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Collision transfers between CdH A 2Πυ′ = 0 rotational states induced by He or Ar
Chemical Physics 71(1982) 279-288 North-Holland Publish& Company
COLLlSlON
TRANSFERS
BETWEEN CdK A 2 %Bu’ = 0 ROTATIONAL
STATES
lNDUCED BY He OR AI ’
J. DUFAYARD and 0. NEDELEC Loboratoire de SpectromPtrie Physique, BP 53X. 38041 Grenoble Cedex, France Received 13 April 1982
CdH is obtained by radiofrequency discharge in Cd vapor mixed with 5% Ha in He or Ar. It is selectively excited by a pulsed dye laser to A 2~1,2,s,2 u’ = 0, J’ = 0.5-i&5. Collision cross sections are measured from several J’ values corresponding to rotational transfers observed up to AJ’ = +7. The total collision cross sections are smaller with He than with Ar.
They decrease as J’ increases. The levels of the same electronic parity as the initial level are strongly privileged for high J’ with He, much less with AL The polarization of the initiai lines decreases appreciably for high J’ with the Ar pressure, much less with the He pressure. Small spin transfers are observed from 113,2 to ft1,2 . The experimental results, especially the propensities, are justified using the Born approximation the effects of He and Ar.
as deveioped
1. Introduction We have recently published experimental results about rotational transfers in BK induced by collisions with He, Ar or H2 [l] . In this paper we describe similar experiments in CdH A211,,2,3,7 U’ = 0. This hydride may be easiiy obtained in a low pressure, low power discharge. I& A 2111,2,3,2 u’ = 0 states may be excited at 24500 and 4300 A respectively. We have made lifetime measurements [2] and electric resonance experiments [3] by selective pulsed dye laser excitation. The synthesis reaction Cd*(3P0 l 2) f H2 + CdH + H has been studied recently ‘[4] _ The CdH A21&X 22 transition has been studied by conventional spectroscopy 151, but the interaction potential with rare gas atoms is not known. Even the poIarisability, the electric dipole and quadrupole moments which may be used to calculate the long-range fcrces are not known. However, the experiments reported in this paper allow us to discuss a few aspects of the collision process. The most interesting observations are: a propensity preserving the electronic parity with He but not with Ar, and the depolarization of ’ This work has been supported
0301-0104/82/0000-00i0/$02.75
by the DPa.
Q 1982 North-Holland
in previous papers. Its validity is discussed in comparing
the parent lines with Ar but not with He. We explain these observations qualitatively using the Born approximation. As the transition probability Pi-f is proportional to the matrix element squared, 1(iI Vi 012, the symmetry properties may be studied simply. The vahdity of this approximation is discussed and the results
obtained
with
He and with
Ar are compared.
2. Experiments 2.1.
&lQ?QiUS
The hydride is obtained by radiofrequency 100 M&, 1 W discharge in Cd and H,. The cell is cylindrical with a side arm containing Cd (fig. 1). It is placed in an oven heated at 250°C by thermocoax providing a Cd pressure smaller than low2 Torr. The relative flow of H, and rare gas is such that the partial pressure of H2 is ~5% of the-total pressure. The pressure is measured with a GranviIle Phillips capacitance manometer calibrated against a McLeod gauge. The estimated uncertainty on the pressure measurements is +lO%. The Cd deposits in the tube out of the oven. With a piece of 1 cm3 Cd, the cell may be operated for about 100 h and then has to be refilled.
280
J.
Dufayani,0. Nedelec / 7hmsfers
in
CdH
al-d Pi_oz on the observed light. The instrumental polarization of the detection system is calibrated in the sane way at each experiment by observing the discharge lines which are not polarized [6] without any change in the optical system. We use Polaroid HN 38 or HNP’N polarizers which have a good efficiency at 4500 A. 2.3. Observed lines
Fig. 1. Esperimcnt, with polarizations for excitation and obseivation.
A Lambda Physik EMG 102 multi-gas laser filled with Nz is used at up to 50 Hz to pump a dye laser with one amplifier cell. The dye provides less than 0.1 _S,hnewidth which is necessary to excite selectively most of the CdH lines, with a beam expander X 35 and a 600 groves/mm ruled grating used in the sixth order. TNs linewidth is much greater ihan the CdH Doppler xtidth which is 0.00s _&at 600 K. The employed dyes are 7-diethylamino4-methylcoumarin at =4500 a to excire A 21T1,2 and dimerhyl popop at ~4300 A to excite A 2RS,2. The observation is made through a THR JobinYvon monochromator providing 2.6 A/mm dispersion and a 3 ns time-spread EMI photomultiplier. The line intensities are integrated with a Brookded boxcar using a gate of 500 ns, much larger than the 80 ns lifetime. The lifetime measurements are made with a PAR 162/I 63 boxcar which samples the fluorescent light with 1 ns gate duration. Several 100 s runs are superposed to be sure of the absence of slow drifts.
The polarization of the laser beam in the cell is parallel to OZ (Gg. I). To measure the populations of the levels independently of the polarization [I] of the observed lines a polarizer at 54’ to 02 is placed on the observed light. The polarization of the lines may be measured by permuting two linear polarizers P,, uz
The lT3j.2 level is 1012 cm-l above the III/2 level. bands are The _421T,,,- X2C and A2R,,&X2x well separated. To each rotational level J’ correspond two A-doubled levels of opposite electronic parity and total (electronic X rotational) pzrity. Each Adoubled level is connected by three lines to the spin doubled ground state. The relative intensities of these lines are caictdable from simple general expressions [7] for 211-22 transitions developed for intermediate coupling between Hund’s case (a) and case (b), knowing the fiie structure constant, A = 1012.77 cm-l, and the rotational constant, I? = 6.00 cm-l, of CdH A 2 II U’ = 0. To measure the relative populations of the levels it is sufficient to select only one lime issued from each Ievel. Fig. 2 shows the relative line intensities issued from each A 2FIy3 3I., J’ levels where the sum of the three lines is norr;;$i;ed
to I_
Fk. 2. The relative lines intensities from each J’ level of %I+ (0,O). strong lines: ebctronic parity + (or e A%l,,-X levels); weak lies: electronic parity - (or f levels)_
J. Dufaymd, 0. Ned&c / Transfers in C&4
2.4. Temperame The plates providing the electric discharge are in the cell. The discharge heats the gas. The temperature is obtained from the A 2II1j2 u’ = 0 + X 2Z+ u” = 0 line intensities in the discharge. The electronic excitation provides essentially dipole transitions, i.e. J’ - J” = 0, il. If J’ S 1, and if there is no rotational perturbations, the distributions of the popurations in the excited state and in the ground state are very similar. if the pressure is low enough so that there is no redistribution of the populations in the excited state, a spectrum allows its to obtain the rotational temperature in the ground state (fig. 3). The first (0.5 < J’ < 8) and the last (14 < J’ < 18) lines are provided by the Pl, band, the intermediate lines by the R1 band, and are selectively observed with 0.2 A resolution. The obtained popuIations may be well fitted with a Boltzmann law: the rotational temperature is homogeneous in the cell over at least 3 kT (fig. 3) within 5% error. This result is due to the fact that the increase of the temperature due to the discharge (
parallel and the discharge looks homogeneous
281
(520 K). It was not the case for RH where the temperature at the center of the discharge reached 900 K to be compared to room temperature, 300 K. This temperature homogeneity in the case of CdH will enable us to make a valuable discussion of the relative satellite line intensities. This geometry of the discharge has provided temperature and cross section values independent of the pressure varying from 0.3 to 2.0 Torr. The electrons of the discharge have no effect on the CdH A211,,2,3,2 level: the measured lifetimes are the same when the discharge is on or turned off 200 ps before the laser pulse, or when the discharge power is varied over a factor 4.
