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Crosssed beam study of the Na(32P32 + N2 quenching process: angular distributions with product state analysis
CHEMICAL
Volume 91, number 5
CROSSED ANGULAR
BEAM STUDY DISTRMJTIONS
OF THE Na(3 2P3,.$ + N, QUENCHING PROCESS: WITH PRODUCT
W. REILAND, C.P. SCHUZZ, H.-U. TITTES InsI~tuCfur Rcccn’cd
Moiekiilphysik,
18 June
24 Scptcmbcr 1982
PHYSICS LCrrERS
STATE
ANALYSIS
and I.V. HERTEL
l+ele Umversit~r Berlin. Artumaliee 14, 1000 Berhn 33, IVeSt GerrmKJ
1982
The transfer of clectromc to vIbrationa rotatIonal cncqy for Na(3 *P, *) + N2(u = OJ>-+ Na(3 *S1p) + Nz(u’./‘) IS studlad m PII crtperimcnl wIh crossed supcrsomc Ns and N2 beams and smglc-mo 1 c EWdye bscr CWIICIIIO~ (rchtnc hmcl~c cncrgy 0.16 eV). At c m fonwrd scattcrmg the u’ = 3 state IS cxcltcd to more than SO%, accompamcd by a nowublc ro~st~onrl evcitatlon smountmg Lo over 0.1 cV. ror backward scattermg the vrbratlonal lcvcls U’ = 2.3 and 4 LUCdommantly pop&ted. TM anguh dfitributlons show 3 pronounced nwow forward m&xrmum and 3 smaller (8-30s) backward peak. The obWViltlOIlS XC rstionahzcd in terms of Ihc bond stretch ~.ttractron model.
1. Introduction
cm. energy EL m. is measured
and may vary between
energy of 2.26 eV [E,,_ + electronic energy of Na(3 ‘PJ ?)I. In the present study, m contrast to previous work / IO,I I 1, both the c.m. scattenng angle ec,,, and EL m are analysed and significant structure as a fun&Ion of both variables ISobserved. The pseudopotentlal calculations by Habitz 171 for the ground (% ?A’) and excited (‘;i *A’ and 2 ?A”) states PESs Indicate that the mechanism for this nonadiabatic process is sunilar to that encountered for Na t II2 [6] : A bond stretchmg attraction between Na* and N2 on the excited state A surface leads to an (avoided) surface crossmg with the % ground state at 0 and the total available
The quenching of alkali resonance radiation by diamolecules has long been subject to mtenslve experimental and theoretical studies. As reviewed elsewhere [l-3] substantial progress in understanding these basic mechamsms has been made during recent years. While earher theoretical approaches [4,5] based on guesses of the mteractlons using the “ionic mtermedate” model served as a useful first guideline for further studies, our present knowledge of the poientlal energy surfaces (PESs) for some prototype systems like NaHZ [6], NaN2 [7] and NaCO [8] allows at least a semiquantitative understanding of certain features of the electronic to vibrational rotational translational energy transfer mechanism (E-VRT). Some results on angular distribution measurements of the differentral quenching cross section with an analysis of the product energy dntribution using a new scattering apparatus are reported elsewhere for Nat Hz [9] and Na + CO [8]. III the present work we wish to present a first detadcd study of the double differential cross section d%/ =i.rn. dRc.m, for the process tomic
Na(3 *PsIZ) + N2(u = 0,11+ Na(3 2S1,1) + N#‘,I? using single-mode cw dye laser excitation of Na in a state of the art experiment with crossed supersonic atomic and molecular beams. The imtial center of mass (cm.) kmetic energy is E,,. = 0.16 eV and the final 0 009~2614/82/OOOO-OCKIO/$O2.750 1982 North-Holland
an internuclear distance R,
= 4.2 no if the molecular
to rc = 2.25 UO.It is energetically most easily accessible in the perpendicular (G,) approach into whrch the system may be partially clamped dunng the approach in the excited state. After a surface hop at R, to the ground state the N, molecule is in a nonequtibrium distance and thus starts to vibrate while Na and Nz quickly receed on the strongly repulsive ground state surface. At present only prehmmary classical trajectory calculations are completed [19-l. ‘The present experimental observations lend strong support to the qualitative picture sketched above and it is hoped that they will stimulate increased theoretical efforts for a full ab initio understanding of this prototype molecular dynamical process. N2 bond is stretched
329
Volume 9 I. number 2.
