 October1 986
CHEMICAL PHYSICS LETTERS
Volume 130,number 6
(k)
- gi
k + Ckk)(i
ipq
j#i
+j)jpt t W$Soi ,
(1)
where 0, i, j numerate different levels in the rotational manifold of the excited state, 0 denotes the level being optically excited; Wt is a source term describing laser excitation of the zeroth level; and ir is the radiative width of the ith level (we neglect predissociation as another possible source of decay). Collisional effects in eq. (1) are divided into two parts: (i) Rate constantsgi (k) for various processes that cause a decrease in ipi* They can be presented as follows: gi’k) = (gi(k) - gi’u)) + gi’u’ , g(O) = CgCO,(jci)tgiQ I j#i
(2)
.
The term in parentheses in eq. (2) describes purely elastic depolarisation inside the ith level (decay of the kth multipole (k # 0) within the ith level); the second term describes population loss from that level. The latter process can occur (eq. (3)) either by transfer to all other rotational levels ($0) (i + i)) or by other ossible mechanisms such as vibrational transfer, quenching or collision induced dissociation (all gathered as gi6 ). (ii) Rate constantsg(kl (i+j) (multipolar rate of transfer between levelsj and i) causing an increase in ip;: due to rotational transfer from other levels, which is non-negligible when multiple-collisions occur. The rate at which molecules undergo collisions of a specific type is given by: gi’k’ = nuo(k’ ,
(4)
where n is the number of perturbers per unit volume, U= (8kBT/trp)l I2 is the mean relative speed and ~i(~l is the cross section (Maxwell-Boltzmann averaged). For simplicity we assume that ir = I’ and gjk’ = gck) for all levels taken into consideration. Of interest is the stationary solution of eq. (1) because the continuous excitation used in the experiment creates a state of equilibrium between different competing mechanisms. We will discuss the two limiting cases of low and high density of perturbers, or in other words single- and multiple-collision conditions. If the density of perturbers is low one can neglect secondary transfer. For the level being optically excited (results for that level only are presented because it is the one observed in our experiment): opi = w@
+ g’k’) .
(5)
If the density of perturbers is high, collisional repopulation can play a significant role. Using a perturbative approach the stationary solution of eq. (1) is found to be: %
P,,L
+j)[rl O’ @‘dk)){l- Xfzt [Z/i+og’k’(O
(6) g(k)G + o)/(r
+g(k))r+l]
1
’
where ir 1 gck) (i + j) is defined by a recurrence relation: [rlg(k>(itj)=
C g(k)(icI)[r-llg(k)(ltj),
[llg(k)(itj)=g(k)(icj).
1Zi
The order of the approximation p is connected with the maximum multiplicity of the collisional processes taken into account. Ifgck) S I’ (collisional relaxation significantly exceeds spontaneous decay) we can approximate the right-hand side of the denominator in eq. (6) by the first two terms of its development in a power series. The result is (we drop the index p for simplicity): up;=
,#,kl(r
f effg’k’) ,
(7)
with
499
CHEMICAL PHYSICS LETTERS
Volume 130, number 6
effWqk = w;/( 1 t dik’) , P-1
dik)=C r=l
effg(k) =g@)(l
z.,ogw(O (rt
1)
I
-
4-j)[dgW(j (gW)r+
24 October1 986
d’2k’)/(lt dik’) , c 0) ,
1
#) 2
J!!l
+-Jg’W
r=l
+i) [rlgvi+(gWy+l
0) .
Both dIk’ and dik) are density independent. Comparison of eqs. (7) and (5) shows that secondary collisional transfer modifies the destruction rate of each multipole. In this case collisions appear less efficient in the destruction of population and higher multipoles than encounters occurring at low density. In the experiment the degree of linear polarisation of the fluorescence was measured as a function of the inert gas pressure. One can deduce some collisional relaxation rates from such a dependence [4]. If I,, (IL) denotes the component of the fluorescence polarised parallel (perpendicular) to the direction of the exciting laser linear polarisation one can write R = (I,, + 21,)/V,, - IL) a P:/P;
.