3. Results 3.1. Total transfer co!lision cross sections The total transfer collision cross sections are provided by the lifetime reduction with pressure measured by selective excitation and observation of a line. Vibrational transfers from v’ = 0 to u’ = 1 are unliiely to occur as the energy defect is great (1600 cm-l) compared to kT (500 cm-l). Downwards ll,jz + 11112 spin transfers have been observed but not uppenvards n,/z
I 0
B.J’U+l)
lopa 9.5
145
cm4
185 J
pi. 3. the variation of ln[N~/(2J+ I)] with J(J+ 1) fitted with a Boltzmann law, T= @“hc/k)J((J+ l)/{ln[N~/W+ l)] - III(NJ=~)}. B” = 5.32 cm-’ for X ?, u” = 0.
+ 4/z. From IIll2 the total collision cross section is due only to rotational transfers. For 113,2 it also inchrdes spin transfers which are’one order of magnitude smaller than the rotational transfers, as observed on a spectrum. In a first experiment we have measured the lifetimes for several pressures, to be sure that the variation of l/r withP is linear (fig. 4). We have also measured the radiative lifetimes of A 211112 and A 2113,z very precisely at very low H2 pressures(lO-’ Torr) and with a wideband (24 A) observation. The radiative lifetimes do not depend on J’ up to J’ = 16.5; for the A211,,, state 7 = 83 + 2 ns and for A2113j2 T = 67 + 2 ns. The lifetimes for several J’ values of A211,,2 and A2ll,,, with He or P.r have been measured consecutively at a given pressure and a temperature determination has been made associated.with each series of measurements. The obtained cross sections are given in fig. 5. As in all oar papers, the cross section o is defined by the following expression, where r is the deexcitation frequency (s-l):
.
J. Dufoyard.0. Nedeiec / Tkansfenin C&Y
282
Ar
140 0
1
Fig. 4. Variation of the miththe AI pressure.
likiti~
Pressure iT2rrI
of A 7113,2 u’ = 0, J’ = 3.5
The sum of the intensities of the satehhe lines compared to the intensities of the parent lines allows us to verify that the total cross sections obtained from lifetime measurements are actually due to rotational transfers. As mentioned in a previous paper [I], the A-doubled J’+ levels give the same cr values, indicated by only one point in fig. 5. The observed decrease of ETwhen J’ increases is due to the increase of the energy difference between the rotational levels, as it is not small compared to kT. For collisions of A’IIr,z with
He, u show an unexpected feature as they remain constant for J’ > 3.5. Except for this anomaly, the cross sections are greater with Ar than with He and are similar for the Ii,/, and I13j2 levels. The long-range forces in the reference frame of the molecule depend on electronic parameters which do not depend explicitly on the electron spin, and are expected to be the same for II,,, and II,,,. The short-range forces, more important for small cross sectiors, may depend on the spin. On the other hand, the A% levels are affected by X32? and B2C*-for A211 rj2 by strong homogeneous perturbations and’for A 21T~,2 by light heterogeneous perturbations [8], which determine the proportions of the s and p orbitals of the excited electron. These perturbations provide differences between the radiative lifetimes of the two levels and very likely between their collision effects. 3.2. Propensities in rototiorzal transfers A selective excitation of several leve!s may be obtamed as the laser hnewidth is smaller than 0.1 Ii. A selective observation of at least one line issued from each level is difficult to be made as the monochromator resolution must be greater than 0.5 A in most cases otherwise there is not enough light limited by the quantity of hydride synthesized in the discharge. In a few cases a resolution up to 0.15 A has been used. The relative populations of the rotational 1eveIs Jf excited
\
Ar 650KI
40.
0
5
10
15
J
Fig. 5. Total transfer cross sections for co&ion with He (+) or with Ar (o), from A *n,,, U’= 0, J’ = 0.5-, l-5-, 3.5-, 7.5-and 16.5= ,and from A2n3,2, u’= 0, J’ = IS-, 3.5+,6.5- and 15.5c.The signsreferto the totdptities.
283
J. Dufoymd, 0. Nedelec / ?Fansfers in CdH
3 b ext. S,
a
0.5” fArI.
3
ext. S=3.S-R-iel
t
exe. 3 = 3..S(Arl
I
)
exe J-=X5-
-
j/L!/
h-1
eIi 1
o 5
exc.J‘=
exe: J”= 2S
I
(He1
I
7I.S Itie
j
i
65
Fig, 6
fo be contimced
on
nexr page
J. Dufiyard.
0. Nedelec j Transfets
ext. J’=16S*CHel
:I
i&5
J
ext. J=16.5c IArl
in CdH
With Ar it is weak and seems to disappear at J: = 16.5. Such a propensity has already been noticed in YO A ?Il with Ar, for J; > 20, T = 1800 K, the lines with electronic parity change being completely missing [9]. (2) A small propensity preserves the total parity -within sets of satellite levels without electronic parity change. It appears only for Ji = 0.5 in He_ This alternation is much less evident than in the case of BH J~=4w+thHe [l]. (3) These propensities do not depend on the parity of the initial level. in previous experiments on llI levels of alkaline dimers [lo] or of BH [I], upwards or downwards propensities had been observed for transfers with electronic parity change. Such propensities which depend on the parity of J; have not been observed in the present experiment_ 3.3. Disaii~ment
Fig. 6. Relative populntions of the levels populated by collision transfers with He or with Ar after selective Iz~er excita:ion of CdH, Asnl,~, U*= 0, J’ = OS-, 3.5-, 7.5, ?.5i and 16..5+. Strong lines: electronic parity +, weak lines: electronic parity -. Pressure: 1 Tom Temperatures: 590 i 50 K for He, 660 + 50 K for AI. Typical relative errors on the partial cross sections: 50.2 A?.