CHChtlCAL
5
PHYSICS
shows that in this elastic scattering
Experimental
~hc experimental schematlc of the crossed beam apparatus IS cssentlally that described in ref. [IO]. The nqor
lmprovemcnt
Is the use of a supersomc
molecu-
lar N1
beam and the accesslblhty of c.m. scattermg angles from tJcm = 0 to 180” 1~1th an estinlated overall rcsolutlon of 23”. The method to transform laboratory scattering data into the center of mass system ISdescribed in ref. [lo], details on the current procedure of data taking as well as on the beam properties is given m ref. [8] for the kinematlcally identical Na-CO case and a full descrlptlon of the apparatus and a hlonte Carlo sunulatlon of the kinematics together with new data on NaNO and NaO? wrll be pubhshcd elsewhere 1131. Two types of measurements arc reported in the present work. (I) Energy transfer spectra, I.e. the double dlfferentlal cross sectlon dIo/dE’, m_da,,,. for the quenchmg process is observed as a function of the fmal relative cm. translational energy I!&, for fixed cm. scattermg angle, which is equivalent to a determmatlon of the energy AEvlbrot = 2 26 eV - EL,, transferred tnto vlbrattonal rotational energy of the molecule. (h) Angular
dlsrriiutions,
mlncd as a function
I.e. d2u/dE;,,,,
dSZc ,.,,. 1s deter-
of the scattermg
angle 0, m_ for a
filed value of Ei m.. Both types of measurements neccssitate an appropriate change of the laboratory velocity and scattering
angle of the so&urn
atoms
detected
after
the
colhslon process as determmed from the Newton diagram [8] _In the present work energy transfer spectra and angular distnbutlons are normahzed to each other by fittmg the ratio of forward to backward scattering as obtained from the angular dlstrlbutlons to the energy transfer spectra at 0, ,,,, = 0” and 180”, with an estunatcd uncertamty of less than 15%. Scattermg from the background gas was subtracted by appropriate chop. ping of the molecular beam. All results on the double differential quenclung cross section reported here originate from a measurement of the lfference between signals with and without the dye laser for Na excitation switched on, so that scattermg from
unexcited
atoms
was subtracted.
However,
as dls-
cussed previously [IO], purely elastic scattermg from excited Na* cannot be distinguished from quenchmg Lmthout energy analysis of the scattered particles and thus m the range of small EL,,. the scattermg data can no longer bc umquely evaluated. A sunple analysis even 330
24 Septcmbcr
LITI-ERS
a difference
between
thus energy
analysis
region
several cross sections
1982
the slgnal is [14,lS]
and
with Hugh background
suppresslon ISa necessary prerequisite for any rehable crossed beam quenchmg study For the present work we are confident m evaluating the data unambiguously for Ef.m, > 0 4 TV as estimated from a more detailed study of the elastic region [ 131 and we report scattering dlstnbutions only for ES.m. above this hmit.
3. Results and discussion 3.1. Energy transfer spectra Fig. I shows the measured energy transfer spectra for Nz withE,, =O.l6eVinWal relative kinetic energy at three center of mass scattering angles, 0, m = O”, 90” and 180”. The error bars indicate a typical 67% confidence Interval as derived from statlstlcal uncertainties of the measured count rates. The experunental results illustrate that roughly 50% of the nvailable total energy E. = 2.26 eV = E,_ + 2.1 eV IS transferred into internal motion of N2. 731sagreeswith
quenchmgofNa*by
our prevlrus
findings
[lo]
and the present
B,,,.
= O”
the earher data.