O-9
For the sake of convenience we define R as the inverse of the conventionally used degree of polarisation. pi (~8) denotes the density matrix component of the fluorescing level. Using eq. (5) (single-collision limit) and eq. (4) gives:
R = R. [1 t ~@cJ(~) - o(O))/(F + n%r(O))] ,
(9)
where R. denotes the polarisation in the absence of collisions. If the rate of collisional decay is small in comparison with the radiative width (~TKJ(~) & I) one gets linear dependence:
R = Ro(1 + nuUdi,/r)
,
(10)
which enables a direct determination of the disalignment cross section odis = uc2) - u(O) (describing purely elastic disalignment) from the data knowing only the radiative width I’. Such a method was employed, e.g., in ref. [ 111. Under multiple-collision conditions one gets similarly to eq. (9):
R = AR o[it
c&~f,l(rt
n~~u(o))]
,
(11)
with ($f = Ro(2) - Co(O) , A=(l+d(l”))/(l+d;2)),
B=(1-d(22))/(l+d12)),
C=(l-d(z”‘)/(l+d~o)).
If C< 1 the situation is similar to that in eq. (10). Because it seems likely that the constants C and B are close to each other, the observed effective cross section a$: can be considerably lower than the cross section for disalignment odis measured under single-collision conditions. In contrast to the latter, the former also encompasses inelastic collisions leading to a partial rebuilding of the alignment in the observed level.
3. Experimental The experimental apparatus is shown in fig. 1. The vertically polarised laser beam from a single-line, multimode argon-ion laser (ILA 120-1, Zeiss) excited Na2 dimers contained in a temperature-controlled crossed heatpipe oven. Fluorescence was collected perpendicular to the laser beam. Its polarisation was analysed by a rotating polariser followed by a 45” oriented linear polariser and focused onto the slit of a double monochromator (GDM 1000, Zeiss). We also used another configuration with interchangeable fxed polarizers and chopping wheel; both methods give consistent results. Signals were detected by means of a PM tube. A two-phase lock-in amplifier (Ithaca model 393) was used for simultaneous recording of two amplitudes proportional to Z,, t ZJ.and I,, - I* respectively. A gas handling system controlled the density of He gas which served as a collision partner for excited sodium dimers. 500
CHEMICAL PHYSICS LETTERS
Volume 130. number 6
24 October1986
Fig, 1. Experimental apparatus: RP, rotating linear polariscr; P, fmed 45” oriented linear polariser; Ll and L2, lenses; DP, DOWprism; PM, photomultiplier; Vl and V2, digital voltmeters.
We varied the pressure of He from ~20 Torr up to a few hundred Torr, measured independently by convection gauge and diaphragm gauge (precision = 5 Torr). Under our experimental conditions, in the observation region of the oven, sodium vapour was mixed uniformly with inert gas. The oven was operated at 430°C measured by a thermocouple fastened on the outer skin of the oven; the sodium vapour pressure at this temperature is 0.75 Torr and the partial pressure of sodium dimers 1.9 X 1O-2 Torr. Laser power was kept at ~5-7 mW which was low
enough to avoid saturation in the absorption of laser light.
4. Results and discussion Three different transitions were studied: one a QtQ$ type (fluorescence from the u’ = 6, J’ = 43 level excited by a 4880 A line) and the other two Pt RJ type (fluorescence from the (6,27) and (10,12) levels, both excited by a 4765 A line). By measuring the dependence of fluorescence polarisation on He pressure one can infer the collisional reorientation of the molecular angular momenta. The results for the (6,43) level are summarized in fig. 2. Only weak depolarisation of the fluorescence is observed with increasing pressure of the perturbing gas. Similar ,+ I,,+21, I,, -I*
Fig. 2. Variation of the linear polarisation of the fluorescence from Naa (B ‘II,) included in the Qt QI type resonance transition against He pressure. Upper level of the transition (u’, J’) =
(6,43). 501
Volume 130, number 6
CHEMICAL PHYSICS LETTERS
24 October 1986
Table 1 Effective cross sections for reorientation (disalignment) of the angular momentum of Naa (B ’ II,) molecules interacting with He atoms Perturbed level v’, J’
o$i (A2)
6,43 6,27 10,12
0.25 f 0.10 0.10 k 0.25 1.4 f 0.5