The polarizations of the lines may be calculated from formulas (2) and (3) of ref. [l] _The nuclear spin is I = 0 for 50% of the isotopes in natural Cd and I = l/2 for the other isotopes_ The H nuclear spin is also l/2. If the hyperfme structure is much greater than the natural width, the nuclear spins reduce the polarization for the smallest values of the total angular momentum J’ (table 1). The experimental results are shown in tables 1 and 2 and fig. 7. The relaxation of the total angular momentum of an atomic or molecular state, or of the emitted light, depends on the symmetry considered [ 111: for the population, r,
by transfers from Azllli2 v’ = 0, Ji =0.5,3.5,7.5 and 16.5, are given in fig. 6 by interaction with He and Ar, respectively_ The chosen pressure is small enough, as shown in fig. 4 to have single collision conditions. Very similar resulis have been obtained from any two A-doubled J’ levels. On the other hand, A 2Hj,2, II’ = 0 J’ levels give the same relative transfer populations as the same J’ levels of A 2K1112,v’ = 0. The comments that can be made about the results of fig. 6 are as follows: (1) A propensity preserves the electronic parity. With He it is strong and increases when J{ increases.
f;, C 21,:
=r radiation •t rtransfer 9
Table 1 P = (111- I~)/(111 +&I of CdH, A ‘fIra, u’ = 0. lines: J’ = 3.5 +QtPI,J’=7.StQtPr,J’=16.5-QtR&.calculatedwith I = il.112 or 1, and &pe&ental extrap&ated to zero pressure. Typical absolute uncertainty on experimentali’: +-0.02
calculated
2=0 I= l/2 I=1
experimental
I’ = 3.5
J’ = 7.5
J’ = 16.5
0.214 0.193 0.186
0.269 0.261 0.253
0.367 0.365 0.361
0.17
0.24
0.34
Table 2 Disalignment cross section ‘12(A’)
rrad
-=tF
fpzO
A2ixln. J’
3.s
7.5+
He, 620 K. Ar, 680 K
Or2
I*2
16..51+2
7+3
13 24
32 f S
&d
+rtr
+ qr + hs
(2)
,
where r;, = uoNW, r,, = u2N!u). The depolarization cross section u2 relative to rdiS has been calculated (table 2) from the depolarization with pressure (fig. 7), knowing the transfer cross sections u. (fig. 5) and the radiative lifetirires.
4. Discussion
L
L
J’.?5
L
;
t
7
1’
0.1 HELIUM I
a ar
OS
1
1.5
2
P IToorcJ
Most of the comments that we make about the experimental results deal with the parity [S] of the levels_ The parity of a molecular level depends on the orbital L and rotational X angular momenta. In the G or b coupling caSes L and R are not good quantum numbers. The eigenfunctions of the molecular II state in the reference frame of the molecule have to be written as linear combinations of the eigenfunctions of angular momentum J and projections A = +I on the molecular axiS
The electronic parity depends on the relative phase of ]+iX:=,l), it is even or odd according to e = i-1 or E = -1. These levels are called [ 121 e or f levels respectively. The total parity alternates with the total angular momentumJ. The A-doubled levels have opposite electronic and total parities. 4.1. Collisions in the Born approximation
I 001
c5
,
I5
2
> PtBrd
Fig. 7.
Depolarizationby colkions with He or AI of CdH A2n,,~d=Olines:J’=3.5tQPP~,J’=7.5+QtP~,J’ = 16.5 - QtPI.
for the alignment, I,, - I,: r2 = rndiation ’ rtransfer f rdtignment . As each term is in inverse ratio to the corresponding relaxation, the expression (I,, - I,)/@,,, + 21,) = tp decreases with the pressure if rdis is not small compared t0 rrad +rtr:
[I33I.51
The time dependent perturbation theory is used in first order and the collisions are supposed to be sudden. The interaction potential is expanded in spherical harmonics in the reference frame of the molecule:
Y,“(O,#J)are sphedca! harmonics, where B, Q are the orientation of the atom with respect to the molecule. V[ = V$ in a linear molecule. In homonuclear molecules k can also be odd. The transition probability amplitude uj_f is such as:
J. Dufuyard,0. Medelec/ lhmsfers in CdH
286
(3 The Ai contain the radial terms, summed over the
moiecule-atom relative distances and speeds, and the normalization terms for the matrix element of an operator k, 4. Odd (even) values of X-change (do not change) the total parity. In a II level 4 = O,i3. The 4 = f2 (4 = 0) change (do not change) the sign of A. in the 3J symbols (2, 2Z $, when the signs of aLl the m are changed, the 3J symbol is multipiied by (-)zJ. The electronic parity is changed if Ji + k + J, is odd. The transition probabilities are given by the formula which is similar to those which have been written previously [14] fork = 2: ‘Ji,i-jf,c=
(2Jf + 1)
The values of k and k’ associated with a given transition must have the same parity. 9 = 0 and 4 = ?2 refer to momentum transfers parallel and not parallel to the molecular axis, respectively. The transfer probabilities provided by an operator k, q are normalized to unity:
The term A,kt = AiAgk wei&t the contribution of each operato; k, q. As the effect of the operators does not depend on the relative molecule-atom distance and speed in the same way,_.@ < dkAk: fork + k’ or q f q’_ The term in brackets in eq.16rNith 4 = 0 and 4’ = +2 or conversely, has the same signs for +4J and -AJ if the electronic parity does not change but opposite signs if the electronic parity does change, providing in this case important upwards/downwards propensities [14]. The tiumerical calculation of the 3J symbols in eq. (6) shows that the (2Jr + l)(_? t 7)’ term for transitions with electronic parity change decreases very rapidly 3s Ji increases. The other terms do not experience such a variation with Ji. The result is that if the A$ are predominant, the probability of transitions with elecrronic parity change will decrease to zero when .Ji increases while the probability of transitions without electronic parity change will not experience such a decrease. If the A::! are predominant, this strik-
ing .I; dependent propensity does not appear. Kumerical values are given in fig. 8. From experiments it seems that A!!!/A(j * 0.1and 1 withHe and Arrespectively. The addition of angular momenta to the initial Ievel, without excitation transfers, provides a disalignment of the emitted light. With the aboveA$ and A$ relative vaIues, this probability is about half of that for the transfer to one AJ = rl level of the same electronic parity with He rmd equal to it with Ar. In any case the
subsequent depolarization is expected to be weak almost for hi:& J’ values which may be great compared to the added angular momenta k. Here again the experimental results in Ar (fig. 7) disagree with the
results calculated in the Born approximation.