However, since the angular resolution is now substantially improved (AfI,,_ = 5”) the maximum cross section appears now at &?nbrot = 0.9 eV which is slightly less than previously reported for the data averaged over 115”. Sliver et al. [ I1 1 have reported 0.83 eV but their raw data (fig. 4 of ref. [ 161) would be consistent with a significantly different energy transfer as well. while our present results are conclusive to wlthin a few per cent. One of the especially remarkable features displayed in fig. 1 is the clearly recognizable structure in the backward scattermg which proved to be highly reproducible in several experimental runs under different conditions of the apparatus such as signal-to-noise ratio, Na-beam density, etc. Although the present experiment cannot uniquely distinguish between rotatlonal and vibrational N, energy, the observed struchue emphasizes dominanlspectrum
cssentlaUy
reproduces
ly vibrational excitation for the backward scattering:
A least-squares fit with 6 gaussian profdes of variable width and height centered at the energetic positlons for pure vibrational excitation gives excellent agreement with the measured data as indicated in fig. I. The wdt.h
Volume 9 I. number 5
-
CHLhllCAL
AEwbrot 1 ev
PHYSICS
-
24 Sep~smbcr
LLTTCRS Table Rclatw h’Ck+
1982
I N2 cwtation probdbdity for dlffcrcnt vrbrrtion.rl dcnvcd from the “deconvolu~~on” whcatcd In fig
u’ 3s
I v’
Rclalwc drffcrcntul 0 cm.
qO0
cross section (in !Z)
O,,
=90°
o,m.=
0
9
0
I
t
0
I
2
5
8
8
0
3
52
I7
22
4
22
36
30
5
II
24
29
9
IO
6 7
9
180°
6
= 0” near the maxrmum. the data for 0,. favour an even larger amount of energy transfer mto the molecule. We thus have to conclude that for O,,. = 90” and k particularfor B,,. = 0’ rotationalexcitatiorz becomes significant and amounts to at least 0.1 e’ particular
From the mcasurcd data an even larger amount of rotntronnl exatntron cannot be excluded s,r~ce no wbra-
E;, IeV FIN. I _Double ddkcnkd qucnchmg cross scctrons for Na*+N2 at diffcrcnt cm. swttcrmg angles 0, m as a functron of the final rehtivc kmetic c m. cnrrgy Ei m. anh of the cncrgy transfcrrcd to the molcculc ti,b,ot =.&o - Ei m., with Eo = 2 26 cV. l-01 comparison the cncrgy SC& IS also gwcn in units of tiial Nz nbratlonal quanta IJ’. Elperlmcntal pomts (0) wth st.rtatiwl error bars(f) arc gwcn togclhcr wth a least squares frt (-) by 6 gaussian drstributlons (- - -) ccntcrcd at each u’. Now the dlrfcrcnt scrlcs for the three spectra normahzcd to the mcdsurcd angular rhstributrons.
tional structure is distinguishable at these scattering angles. Preliminary results from trajectory calculations by Achirel and Habitz [ 121 show indeed that rotation, quanta up to j’> 60 may be excited and a convolutior of theirj’ state distrtbution for the U’ = 2 level with ou energy profile shifts the peak msxlmum by 0.15 eV an increases the energy fwhm by 0.2 eV as compared to purej’ = 0 excitation. The explanation for these obscr vatlons IS probably similar to the simple model for the rotational excitation that has been introduced when di cussing a solar energetic shift of the vlbratlonal peak: observed for Na* + Hz [9] . The experimental tits to our data in fig. I, even though somewhat arbitrary for e rm. = 0” and 90°, allow to give a quantitative summa ry of the energy transfer spectra in terms of “deconvoluted” relative probablhties for excitation of the d6 ferent u’ vibrational levels as displayed in table I.
of the “vibrational”
peaks is in good agreement with the energy resolution estimated from the molecular
for forward scattering as well as for dcm_ = 90” the same fitting procedure givespeak widths (fwhm) which are up to 0.1 eV wider
3.2. Angular distributions
beam kinematics. In contrast,
than the estimated energy resolution and, as seen in
Our results for energy and angle resolved double dif ferential cross sections I@,_ ) = d2aldE&. dQ,_ as a function of center of mass scattering angle is shown 331
Volume 9 I, number 5
-
scallerlng
angle o.,
CHEMICAL
PHYSICS LETTERS
24
September 1982
-
Fg. 2. Double rhffcrcntlal quenchmg cross sc~t~ons;ISB funcllon ol center of masssnttermg angle Bc m (+). The pammeter 1s to the indleculc ~~cn ut ututs of the Cllerg)’ tILlllSfC1 ti,,,brot vibrational quanta U%J of the Nz. For complvlson with fig. 1 the ecm = O” energy transfer spectrum ISalso shown (0).