dependences were obtained for both the other transitions. In each case a straight line fits the data satisfactorily, Estimation of the number of encounters between perturbers and the excited molecule using geometric cross sections gives mO.5 per Torr of He per lifetime (r-l = 7.1 ns). Elastic collisions are likely to occur with much higher frequency [9], so that our pressure range ensures multiple-collision conditions. Using eq. (11) and assuming C Q 1 effective cross sections for disalignment were determined (see table 1). The results do not contradict the suggestion [lo] that the cross section for reorientation increases with decreasing angular momentum of the disturbed level. Table 2 lists other results for comparison. One can see qualitative agreement between the numbers in both tables. It seems important, however, to notice that while the experimental conditions in refs. [ 10,l l] are in the single-collision regime, in the case of refs. [4,5] the high pressure of inert gas used (20- 100 Torr) indicates that the results should in our opinion be interpreted using a multiple-collision approach. Thus the corresponding numbers represent effective cross sections similar to those measured in this experiment. In the above discussion, the influence of collisions with atomic sodium has been neglected. Assuming that the ratio of Na2-He to Na2-Na cross sections is roughly 1 : 10 one gets for 40 Torr of He and 0.75 Torr of Na at 430°C a ratio of respective relaxation rates r = nBa, of about 10 : 1. Thus, such an approach seems reasonable under our conditions. Finally, we draw the following conclusions: (i) The results of the polarisation experiment show that collisional reorientation of the angular momentum of Na2 (B 1Il,) is weak even for a high density of He. This is in qualitative agreement with earlier observations for other systems [4,5,10,11]. (ii) Theoretical considerations suggest that under multiple-collision conditions both elastic and inelastic en-
Table 2 Cross sections for reorientation
by perturbers of the molecular angular momentum
Molecule and level studied
Collision partner
Jl)_o(O)
(A2)
(A2) 0.35 f 0.15 0.65 f 0.3
I41
0.1 f 0.2
151
S=lO
NaK (C ’ H)
J’= 30
He
CdH (A 2n,,2)
J’ = 3.5
He Ar He Ar He AI
0*2 Ii3 li.2 13* 4 1*2 32i5
ill1
H2
<0.05 o(O)
[lOI
J’= 16.5 co(x’I:+)
J’ = 7
He AI
Ref.
Liz (A ‘Xi)
J’ = 7.5
502
o(a)_o(o)
Volume 130, number 6
CHEMICAL PHYSICS LETTERS
24 October1 986
counters (the latter due to repopulation) contribute to the effective reorientation of the angular momentum. (iii) The cross section for purely elastic decay of alignment as measured under single-collision conditions can be higher than its effective counterpart measured in the multiple-collision regime (eq. (11)). Thus table 1 gives lower limits to the cross sections for reorientation of the respective levels.
Acknowledgement This work was supported by research project CPBP 01.06.
References [l] [2] [3] [4]
[5] [6] [7] [ 81 [9] [lo] [ll] [121 [13]
T.A. Brunner, R.D. Driver, N. Smith and D.E. Pritchard, Phys. Rev. Letters 41 (1978) 856. T.A. Brunner, R.D. Driver, N. Smith and D.E. Pritchard, J. Chem. Phys. 70 (1979) 4155. A. Mattheus, A. Fischer, G. Ziegler, E. Gottwald and K. Bergmann, Phys. Rev. Letters 56 (1986) 712. M.D. Rowe and A.J. McCaffery, Chem. Phys. 43 (1979) 35. J. McCormack, A.J. McCaffery and M.D. Rowe, Chem. Phys. 48 (1980) 121. J. McCormack and A.J. McCaffery, Chem. Phys. 51 (1980) 405. S. Dexheimer, M. Durand, T. Brunner and D. Pritchard, J. Chem. Phys. 76 (1982) 4996. J. Derouard, These, Universite de Grenoble, Grenoble (1983). R. Clark and A.J. McCaffery, Mol. Phys. 35 (1978) 617. Ph. Bre’chignac, A. Picard-BerseIIini, R. Charneau and J.M. Launay, Chem. Phys. 53 (1980) 165. J. Dufayard and 0. Nddelec, Chem. Phys. 71 (1982) 279. M. Giroud and 0. N&lec, Chem. Phys. 93 (1985) 127. J. Derouard, Chem. Phys. 84 (1984) 181.
503
CHEMICAL PHYSICS LETTERS
24 October1986
REORIENTATION OF Na, BY He UNDER MULTIPLE-COLLISION CONDITIONS M. KOLWAS and J. SZONERT Institute of Physics of the Polish Academy of Sciences, Al. Lotnikbw 32/44
02-668 Warsaw, Poland
Received 17 June 1986; in final form 18 August 1986
Collisional depolarisation of molecular fluorescence is studied under multiple-collision conditions. Simple theoretical considerations suggest that the observed effective cross section for reorientation can be lower than in the single-collision limit. As an example we consider Naz(B ‘II,) interacting with He in a heat-pipe.