3. Du~Q~Q& 0. Nedeiec f Tmnsfers in CdH
t 01
4
a
16
Ji
Fig. 8. Ratio of the averaged values of the transitions proba-1) OYS with IIO bilities. ~~J=~~, +.J with &qe(~i~f= Change(EiEf= +I) Of CleCtrOniC pa&y. EY+erimental, II*,* with He: i, with Ar: X. Cakuiated with equalAk fork = 1,2, 3and4,A$=1andA$2=0:(-),ii~=Oand&p=1:(o).
4.2. The validity of the Born approximation In the time-dependent perturbation theory, the transition probability oscillates and goes to zero if this period is short compared to the collision time [13,15]. Integrals have to be solved and the transition probability P(b, u) is found to be proportional to polynomials R&,x) which decrease whenx = (U/i)@&) increases. For instance, we calculate R(k = 2) for 1AJi = 2 with b = (r#/*, u being the partial cross sections for these transitions (fig. 6) and GJ>the mean relative speed. At T = 600 K, for CdH + He, (u) = 20 X lo4 cm/s, for CdH+Ar,(u)=7X 104cm/s.ForJ~=1,4,8and16 weobtainR=I,1,0.8and0.3withHeandR=0.5, 0.2,0.02 and 0.00 with Ar. Of course ifR = 0 so calculated, R(x) may be > 0 for greater u or smaller b. This comment allows us to justify a few experimental results which cannot be justified in the Born approximation. The total transfer cross sections decrease as J’ increases, more rapidly with Ar than with He (fig. 5). From a given J’ value, greater downwards AJ’ transitions are excited with He than with Ar (fig. 6). The excitation transfer probability to the A-doubled level is not attenuated by the ii values as calculated above, as AE < 10 cm-l [5,3], and may be much greater than to any AJ= +l level almost for high J’ with Ar (fig. 6). For the same reason, the depolarization of the emitted light may be much more impor-
281
tant than expected from the rotational transfer populations (see ref. [l]). The depolarization is important with Ar and increases as J{ increases (table 2). It seems that the addition of angu!ar momentum leading to a change of the Ji direction only, i.e. to AJ’ = 0 transitions, becomes more important when the rotational transfers, i.e. the AJ’ + 0 transitions, are made less probable by the increase of the energy differences between ‘Je levels. At each collision, the total transition probability must be much smaller than unity unless successive transitions may occur between the initial state i and the final state f, and higher orders of perturbation theory would have to be considered. If many successive transitions occur, the propensities are attenuated and the relative rotational cross sections.are determined by the energy difference between the initial ani final levels and by the temperature. The mean impact parameter values at which the total transfer probability reaches its maximum value 1, i.e. b = (oi~)~/*, are 5-2.5 A with Ar and 3.2-I .8 i$ with He, for the studied 1;. In most cases it is greater than the radius of Cd 5 sp, 1.95 a according to Slater’s calculations [ 161, to which the molecular radius may be approximated. Successive excitation transfers are expected to be of little importance in He but great in Ar. Moreover, if these values of b are associated with (u) to calculate the collision times, these durations are found smaller than the rotational period for any J’ with He but not for J’ > 6 with Ar. Even in He for Ji = 16.5 the collision lasts 0.7 rotational period and cannot be considered as sudden. TheAr2/A0 ratio is probably smaller than it seems from fig. 8, in agreement with the fact that no upwards/downwards propensity have been observed up to J; = 16.5. This discussion shows that for quantitative calculations, the first order perturbation theory may be used to describe rotational collision transfers in CdH A 211 Ji d 7.5 with He but not with Ar.
Note added in proof An extensive theoretical paper about the same subject has been made by Alexander [17] _It appears that our schematic theory where the S = l/2 electron spin has been neglected may apply to Ill but not to 2Il case (a) corresponding to our experiments ti CJH. If
1. Dufa_vani, 0. Nedelec / ?hzsfers
288
ihe spin is unaffected by the cohision, the non-vanishing matrix elements of the interaction potential within a given B = l/2 or 3/2 level arc those of q = 0 only, those of q = k2 vanish. The absence of upwardsidownwards propensities in our experiments confirms this assumption For q = 0, the calculated ratios of fig. 8 decrease still more rapidly for ‘Ii case (a) than for ITi : 0.62,0.07,0.02 and 0.00 for J’= OS, 3.575 and 16.5. The discrepancy between the experiment and these calculations must be attributed to the departure from the Born approximation : for low J{, the saturation of the transition probabilities 1151 and for high J’,, the rotation of the moIecule during the interaction_ With He, the ti = 0 A-doubled level is slightly less populated (fig. 6) than its neighbors of the same eiectronic parity in agreement with *he calculations with q = 0 orly.
References [ I] 0. Nedelec and 3. Dufayaxd, 3. Chem. Phys. 76 (1’982)
378.
[ 21 A. Jourdan. J.M. Negro, J. Dufayard and 0. Ned&c, J. Phys. (Paris) 37 (1976) L29. [3] J. Dufayard and 0. Nedelec, J. Phys. (Pais) 38 (1977) 449. [4] 0. Nedelec and J. DilLyard, J. Phys. (Paris) 37 (1976) 81.
in C&l
[5] G. Heabeq,
[6]
[ 71 [S] [9] [IO]
[II]
Spectra of diatomic molecules (Van
Nostrand, Princeton, 1950); E. Svensson, Z. Physik 59 (1930) 333; 0. Dei!e, Z. Physik 106 (1937) 405. J. Dufayard, M. Lombardi and 0. Nedelec, Compt. Rend. Acad. Sci. Paris B276 (1973) 471. T.L. Earls, Phys. Rev. 48 (1935) 423. RS. MulEken and A. Christy, Phys. Rev. 48 (1931) 87; L. Veseth, J. ?hys. 33 (1970) 1677, I. Mol. Spect-y. 44 (1972) 251; 38 (1971) 228. R-4. Got&ho, Chem. Phys. Letters 81(1931) 66; C. Linton, J. Mol. Spectry. 69 (1978) 351. Ch. Ottinger, R. Velasco and R.N. Zare, J. Chem. Phys. 52 (1970) 1636: Ch. Oitinger and D. Poppe, Chem. Phys. Letters 8 (1971) 513. A. Omont, J. Phys. (Paris) 26 (1965) 26;
J.P. Barrat, D. Casalta, J.L. Cojan and J. Hamef, J. Phys. (Paris) 27 (1966) 608. [12] J.M. Brow, J.T. Hougen, K.-P. Huber, J.W.C. Johns, i. Kopp, H. Lefebvre-Brian, A.J. Merer, D.A. Ramsay, J. Rostas and R.N. Zare, J. Mol. Spectry. 55 (1975) 500. 1131 A. Xessiah, MCcanique quontique (Dunod, Paris, 1959). [ 141K. Begman, H. Klar and IV. Schlezht, Chem. Phys. Letters 12 (1972) 522: D. Poppe, Chem. Phys. Letters 19 (1973) 63; H. Klar and hf. Klar, J. Phys. B8 (1975) 129. [15] Ch. Ottinserand M. Schrader, J. Phys. B13 (1980) 4163; H.A. Rabitz and R.C. Gordon, 3. Chem. Phys. 53 (1970) 1831. [ 161 J.C. Slater, Phys. Rev. 36 (1930) 57. 1171 h1.H. Akxander, J. Chem. Phys. 76 (1982) 5474.