2 for different amounts of energy transfer. At present, no attempt has been made to “deconvolute” the angular distribution for energy and angular resolution, so that the experimental material IS presented as unbiased as possible, merely using the sunple kinematin fig.
ic transformation
from lab to c.m. frame wth the ap-
propnate jacobian. The angular resolution as estimated from beam kmematics is better than +3O. In contrast, Sliver et al. [ 111 have used a “deconvolutlon” procedure based on the (obviously wrong) assumption of the angular distributions being independent of &?Wbrot_ Thus only data for energy unresolved cross sections were reported in ref. [ 1l] apparently Including the elastic scattering region as well. For reasons dlscussed in section 2 data evaluation in this range of E’,. energies is highly ambiguous. The pronounced and narrow forward peak at all values of the energy transfer appears to be most sigmficant, in particular so for &,brot = 3fiiw. Whde this findmg ISsuntlar to the Na*-H2 case [9], the clear backward peak seen presently was not observed there. It amounts to in between 8% and 30% of the forward maxunum increasing in height with the aoumt of energy transferred to the N2. The bond stretching attraction model for the E-VRT process as discussed III section 1 lends itself to a suggestive explanation of this behaviour. The backward peak indicates a tendency towards complex formation dunng the interaction process which becomes more important as larger stretching of the N, 332
Fg. 3. Double dtffercntnl qucnchmg cross section; multiphed m by mec.m. as D function of 17o m._ Pameter IS timjrot umts of Nz nbrattonal quanta 1. These anguku dutributions are normshzcd rektlve to ach other by mans of the ec m = 90” energy transfer spectrum of fig 1.
molecular bond is necessary before reaching the crossmg seam. This is equivalent to saying that it becomes more probable to channel energy into the molecular bond when the interaction time on the excited state PES is prolonged. The observed experimental trends become even more evident when the cross sections are multiplied by sin Ocm. as displayed in fig. 3. (In contrast to the previous procedure we have normahzed these distributions with respect to each other by means of the ec.,, = 90” energy transfer spectrum.) The plotted values (dlu/ #Lrn. dnc_m.Isin ecm. represent the contribution of each scattering angle and energy transfer to the total quenching cross section. In a classical trajectory picture each impact parameter b contributes to this expression as 2nb db dtI/db. The rationalization of the observed angular distribution for u’ = 2 and 3 is then analogue to that given for NaH2 [9]. The pronounced forward hump in the u’ = 3 excitation seen in fig. 3 is explained as a kind of glory behaviour due to positive and negative deflection angles contributing to scattering at small 0,,.. The angular distributions for higher &&rot = 4-6 ho exhibit much stronger contributions from intermediate
CHEhllCAL
Volume 91. numbcr 5
scattering angles and roughly resemble the behaviour of a classical collision complex, which would give a constant value as a function of scattering angle in this type of display. 3.3. Integrated cross sections For
prxtiwl
npphxtions
24 Scptcmber 1982
PHYSICS LEITERS
(see e.g. ref. [17] ) ZISweti
as for comparison with bulk measurements it appears useful to also report angular integrated energy transfer cross sections da/dE’,_ as a function of energy transfer. For this purpose we simply Integrate the normalized I@,_) distributions of fig. 3. The results are shown in fig. 4. Yet one more integration (over &A.) yields the total cross section which may be used to absolutely cahbrate fig. 4. As seen, the maxunum for the angular integrated cross sectlon IS found that an energy transfer of 4fio with approximately da/d&,,_ = 18 A*/eV. The maximum is in agreement ~th cell data for the inverse quenching process, i.e. the excitation of Na* by nbrationally excited N2 as adopted from Buck et al. [IS] _ Although a direct comparison with our data is some-
-r
what arbitrary
due to distinctively
different experimental
* the genera! tendencies agree quite well.
conditions
Both angular
integrated
results are sigmficantly
non-
with a prior translational dlstnbutlon of the Levine type [ 191. From fig. 4 we can also derive an average energy transfer (anbroI) = I .I3 eV or 5% of the total of 2.26 eV awlable which statistlcal
as seen by the comparison
emphasizes
even more the non-statistical
nature
of the
process as the prior translational energy distribution yields 67% average energy transfer.