1. Introduction Transfer of molecular angular momentum is a fundamental effect occurring in the course of atom-diatom or diatom-diatom collisions [ 11. A technique frequently used to study such collisions is laser-induced fluorescence. Intensity and/or polarisation measurements have been carried out for various diatomics such as, e.g., Na2 [l-3], Liz [4], NaK [5,6], I2 [7-g], CO [lo], CdH [ 111, NaH and KH [ 121 interacting with gases like He, Ne, Ar, Xe or Hz. As a result of such studies rate constants (or cross sections) for different transfer processes, scaling laws [6] and propensity rules [2] have been determined. While most of the data come from experiments in the bulk, where thermal and orientational averaging is inevitable, there is a growing number of beam experiments which yield more detailed information on collision dynamics [3]. On the theoretical side, several attempts have been made to clear up experimental observations (see refs. [2,10,13], and references therein). The significant experimental outcome is that in both elastic and inelastic collisions reorientation of the molecular angular momentum is an inefficient process. In this work we studied the depolarisation of molecular fluorescence by perturbing gas of such density that multiple-collision conditions were met, i.e. a molecule underwent several encounters during its excited-state lifetime. The system under study was laser-aligned Na, (B 1Ilu) molecules interacting with He atoms. The aim was to determine the effect of secondary transfer between levels on the resultant reorientation of the molecular angular momenta.
2. Theory We consider a system consisting of diatomic molecules diluted in a bath of inert gas perturbers being selectively excited by resonant laser radiation. By expansion of the rotational density matrix for the ith level in terms of irreducible tensor operators one gets components iPf which are known as kth order multipoles. In practice, if the excitation is weak, the only multipoles created are those with k = 0, 1, 2 which are called population, orientation and alignment, respectively. In the isotropic collisions regime (i.e. an isotropic velocity distribution of perturbers) components of different multipoles remain uncoupled and each multipole relaxes according to its own rate [4,10]. This allows a set of rate equations to be written describing a time evolution of the excited states density matrix components:
498
0 009-2614/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
$k = 4
ir iPi
24 October1 986
CHEMICAL PHYSICS LETTERS
Volume 130,number 6
(k)
- gi
k + Ckk)(i
ipq
j#i
+j)jpt t W$Soi ,
(1)
where 0, i, j numerate different levels in the rotational manifold of the excited state, 0 denotes the level being optically excited; Wt is a source term describing laser excitation of the zeroth level; and ir is the radiative width of the ith level (we neglect predissociation as another possible source of decay). Collisional effects in eq. (1) are divided into two parts: (i) Rate constantsgi (k) for various processes that cause a decrease in ipi* They can be presented as follows: gi’k) = (gi(k) - gi’u)) + gi’u’ , g(O) = CgCO,(jci)tgiQ I j#i
(2)
.
The term in parentheses in eq. (2) describes purely elastic depolarisation inside the ith level (decay of the kth multipole (k # 0) within the ith level); the second term describes population loss from that level. The latter process can occur (eq. (3)) either by transfer to all other rotational levels ($0) (i + i)) or by other ossible mechanisms such as vibrational transfer, quenching or collision induced dissociation (all gathered as gi6 ). (ii) Rate constantsg(kl (i+j) (multipolar rate of transfer between levelsj and i) causing an increase in ip;: due to rotational transfer from other levels, which is non-negligible when multiple-collisions occur. The rate at which molecules undergo collisions of a specific type is given by: gi’k’ = nuo(k’ ,
(4)
where n is the number of perturbers per unit volume, U= (8kBT/trp)l I2 is the mean relative speed and ~i(~l is the cross section (Maxwell-Boltzmann averaged). For simplicity we assume that ir = I’ and gjk’ = gck) for all levels taken into consideration. Of interest is the stationary solution of eq. (1) because the continuous excitation used in the experiment creates a state of equilibrium between different competing mechanisms. We will discuss the two limiting cases of low and high density of perturbers, or in other words single- and multiple-collision conditions. If the density of perturbers is low one can neglect secondary transfer. For the level being optically excited (results for that level only are presented because it is the one observed in our experiment): opi = w@
+ g’k’) .