COLLlSlON
TRANSFERS
BETWEEN CdK A 2 %Bu’ = 0 ROTATIONAL
STATES
lNDUCED BY He OR AI ’
J. DUFAYARD and 0. NEDELEC Loboratoire de SpectromPtrie Physique, BP 53X. 38041 Grenoble Cedex, France Received 13 April 1982
CdH is obtained by radiofrequency discharge in Cd vapor mixed with 5% Ha in He or Ar. It is selectively excited by a pulsed dye laser to A 2~1,2,s,2 u’ = 0, J’ = 0.5-i&5. Collision cross sections are measured from several J’ values corresponding to rotational transfers observed up to AJ’ = +7. The total collision cross sections are smaller with He than with Ar.
They decrease as J’ increases. The levels of the same electronic parity as the initial level are strongly privileged for high J’ with He, much less with AL The polarization of the initiai lines decreases appreciably for high J’ with the Ar pressure, much less with the He pressure. Small spin transfers are observed from 113,2 to ft1,2 . The experimental results, especially the propensities, are justified using the Born approximation the effects of He and Ar.
as deveioped
1. Introduction We have recently published experimental results about rotational transfers in BK induced by collisions with He, Ar or H2 [l] . In this paper we describe similar experiments in CdH A211,,2,3,7 U’ = 0. This hydride may be easiiy obtained in a low pressure, low power discharge. I& A 2111,2,3,2 u’ = 0 states may be excited at 24500 and 4300 A respectively. We have made lifetime measurements [2] and electric resonance experiments [3] by selective pulsed dye laser excitation. The synthesis reaction Cd*(3P0 l 2) f H2 + CdH + H has been studied recently ‘[4] _ The CdH A21&X 22 transition has been studied by conventional spectroscopy 151, but the interaction potential with rare gas atoms is not known. Even the poIarisability, the electric dipole and quadrupole moments which may be used to calculate the long-range fcrces are not known. However, the experiments reported in this paper allow us to discuss a few aspects of the collision process. The most interesting observations are: a propensity preserving the electronic parity with He but not with Ar, and the depolarization of ’ This work has been supported
0301-0104/82/0000-00i0/$02.75
by the DPa.
Q 1982 North-Holland
in previous papers. Its validity is discussed in comparing
the parent lines with Ar but not with He. We explain these observations qualitatively using the Born approximation. As the transition probability Pi-f is proportional to the matrix element squared, 1(iI Vi 012, the symmetry properties may be studied simply. The vahdity of this approximation is discussed and the results
obtained
with
He and with
Ar are compared.
2. Experiments 2.1.
&lQ?QiUS
The hydride is obtained by radiofrequency 100 M&, 1 W discharge in Cd and H,. The cell is cylindrical with a side arm containing Cd (fig. 1). It is placed in an oven heated at 250°C by thermocoax providing a Cd pressure smaller than low2 Torr. The relative flow of H, and rare gas is such that the partial pressure of H2 is ~5% of the-total pressure. The pressure is measured with a GranviIle Phillips capacitance manometer calibrated against a McLeod gauge. The estimated uncertainty on the pressure measurements is +lO%. The Cd deposits in the tube out of the oven. With a piece of 1 cm3 Cd, the cell may be operated for about 100 h and then has to be refilled.
280
J.
Dufayani,0. Nedelec / 7hmsfers
in
CdH
al-d Pi_oz on the observed light. The instrumental polarization of the detection system is calibrated in the sane way at each experiment by observing the discharge lines which are not polarized [6] without any change in the optical system. We use Polaroid HN 38 or HNP’N polarizers which have a good efficiency at 4500 A. 2.3. Observed lines
Fig. 1. Esperimcnt, with polarizations for excitation and obseivation.
A Lambda Physik EMG 102 multi-gas laser filled with Nz is used at up to 50 Hz to pump a dye laser with one amplifier cell. The dye provides less than 0.1 _S,hnewidth which is necessary to excite selectively most of the CdH lines, with a beam expander X 35 and a 600 groves/mm ruled grating used in the sixth order. TNs linewidth is much greater ihan the CdH Doppler xtidth which is 0.00s _&at 600 K. The employed dyes are 7-diethylamino4-methylcoumarin at =4500 a to excire A 21T1,2 and dimerhyl popop at ~4300 A to excite A 2RS,2. The observation is made through a THR JobinYvon monochromator providing 2.6 A/mm dispersion and a 3 ns time-spread EMI photomultiplier. The line intensities are integrated with a Brookded boxcar using a gate of 500 ns, much larger than the 80 ns lifetime. The lifetime measurements are made with a PAR 162/I 63 boxcar which samples the fluorescent light with 1 ns gate duration. Several 100 s runs are superposed to be sure of the absence of slow drifts.