4. Conclusions The pronounced structures observed in the present crossed beam study for this prototype non-adiabatic molecular process appear quite surprising in the light of earher theoretical quenching models. The new bond stretch attraction mechanism revealed by recent PES calculations [6-S] allows a qualitative discussion_ The remarkable features observed III the present work together wllh refmed studlcs of polarization dependences for this process [20] should serve as a crucial test to forthcoming theoretical efforts. Improved PES calculaions for the NaN, system with large scale Cl methods are on the way [2i 1. One may thus hope that an adequate scattering dynamical theory can be developed and may eventually lead to a full ab initio understanding for this type of elementary photochemlcal reactlon.
Acknowledgement Continuous sypport by the Deutsche Forschunggemeinschaft through Sonderforschungsbercich 161 is gratefully acknowledged. * WC have thcrcforc arlxtrardy normabzed rhc Buck data 10 our results for the maumum st u’ = 4. E&I&'-
Fig. 4. Angle mtcgmtcd quenchmg cross section (4) d&Ek_m. 3s 3 function of EL_m_ .. as evaluated for an cncrgy transfer ALT“&rot concspondmg lo u’ viirahonal quanta of Nz.Thcsc data for an imthl kinettc energy _- of 0.16 eV arc normahzcd to 3 to131 qucnchmg uoss scdlon of I7 A* 3s adopted from Barker and Weston [ 161. For comparnon uwcrse qucnchmg rates from Buck et PL [IS] (0) and a prior translational cncrgy dtiibutlon [ 191 are shown (-).
References [I ] S. Lemon1 and G.W. Flynn, Ann Rev. Phys. Chcm. 28 (1977) 261 [2[ W H. Brcckcnrldgc and H. Umcmoto, m: The dynamla of the cvclted state. cd. K. Lwlcy (Wdcy. New York, 1982)
333
Volume 91. number 5
CHCMICAL
PHYSICS LETTERS
13 I I.V. Hcrtcl, m The dynarnlcs of the cvcllcd stale, cd K. LawIcy (Wrlcy, New York, 1952). ]4] A. BJCIK and E.E. Ndatm. Chcm. Phys. Letters I (1967) 179 [S] E. Baucr, E-R. rrshcr and F.R. Glmorc, J. Chcm. Phys. 51 (1969)4173. [6] P. Botschwina. W. hlcycr, I V. Hcrtcl and W. Rcibnd. J Chcm Phys. 75 (1981) 5438. 171 P. Hab&z.Chcm. Phys. 54 (1980) 131. 181 W. Rcilmd, H.-U Trttcs, LV. Hcricl, V. Bona&-Koutcc~y and hl. Pcrsico. 1. Chcm. Phys , to be published. 191 W. Rclland, H.-U. T~ttcs snd I.V. Hcrtcl. Phys. Rev. Lctlcrs 48 (1982) 1389. lo] I.V. H&l. H. Hofmann and K A. Rat, J. Chem Phys. 71 (1979) 674. t 11 J A S~lvcr, N.C. BLlsand H. KWCI, J. Chcm. Phys. 7 I (1979) 3417.
334
24 September 1982
[ 121 P. Archuzl and P. Hab&z, to bc pubhshcd. [ 131 G. Jamrcson, W. Rcdand, C.P. Schulz, H.-U. Trttcs and
[ 141
I.V. Hcrtel, J. Chcm. Phye. lo bc published. R. Diircn. H-0. Hoppc and H. Pauly, Phys. Rev. Lcttcrs
37 (1976) 743. [ 151 I.V. Hcr~cl and W. Stall, Advan. At. hfol. Phys. 13 (1978) 113. [ 161 J R. Barker and R.E. Weston. J. Chcm. Phys. 65 (1976) 1427. 1171 D.H Campbell and J.W.L. Lcw~s, Appl. Opt. 20 (1981) 4102. [ 181 U. Buck, E. Lcssncr and D. PUSI, J. Phys. 813 (1980) L 125 [ 191 A.D. Wdson and R-D. Lcvmc, Mol. Phys. 27 (1974) 1197. 1201 W. Relnd, G. Jamieson, H.-U. Tit& and 1-V. Hertcl, 2. Physrk A306 (1982), IO bc publihscd. 1211 V. Bonacr&KouIccky and D. Paplcrowska, pnvatc commurucahon.