(5)
If the density of perturbers is high, collisional repopulation can play a significant role. Using a perturbative approach the stationary solution of eq. (1) is found to be: %
P,,L
+j)[rl O’ @‘dk)){l- Xfzt [Z/i+og’k’(O
(6) g(k)G + o)/(r
+g(k))r+l]
1
’
where ir 1 gck) (i + j) is defined by a recurrence relation: [rlg(k>(itj)=
C g(k)(icI)[r-llg(k)(ltj),
[llg(k)(itj)=g(k)(icj).
1Zi
The order of the approximation p is connected with the maximum multiplicity of the collisional processes taken into account. Ifgck) S I’ (collisional relaxation significantly exceeds spontaneous decay) we can approximate the right-hand side of the denominator in eq. (6) by the first two terms of its development in a power series. The result is (we drop the index p for simplicity): up;=
,#,kl(r
f effg’k’) ,
(7)
with
499
CHEMICAL PHYSICS LETTERS
Volume 130, number 6
effWqk = w;/( 1 t dik’) , P-1
dik)=C r=l
effg(k) =g@)(l
z.,ogw(O (rt
1)
I
-
4-j)[dgW(j (gW)r+
24 October1 986
d’2k’)/(lt dik’) , c 0) ,
1
#) 2
J!!l
+-Jg’W
r=l
+i) [rlgvi+(gWy+l
0) .
Both dIk’ and dik) are density independent. Comparison of eqs. (7) and (5) shows that secondary collisional transfer modifies the destruction rate of each multipole. In this case collisions appear less efficient in the destruction of population and higher multipoles than encounters occurring at low density. In the experiment the degree of linear polarisation of the fluorescence was measured as a function of the inert gas pressure. One can deduce some collisional relaxation rates from such a dependence [4]. If I,, (IL) denotes the component of the fluorescence polarised parallel (perpendicular) to the direction of the exciting laser linear polarisation one can write R = (I,, + 21,)/V,, - IL) a P:/P;
.
O-9
For the sake of convenience we define R as the inverse of the conventionally used degree of polarisation. pi (~8) denotes the density matrix component of the fluorescing level. Using eq. (5) (single-collision limit) and eq. (4) gives:
R = R. [1 t ~@cJ(~) - o(O))/(F + n%r(O))] ,
(9)
where R. denotes the polarisation in the absence of collisions. If the rate of collisional decay is small in comparison with the radiative width (~TKJ(~) & I) one gets linear dependence:
R = Ro(1 + nuUdi,/r)
,
(10)
which enables a direct determination of the disalignment cross section odis = uc2) - u(O) (describing purely elastic disalignment) from the data knowing only the radiative width I’. Such a method was employed, e.g., in ref. [ 111. Under multiple-collision conditions one gets similarly to eq. (9):
R = AR o[it
c&~f,l(rt
n~~u(o))]
,
(11)
with ($f = Ro(2) - Co(O) , A=(l+d(l”))/(l+d;2)),
B=(1-d(22))/(l+d12)),
C=(l-d(z”‘)/(l+d~o)).
If C< 1 the situation is similar to that in eq. (10). Because it seems likely that the constants C and B are close to each other, the observed effective cross section a$: can be considerably lower than the cross section for disalignment odis measured under single-collision conditions. In contrast to the latter, the former also encompasses inelastic collisions leading to a partial rebuilding of the alignment in the observed level.
3. Experimental The experimental apparatus is shown in fig. 1. The vertically polarised laser beam from a single-line, multimode argon-ion laser (ILA 120-1, Zeiss) excited Na2 dimers contained in a temperature-controlled crossed heatpipe oven. Fluorescence was collected perpendicular to the laser beam. Its polarisation was analysed by a rotating polariser followed by a 45” oriented linear polariser and focused onto the slit of a double monochromator (GDM 1000, Zeiss). We also used another configuration with interchangeable fxed polarizers and chopping wheel; both methods give consistent results. Signals were detected by means of a PM tube. A two-phase lock-in amplifier (Ithaca model 393) was used for simultaneous recording of two amplitudes proportional to Z,, t ZJ.and I,, - I* respectively. A gas handling system controlled the density of He gas which served as a collision partner for excited sodium dimers. 500
CHEMICAL PHYSICS LETTERS
Volume 130. number 6
24 October1986
Fig, 1. Experimental apparatus: RP, rotating linear polariscr; P, fmed 45” oriented linear polariser; Ll and L2, lenses; DP, DOWprism; PM, photomultiplier; Vl and V2, digital voltmeters.