The polarization of the laser beam in the cell is parallel to OZ (Gg. I). To measure the populations of the levels independently of the polarization [I] of the observed lines a polarizer at 54’ to 02 is placed on the observed light. The polarization of the lines may be measured by permuting two linear polarizers P,, uz
The lT3j.2 level is 1012 cm-l above the III/2 level. bands are The _421T,,,- X2C and A2R,,&X2x well separated. To each rotational level J’ correspond two A-doubled levels of opposite electronic parity and total (electronic X rotational) pzrity. Each Adoubled level is connected by three lines to the spin doubled ground state. The relative intensities of these lines are caictdable from simple general expressions [7] for 211-22 transitions developed for intermediate coupling between Hund’s case (a) and case (b), knowing the fiie structure constant, A = 1012.77 cm-l, and the rotational constant, I? = 6.00 cm-l, of CdH A 2 II U’ = 0. To measure the relative populations of the levels it is sufficient to select only one lime issued from each Ievel. Fig. 2 shows the relative line intensities issued from each A 2FIy3 3I., J’ levels where the sum of the three lines is norr;;$i;ed
to I_
Fk. 2. The relative lines intensities from each J’ level of %I+ (0,O). strong lines: ebctronic parity + (or e A%l,,-X levels); weak lies: electronic parity - (or f levels)_
J. Dufaymd, 0. Ned&c / Transfers in C&4
2.4. Temperame The plates providing the electric discharge are in the cell. The discharge heats the gas. The temperature is obtained from the A 2II1j2 u’ = 0 + X 2Z+ u” = 0 line intensities in the discharge. The electronic excitation provides essentially dipole transitions, i.e. J’ - J” = 0, il. If J’ S 1, and if there is no rotational perturbations, the distributions of the popurations in the excited state and in the ground state are very similar. if the pressure is low enough so that there is no redistribution of the populations in the excited state, a spectrum allows its to obtain the rotational temperature in the ground state (fig. 3). The first (0.5 < J’ < 8) and the last (14 < J’ < 18) lines are provided by the Pl, band, the intermediate lines by the R1 band, and are selectively observed with 0.2 A resolution. The obtained popuIations may be well fitted with a Boltzmann law: the rotational temperature is homogeneous in the cell over at least 3 kT (fig. 3) within 5% error. This result is due to the fact that the increase of the temperature due to the discharge (
parallel and the discharge looks homogeneous
281
(520 K). It was not the case for RH where the temperature at the center of the discharge reached 900 K to be compared to room temperature, 300 K. This temperature homogeneity in the case of CdH will enable us to make a valuable discussion of the relative satellite line intensities. This geometry of the discharge has provided temperature and cross section values independent of the pressure varying from 0.3 to 2.0 Torr. The electrons of the discharge have no effect on the CdH A211,,2,3,2 level: the measured lifetimes are the same when the discharge is on or turned off 200 ps before the laser pulse, or when the discharge power is varied over a factor 4.
3. Results 3.1. Total transfer co!lision cross sections The total transfer collision cross sections are provided by the lifetime reduction with pressure measured by selective excitation and observation of a line. Vibrational transfers from v’ = 0 to u’ = 1 are unliiely to occur as the energy defect is great (1600 cm-l) compared to kT (500 cm-l). Downwards ll,jz + 11112 spin transfers have been observed but not uppenvards n,/z
I 0
B.J’U+l)
lopa 9.5
145
cm4
185 J
pi. 3. the variation of ln[N~/(2J+ I)] with J(J+ 1) fitted with a Boltzmann law, T= @“hc/k)J((J+ l)/{ln[N~/W+ l)] - III(NJ=~)}. B” = 5.32 cm-’ for X ?, u” = 0.
+ 4/z. From IIll2 the total collision cross section is due only to rotational transfers. For 113,2 it also inchrdes spin transfers which are’one order of magnitude smaller than the rotational transfers, as observed on a spectrum. In a first experiment we have measured the lifetimes for several pressures, to be sure that the variation of l/r withP is linear (fig. 4). We have also measured the radiative lifetimes of A 211112 and A 2113,z very precisely at very low H2 pressures(lO-’ Torr) and with a wideband (24 A) observation. The radiative lifetimes do not depend on J’ up to J’ = 16.5; for the A211,,, state 7 = 83 + 2 ns and for A2113j2 T = 67 + 2 ns. The lifetimes for several J’ values of A211,,2 and A2ll,,, with He or P.r have been measured consecutively at a given pressure and a temperature determination has been made associated.with each series of measurements. The obtained cross sections are given in fig. 5. As in all oar papers, the cross section o is defined by the following expression, where r is the deexcitation frequency (s-l):
.
J. Dufoyard.0. Nedeiec / Tkansfenin C&Y
282
Ar
140 0
1
Fig. 4. Variation of the miththe AI pressure.
likiti~
Pressure iT2rrI
of A 7113,2 u’ = 0, J’ = 3.5
The sum of the intensities of the satehhe lines compared to the intensities of the parent lines allows us to verify that the total cross sections obtained from lifetime measurements are actually due to rotational transfers. As mentioned in a previous paper [I], the A-doubled J’+ levels give the same cr values, indicated by only one point in fig. 5. The observed decrease of ETwhen J’ increases is due to the increase of the energy difference between the rotational levels, as it is not small compared to kT. For collisions of A’IIr,z with
He, u show an unexpected feature as they remain constant for J’ > 3.5. Except for this anomaly, the cross sections are greater with Ar than with He and are similar for the Ii,/, and I13j2 levels. The long-range forces in the reference frame of the molecule depend on electronic parameters which do not depend explicitly on the electron spin, and are expected to be the same for II,,, and II,,,. The short-range forces, more important for small cross sectiors, may depend on the spin. On the other hand, the A% levels are affected by X32? and B2C*-for A211 rj2 by strong homogeneous perturbations and’for A 21T~,2 by light heterogeneous perturbations [8], which determine the proportions of the s and p orbitals of the excited electron. These perturbations provide differences between the radiative lifetimes of the two levels and very likely between their collision effects. 3.2. Propensities in rototiorzal transfers A selective excitation of several leve!s may be obtamed as the laser hnewidth is smaller than 0.1 Ii. A selective observation of at least one line issued from each level is difficult to be made as the monochromator resolution must be greater than 0.5 A in most cases otherwise there is not enough light limited by the quantity of hydride synthesized in the discharge. In a few cases a resolution up to 0.15 A has been used. The relative populations of the rotational 1eveIs Jf excited
\
Ar 650KI
40.
0
5
10
15
J
Fig. 5. Total transfer cross sections for co&ion with He (+) or with Ar (o), from A *n,,, U’= 0, J’ = 0.5-, l-5-, 3.5-, 7.5-and 16.5= ,and from A2n3,2, u’= 0, J’ = IS-, 3.5+,6.5- and 15.5c.The signsreferto the totdptities.
283
J. Dufoymd, 0. Nedelec / ?Fansfers in CdH
3 b ext. S,
a
0.5” fArI.
3
ext. S=3.S-R-iel
t
exe. 3 = 3..S(Arl
I
)
exe J-=X5-
-
j/L!/
h-1
eIi 1
o 5
exc.J‘=
exe: J”= 2S
I
(He1
I
7I.S Itie
j
i
65
Fig, 6
fo be contimced
on
nexr page
J. Dufiyard.
0. Nedelec j Transfets
ext. J’=16S*CHel
:I
i&5
J
ext. J=16.5c IArl
in CdH
With Ar it is weak and seems to disappear at J: = 16.5. Such a propensity has already been noticed in YO A ?Il with Ar, for J; > 20, T = 1800 K, the lines with electronic parity change being completely missing [9]. (2) A small propensity preserves the total parity -within sets of satellite levels without electronic parity change. It appears only for Ji = 0.5 in He_ This alternation is much less evident than in the case of BH J~=4w+thHe [l]. (3) These propensities do not depend on the parity of the initial level. in previous experiments on llI levels of alkaline dimers [lo] or of BH [I], upwards or downwards propensities had been observed for transfers with electronic parity change. Such propensities which depend on the parity of J; have not been observed in the present experiment_ 3.3. Disaii~ment
Fig. 6. Relative populntions of the levels populated by collision transfers with He or with Ar after selective Iz~er excita:ion of CdH, Asnl,~, U*= 0, J’ = OS-, 3.5-, 7.5, ?.5i and 16..5+. Strong lines: electronic parity +, weak lines: electronic parity -. Pressure: 1 Tom Temperatures: 590 i 50 K for He, 660 + 50 K for AI. Typical relative errors on the partial cross sections: 50.2 A?.