Volume 91, number 5
CROSSED ANGULAR
BEAM STUDY DISTRMJTIONS
OF THE Na(3 2P3,.$ + N, QUENCHING PROCESS: WITH PRODUCT
W. REILAND, C.P. SCHUZZ, H.-U. TITTES InsI~tuCfur Rcccn’cd
Moiekiilphysik,
18 June
24 Scptcmbcr 1982
PHYSICS LCrrERS
STATE
ANALYSIS
and I.V. HERTEL
l+ele Umversit~r Berlin. Artumaliee 14, 1000 Berhn 33, IVeSt GerrmKJ
1982
The transfer of clectromc to vIbrationa rotatIonal cncqy for Na(3 *P, *) + N2(u = OJ>-+ Na(3 *S1p) + Nz(u’./‘) IS studlad m PII crtperimcnl wIh crossed supcrsomc Ns and N2 beams and smglc-mo 1 c EWdye bscr CWIICIIIO~ (rchtnc hmcl~c cncrgy 0.16 eV). At c m fonwrd scattcrmg the u’ = 3 state IS cxcltcd to more than SO%, accompamcd by a nowublc ro~st~onrl evcitatlon smountmg Lo over 0.1 cV. ror backward scattermg the vrbratlonal lcvcls U’ = 2.3 and 4 LUCdommantly pop&ted. TM anguh dfitributlons show 3 pronounced nwow forward m&xrmum and 3 smaller (8-30s) backward peak. The obWViltlOIlS XC rstionahzcd in terms of Ihc bond stretch ~.ttractron model.
1. Introduction
cm. energy EL m. is measured
and may vary between
energy of 2.26 eV [E,,_ + electronic energy of Na(3 ‘PJ ?)I. In the present study, m contrast to previous work / IO,I I 1, both the c.m. scattenng angle ec,,, and EL m are analysed and significant structure as a fun&Ion of both variables ISobserved. The pseudopotentlal calculations by Habitz 171 for the ground (% ?A’) and excited (‘;i *A’ and 2 ?A”) states PESs Indicate that the mechanism for this nonadiabatic process is sunilar to that encountered for Na t II2 [6] : A bond stretchmg attraction between Na* and N2 on the excited state A surface leads to an (avoided) surface crossmg with the % ground state at 0 and the total available
The quenching of alkali resonance radiation by diamolecules has long been subject to mtenslve experimental and theoretical studies. As reviewed elsewhere [l-3] substantial progress in understanding these basic mechamsms has been made during recent years. While earher theoretical approaches [4,5] based on guesses of the mteractlons using the “ionic mtermedate” model served as a useful first guideline for further studies, our present knowledge of the poientlal energy surfaces (PESs) for some prototype systems like NaHZ [6], NaN2 [7] and NaCO [8] allows at least a semiquantitative understanding of certain features of the electronic to vibrational rotational translational energy transfer mechanism (E-VRT). Some results on angular distribution measurements of the differentral quenching cross section with an analysis of the product energy dntribution using a new scattering apparatus are reported elsewhere for Nat Hz [9] and Na + CO [8]. III the present work we wish to present a first detadcd study of the double differential cross section d%/ =i.rn. dRc.m, for the process tomic
Na(3 *PsIZ) + N2(u = 0,11+ Na(3 2S1,1) + N#‘,I? using single-mode cw dye laser excitation of Na in a state of the art experiment with crossed supersonic atomic and molecular beams. The imtial center of mass (cm.) kmetic energy is E,,. = 0.16 eV and the final 0 009~2614/82/OOOO-OCKIO/$O2.750 1982 North-Holland
an internuclear distance R,
= 4.2 no if the molecular
to rc = 2.25 UO.It is energetically most easily accessible in the perpendicular (G,) approach into whrch the system may be partially clamped dunng the approach in the excited state. After a surface hop at R, to the ground state the N, molecule is in a nonequtibrium distance and thus starts to vibrate while Na and Nz quickly receed on the strongly repulsive ground state surface. At present only prehmmary classical trajectory calculations are completed [19-l. ‘The present experimental observations lend strong support to the qualitative picture sketched above and it is hoped that they will stimulate increased theoretical efforts for a full ab initio understanding of this prototype molecular dynamical process. N2 bond is stretched
329
Volume 9 I. number 2.