We varied the pressure of He from ~20 Torr up to a few hundred Torr, measured independently by convection gauge and diaphragm gauge (precision = 5 Torr). Under our experimental conditions, in the observation region of the oven, sodium vapour was mixed uniformly with inert gas. The oven was operated at 430°C measured by a thermocouple fastened on the outer skin of the oven; the sodium vapour pressure at this temperature is 0.75 Torr and the partial pressure of sodium dimers 1.9 X 1O-2 Torr. Laser power was kept at ~5-7 mW which was low
enough to avoid saturation in the absorption of laser light.
4. Results and discussion Three different transitions were studied: one a QtQ$ type (fluorescence from the u’ = 6, J’ = 43 level excited by a 4880 A line) and the other two Pt RJ type (fluorescence from the (6,27) and (10,12) levels, both excited by a 4765 A line). By measuring the dependence of fluorescence polarisation on He pressure one can infer the collisional reorientation of the molecular angular momenta. The results for the (6,43) level are summarized in fig. 2. Only weak depolarisation of the fluorescence is observed with increasing pressure of the perturbing gas. Similar ,+ I,,+21, I,, -I*
Fig. 2. Variation of the linear polarisation of the fluorescence from Naa (B ‘II,) included in the Qt QI type resonance transition against He pressure. Upper level of the transition (u’, J’) =
(6,43). 501
Volume 130, number 6
CHEMICAL PHYSICS LETTERS
24 October 1986
Table 1 Effective cross sections for reorientation (disalignment) of the angular momentum of Naa (B ’ II,) molecules interacting with He atoms Perturbed level v’, J’
o$i (A2)
6,43 6,27 10,12
0.25 f 0.10 0.10 k 0.25 1.4 f 0.5
dependences were obtained for both the other transitions. In each case a straight line fits the data satisfactorily, Estimation of the number of encounters between perturbers and the excited molecule using geometric cross sections gives mO.5 per Torr of He per lifetime (r-l = 7.1 ns). Elastic collisions are likely to occur with much higher frequency [9], so that our pressure range ensures multiple-collision conditions. Using eq. (11) and assuming C Q 1 effective cross sections for disalignment were determined (see table 1). The results do not contradict the suggestion [lo] that the cross section for reorientation increases with decreasing angular momentum of the disturbed level. Table 2 lists other results for comparison. One can see qualitative agreement between the numbers in both tables. It seems important, however, to notice that while the experimental conditions in refs. [ 10,l l] are in the single-collision regime, in the case of refs. [4,5] the high pressure of inert gas used (20- 100 Torr) indicates that the results should in our opinion be interpreted using a multiple-collision approach. Thus the corresponding numbers represent effective cross sections similar to those measured in this experiment. In the above discussion, the influence of collisions with atomic sodium has been neglected. Assuming that the ratio of Na2-He to Na2-Na cross sections is roughly 1 : 10 one gets for 40 Torr of He and 0.75 Torr of Na at 430°C a ratio of respective relaxation rates r = nBa, of about 10 : 1. Thus, such an approach seems reasonable under our conditions. Finally, we draw the following conclusions: (i) The results of the polarisation experiment show that collisional reorientation of the angular momentum of Na2 (B 1Il,) is weak even for a high density of He. This is in qualitative agreement with earlier observations for other systems [4,5,10,11]. (ii) Theoretical considerations suggest that under multiple-collision conditions both elastic and inelastic en-
Table 2 Cross sections for reorientation
by perturbers of the molecular angular momentum
Molecule and level studied
Collision partner
Jl)_o(O)
(A2)
(A2) 0.35 f 0.15 0.65 f 0.3
I41
0.1 f 0.2
151
S=lO
NaK (C ’ H)
J’= 30
He
CdH (A 2n,,2)
J’ = 3.5
He Ar He Ar He AI
0*2 Ii3 li.2 13* 4 1*2 32i5
ill1
H2
<0.05 o(O)
[lOI
J’= 16.5 co(x’I:+)
J’ = 7
He AI
Ref.
Liz (A ‘Xi)
J’ = 7.5
502
o(a)_o(o)
Volume 130, number 6
CHEMICAL PHYSICS LETTERS
24 October1 986
counters (the latter due to repopulation) contribute to the effective reorientation of the angular momentum. (iii) The cross section for purely elastic decay of alignment as measured under single-collision conditions can be higher than its effective counterpart measured in the multiple-collision regime (eq. (11)). Thus table 1 gives lower limits to the cross sections for reorientation of the respective levels.
Acknowledgement This work was supported by research project CPBP 01.06.
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