The polarizations of the lines may be calculated from formulas (2) and (3) of ref. [l] _The nuclear spin is I = 0 for 50% of the isotopes in natural Cd and I = l/2 for the other isotopes_ The H nuclear spin is also l/2. If the hyperfme structure is much greater than the natural width, the nuclear spins reduce the polarization for the smallest values of the total angular momentum J’ (table 1). The experimental results are shown in tables 1 and 2 and fig. 7. The relaxation of the total angular momentum of an atomic or molecular state, or of the emitted light, depends on the symmetry considered [ 111: for the population, r,
by transfers from Azllli2 v’ = 0, Ji =0.5,3.5,7.5 and 16.5, are given in fig. 6 by interaction with He and Ar, respectively_ The chosen pressure is small enough, as shown in fig. 4 to have single collision conditions. Very similar resulis have been obtained from any two A-doubled J’ levels. On the other hand, A 2Hj,2, II’ = 0 J’ levels give the same relative transfer populations as the same J’ levels of A 2K1112,v’ = 0. The comments that can be made about the results of fig. 6 are as follows: (1) A propensity preserves the electronic parity. With He it is strong and increases when J{ increases.
f;, C 21,:
=r radiation •t rtransfer 9
Table 1 P = (111- I~)/(111 +&I of CdH, A ‘fIra, u’ = 0. lines: J’ = 3.5 +QtPI,J’=7.StQtPr,J’=16.5-QtR&.calculatedwith I = il.112 or 1, and &pe&ental extrap&ated to zero pressure. Typical absolute uncertainty on experimentali’: +-0.02
calculated
2=0 I= l/2 I=1
experimental
I’ = 3.5
J’ = 7.5
J’ = 16.5
0.214 0.193 0.186
0.269 0.261 0.253
0.367 0.365 0.361
0.17
0.24
0.34
Table 2 Disalignment cross section ‘12(A’)
rrad
-=tF
fpzO
A2ixln. J’
3.s
7.5+
He, 620 K. Ar, 680 K
Or2
I*2
16..51+2
7+3
13 24
32 f S
&d
+rtr
+ qr + hs
(2)
,
where r;, = uoNW, r,, = u2N!u). The depolarization cross section u2 relative to rdiS has been calculated (table 2) from the depolarization with pressure (fig. 7), knowing the transfer cross sections u. (fig. 5) and the radiative lifetirires.
4. Discussion
L
L
J’.?5
L
;
t
7
1’
0.1 HELIUM I
a ar
OS
1
1.5
2
P IToorcJ
Most of the comments that we make about the experimental results deal with the parity [S] of the levels_ The parity of a molecular level depends on the orbital L and rotational X angular momenta. In the G or b coupling caSes L and R are not good quantum numbers. The eigenfunctions of the molecular II state in the reference frame of the molecule have to be written as linear combinations of the eigenfunctions of angular momentum J and projections A = +I on the molecular axiS
The electronic parity depends on the relative phase of ]+iX:=,l), it is even or odd according to e = i-1 or E = -1. These levels are called [ 121 e or f levels respectively. The total parity alternates with the total angular momentumJ. The A-doubled levels have opposite electronic and total parities. 4.1. Collisions in the Born approximation
I 001
c5
,
I5
2
> PtBrd
Fig. 7.
Depolarizationby colkions with He or AI of CdH A2n,,~d=Olines:J’=3.5tQPP~,J’=7.5+QtP~,J’ = 16.5 - QtPI.
for the alignment, I,, - I,: r2 = rndiation ’ rtransfer f rdtignment . As each term is in inverse ratio to the corresponding relaxation, the expression (I,, - I,)/@,,, + 21,) = tp decreases with the pressure if rdis is not small compared t0 rrad +rtr:
[I33I.51
The time dependent perturbation theory is used in first order and the collisions are supposed to be sudden. The interaction potential is expanded in spherical harmonics in the reference frame of the molecule:
Y,“(O,#J)are sphedca! harmonics, where B, Q are the orientation of the atom with respect to the molecule. V[ = V$ in a linear molecule. In homonuclear molecules k can also be odd. The transition probability amplitude uj_f is such as:
J. Dufuyard,0. Medelec/ lhmsfers in CdH
286
(3 The Ai contain the radial terms, summed over the
moiecule-atom relative distances and speeds, and the normalization terms for the matrix element of an operator k, 4. Odd (even) values of X-change (do not change) the total parity. In a II level 4 = O,i3. The 4 = f2 (4 = 0) change (do not change) the sign of A. in the 3J symbols (2, 2Z $, when the signs of aLl the m are changed, the 3J symbol is multipiied by (-)zJ. The electronic parity is changed if Ji + k + J, is odd. The transition probabilities are given by the formula which is similar to those which have been written previously [14] fork = 2: ‘Ji,i-jf,c=
(2Jf + 1)
The values of k and k’ associated with a given transition must have the same parity. 9 = 0 and 4 = ?2 refer to momentum transfers parallel and not parallel to the molecular axis, respectively. The transfer probabilities provided by an operator k, q are normalized to unity:
The term A,kt = AiAgk wei&t the contribution of each operato; k, q. As the effect of the operators does not depend on the relative molecule-atom distance and speed in the same way,_.@ < dkAk: fork + k’ or q f q’_ The term in brackets in eq.16rNith 4 = 0 and 4’ = +2 or conversely, has the same signs for +4J and -AJ if the electronic parity does not change but opposite signs if the electronic parity does change, providing in this case important upwards/downwards propensities [14]. The tiumerical calculation of the 3J symbols in eq. (6) shows that the (2Jr + l)(_? t 7)’ term for transitions with electronic parity change decreases very rapidly 3s Ji increases. The other terms do not experience such a variation with Ji. The result is that if the A$ are predominant, the probability of transitions with elecrronic parity change will decrease to zero when .Ji increases while the probability of transitions without electronic parity change will not experience such a decrease. If the A::! are predominant, this strik-
ing .I; dependent propensity does not appear. Kumerical values are given in fig. 8. From experiments it seems that A!!!/A(j * 0.1and 1 withHe and Arrespectively. The addition of angular momenta to the initial Ievel, without excitation transfers, provides a disalignment of the emitted light. With the aboveA$ and A$ relative vaIues, this probability is about half of that for the transfer to one AJ = rl level of the same electronic parity with He rmd equal to it with Ar. In any case the
subsequent depolarization is expected to be weak almost for hi:& J’ values which may be great compared to the added angular momenta k. Here again the experimental results in Ar (fig. 7) disagree with the
results calculated in the Born approximation.