CHChtlCAL
5
PHYSICS
shows that in this elastic scattering
Experimental
~hc experimental schematlc of the crossed beam apparatus IS cssentlally that described in ref. [IO]. The nqor
lmprovemcnt
Is the use of a supersomc
molecu-
lar N1
beam and the accesslblhty of c.m. scattermg angles from tJcm = 0 to 180” 1~1th an estinlated overall rcsolutlon of 23”. The method to transform laboratory scattering data into the center of mass system ISdescribed in ref. [lo], details on the current procedure of data taking as well as on the beam properties is given m ref. [8] for the kinematlcally identical Na-CO case and a full descrlptlon of the apparatus and a hlonte Carlo sunulatlon of the kinematics together with new data on NaNO and NaO? wrll be pubhshcd elsewhere 1131. Two types of measurements arc reported in the present work. (I) Energy transfer spectra, I.e. the double dlfferentlal cross sectlon dIo/dE’, m_da,,,. for the quenchmg process is observed as a function of the fmal relative cm. translational energy I!&, for fixed cm. scattermg angle, which is equivalent to a determmatlon of the energy AEvlbrot = 2 26 eV - EL,, transferred tnto vlbrattonal rotational energy of the molecule. (h) Angular
dlsrriiutions,
mlncd as a function
I.e. d2u/dE;,,,,
dSZc ,.,,. 1s deter-
of the scattermg
angle 0, m_ for a
filed value of Ei m.. Both types of measurements neccssitate an appropriate change of the laboratory velocity and scattering
angle of the so&urn
atoms
detected
after
the
colhslon process as determmed from the Newton diagram [8] _In the present work energy transfer spectra and angular distnbutlons are normahzed to each other by fittmg the ratio of forward to backward scattering as obtained from the angular dlstrlbutlons to the energy transfer spectra at 0, ,,,, = 0” and 180”, with an estunatcd uncertamty of less than 15%. Scattermg from the background gas was subtracted by appropriate chop. ping of the molecular beam. All results on the double differential quenclung cross section reported here originate from a measurement of the lfference between signals with and without the dye laser for Na excitation switched on, so that scattermg from
unexcited
atoms
was subtracted.
However,
as dls-
cussed previously [IO], purely elastic scattermg from excited Na* cannot be distinguished from quenchmg Lmthout energy analysis of the scattered particles and thus m the range of small EL,,. the scattermg data can no longer bc umquely evaluated. A sunple analysis even 330
24 Septcmbcr
LITI-ERS
a difference
between
thus energy
analysis
region
several cross sections
1982
the slgnal is [14,lS]
and
with Hugh background
suppresslon ISa necessary prerequisite for any rehable crossed beam quenchmg study For the present work we are confident m evaluating the data unambiguously for Ef.m, > 0 4 TV as estimated from a more detailed study of the elastic region [ 131 and we report scattering dlstnbutions only for ES.m. above this hmit.
3. Results and discussion 3.1. Energy transfer spectra Fig. I shows the measured energy transfer spectra for Nz withE,, =O.l6eVinWal relative kinetic energy at three center of mass scattering angles, 0, m = O”, 90” and 180”. The error bars indicate a typical 67% confidence Interval as derived from statlstlcal uncertainties of the measured count rates. The experunental results illustrate that roughly 50% of the nvailable total energy E. = 2.26 eV = E,_ + 2.1 eV IS transferred into internal motion of N2. 731sagreeswith
quenchmgofNa*by
our prevlrus
findings
[lo]
and the present
B,,,.
= O”
the earher data.
However, since the angular resolution is now substantially improved (AfI,,_ = 5”) the maximum cross section appears now at &?nbrot = 0.9 eV which is slightly less than previously reported for the data averaged over 115”. Sliver et al. [ I1 1 have reported 0.83 eV but their raw data (fig. 4 of ref. [ 161) would be consistent with a significantly different energy transfer as well. while our present results are conclusive to wlthin a few per cent. One of the especially remarkable features displayed in fig. 1 is the clearly recognizable structure in the backward scattermg which proved to be highly reproducible in several experimental runs under different conditions of the apparatus such as signal-to-noise ratio, Na-beam density, etc. Although the present experiment cannot uniquely distinguish between rotatlonal and vibrational N, energy, the observed struchue emphasizes dominanlspectrum
cssentlaUy
reproduces
ly vibrational excitation for the backward scattering:
A least-squares fit with 6 gaussian profdes of variable width and height centered at the energetic positlons for pure vibrational excitation gives excellent agreement with the measured data as indicated in fig. I. The wdt.h
Volume 9 I. number 5
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CHLhllCAL
AEwbrot 1 ev
PHYSICS
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24 Sep~smbcr
LLTTCRS Table Rclatw h’Ck+
1982
I N2 cwtation probdbdity for dlffcrcnt vrbrrtion.rl dcnvcd from the “deconvolu~~on” whcatcd In fig
u’ 3s
I v’
Rclalwc drffcrcntul 0 cm.