3. Du~Q~Q& 0. Nedeiec f Tmnsfers in CdH
t 01
4
a
16
Ji
Fig. 8. Ratio of the averaged values of the transitions proba-1) OYS with IIO bilities. ~~J=~~, +.J with &qe(~i~f= Change(EiEf= +I) Of CleCtrOniC pa&y. EY+erimental, II*,* with He: i, with Ar: X. Cakuiated with equalAk fork = 1,2, 3and4,A$=1andA$2=0:(-),ii~=Oand&p=1:(o).
4.2. The validity of the Born approximation In the time-dependent perturbation theory, the transition probability oscillates and goes to zero if this period is short compared to the collision time [13,15]. Integrals have to be solved and the transition probability P(b, u) is found to be proportional to polynomials R&,x) which decrease whenx = (U/i)@&) increases. For instance, we calculate R(k = 2) for 1AJi = 2 with b = (r#/*, u being the partial cross sections for these transitions (fig. 6) and GJ>the mean relative speed. At T = 600 K, for CdH + He, (u) = 20 X lo4 cm/s, for CdH+Ar,(u)=7X 104cm/s.ForJ~=1,4,8and16 weobtainR=I,1,0.8and0.3withHeandR=0.5, 0.2,0.02 and 0.00 with Ar. Of course ifR = 0 so calculated, R(x) may be > 0 for greater u or smaller b. This comment allows us to justify a few experimental results which cannot be justified in the Born approximation. The total transfer cross sections decrease as J’ increases, more rapidly with Ar than with He (fig. 5). From a given J’ value, greater downwards AJ’ transitions are excited with He than with Ar (fig. 6). The excitation transfer probability to the A-doubled level is not attenuated by the ii values as calculated above, as AE < 10 cm-l [5,3], and may be much greater than to any AJ= +l level almost for high J’ with Ar (fig. 6). For the same reason, the depolarization of the emitted light may be much more impor-
281
tant than expected from the rotational transfer populations (see ref. [l]). The depolarization is important with Ar and increases as J{ increases (table 2). It seems that the addition of angu!ar momentum leading to a change of the Ji direction only, i.e. to AJ’ = 0 transitions, becomes more important when the rotational transfers, i.e. the AJ’ + 0 transitions, are made less probable by the increase of the energy differences between ‘Je levels. At each collision, the total transition probability must be much smaller than unity unless successive transitions may occur between the initial state i and the final state f, and higher orders of perturbation theory would have to be considered. If many successive transitions occur, the propensities are attenuated and the relative rotational cross sections.are determined by the energy difference between the initial ani final levels and by the temperature. The mean impact parameter values at which the total transfer probability reaches its maximum value 1, i.e. b = (oi~)~/*, are 5-2.5 A with Ar and 3.2-I .8 i$ with He, for the studied 1;. In most cases it is greater than the radius of Cd 5 sp, 1.95 a according to Slater’s calculations [ 161, to which the molecular radius may be approximated. Successive excitation transfers are expected to be of little importance in He but great in Ar. Moreover, if these values of b are associated with (u) to calculate the collision times, these durations are found smaller than the rotational period for any J’ with He but not for J’ > 6 with Ar. Even in He for Ji = 16.5 the collision lasts 0.7 rotational period and cannot be considered as sudden. TheAr2/A0 ratio is probably smaller than it seems from fig. 8, in agreement with the fact that no upwards/downwards propensity have been observed up to J; = 16.5. This discussion shows that for quantitative calculations, the first order perturbation theory may be used to describe rotational collision transfers in CdH A 211 Ji d 7.5 with He but not with Ar.
Note added in proof An extensive theoretical paper about the same subject has been made by Alexander [17] _It appears that our schematic theory where the S = l/2 electron spin has been neglected may apply to Ill but not to 2Il case (a) corresponding to our experiments ti CJH. If
1. Dufa_vani, 0. Nedelec / ?hzsfers
288
ihe spin is unaffected by the cohision, the non-vanishing matrix elements of the interaction potential within a given B = l/2 or 3/2 level arc those of q = 0 only, those of q = k2 vanish. The absence of upwardsidownwards propensities in our experiments confirms this assumption For q = 0, the calculated ratios of fig. 8 decrease still more rapidly for ‘Ii case (a) than for ITi : 0.62,0.07,0.02 and 0.00 for J’= OS, 3.575 and 16.5. The discrepancy between the experiment and these calculations must be attributed to the departure from the Born approximation : for low J{, the saturation of the transition probabilities 1151 and for high J’,, the rotation of the moIecule during the interaction_ With He, the ti = 0 A-doubled level is slightly less populated (fig. 6) than its neighbors of the same eiectronic parity in agreement with *he calculations with q = 0 orly.
References [ I] 0. Nedelec and 3. Dufayaxd, 3. Chem. Phys. 76 (1’982)
378.
[ 21 A. Jourdan. J.M. Negro, J. Dufayard and 0. Ned&c, J. Phys. (Paris) 37 (1976) L29. [3] J. Dufayard and 0. Nedelec, J. Phys. (Pais) 38 (1977) 449. [4] 0. Nedelec and J. DilLyard, J. Phys. (Paris) 37 (1976) 81.
in C&l
[5] G. Heabeq,
[6]
[ 71 [S] [9] [IO]
[II]
Spectra of diatomic molecules (Van
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J.P. Barrat, D. Casalta, J.L. Cojan and J. Hamef, J. Phys. (Paris) 27 (1966) 608. [12] J.M. Brow, J.T. Hougen, K.-P. Huber, J.W.C. Johns, i. Kopp, H. Lefebvre-Brian, A.J. Merer, D.A. Ramsay, J. Rostas and R.N. Zare, J. Mol. Spectry. 55 (1975) 500. 1131 A. Xessiah, MCcanique quontique (Dunod, Paris, 1959). [ 141K. Begman, H. Klar and IV. Schlezht, Chem. Phys. Letters 12 (1972) 522: D. Poppe, Chem. Phys. Letters 19 (1973) 63; H. Klar and hf. Klar, J. Phys. B8 (1975) 129. [15] Ch. Ottinserand M. Schrader, J. Phys. B13 (1980) 4163; H.A. Rabitz and R.C. Gordon, 3. Chem. Phys. 53 (1970) 1831. [ 161 J.C. Slater, Phys. Rev. 36 (1930) 57. 1171 h1.H. Akxander, J. Chem. Phys. 76 (1982) 5474.