qO0
cross section (in !Z)
O,,
=90°
o,m.=
0
9
0
I
t
0
I
2
5
8
8
0
3
52
I7
22
4
22
36
30
5
II
24
29
9
IO
6 7
9
180°
6
= 0” near the maxrmum. the data for 0,. favour an even larger amount of energy transfer mto the molecule. We thus have to conclude that for O,,. = 90” and k particularfor B,,. = 0’ rotationalexcitatiorz becomes significant and amounts to at least 0.1 e’ particular
From the mcasurcd data an even larger amount of rotntronnl exatntron cannot be excluded s,r~ce no wbra-
E;, IeV FIN. I _Double ddkcnkd qucnchmg cross scctrons for Na*+N2 at diffcrcnt cm. swttcrmg angles 0, m as a functron of the final rehtivc kmetic c m. cnrrgy Ei m. anh of the cncrgy transfcrrcd to the molcculc ti,b,ot =.&o - Ei m., with Eo = 2 26 cV. l-01 comparison the cncrgy SC& IS also gwcn in units of tiial Nz nbratlonal quanta IJ’. Elperlmcntal pomts (0) wth st.rtatiwl error bars(f) arc gwcn togclhcr wth a least squares frt (-) by 6 gaussian drstributlons (- - -) ccntcrcd at each u’. Now the dlrfcrcnt scrlcs for the three spectra normahzcd to the mcdsurcd angular rhstributrons.
tional structure is distinguishable at these scattering angles. Preliminary results from trajectory calculations by Achirel and Habitz [ 121 show indeed that rotation, quanta up to j’> 60 may be excited and a convolutior of theirj’ state distrtbution for the U’ = 2 level with ou energy profile shifts the peak msxlmum by 0.15 eV an increases the energy fwhm by 0.2 eV as compared to purej’ = 0 excitation. The explanation for these obscr vatlons IS probably similar to the simple model for the rotational excitation that has been introduced when di cussing a solar energetic shift of the vlbratlonal peak: observed for Na* + Hz [9] . The experimental tits to our data in fig. I, even though somewhat arbitrary for e rm. = 0” and 90°, allow to give a quantitative summa ry of the energy transfer spectra in terms of “deconvoluted” relative probablhties for excitation of the d6 ferent u’ vibrational levels as displayed in table I.
of the “vibrational”
peaks is in good agreement with the energy resolution estimated from the molecular
for forward scattering as well as for dcm_ = 90” the same fitting procedure givespeak widths (fwhm) which are up to 0.1 eV wider
3.2. Angular distributions
beam kinematics. In contrast,
than the estimated energy resolution and, as seen in
Our results for energy and angle resolved double dif ferential cross sections I@,_ ) = d2aldE&. dQ,_ as a function of center of mass scattering angle is shown 331
Volume 9 I, number 5
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scallerlng
angle o.,
CHEMICAL
PHYSICS LETTERS
24
September 1982
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Fg. 2. Double rhffcrcntlal quenchmg cross sc~t~ons;ISB funcllon ol center of masssnttermg angle Bc m (+). The pammeter 1s to the indleculc ~~cn ut ututs of the Cllerg)’ tILlllSfC1 ti,,,brot vibrational quanta U%J of the Nz. For complvlson with fig. 1 the ecm = O” energy transfer spectrum ISalso shown (0).
2 for different amounts of energy transfer. At present, no attempt has been made to “deconvolute” the angular distribution for energy and angular resolution, so that the experimental material IS presented as unbiased as possible, merely using the sunple kinematin fig.
ic transformation
from lab to c.m. frame wth the ap-
propnate jacobian. The angular resolution as estimated from beam kmematics is better than +3O. In contrast, Sliver et al. [ 111 have used a “deconvolutlon” procedure based on the (obviously wrong) assumption of the angular distributions being independent of &?Wbrot_ Thus only data for energy unresolved cross sections were reported in ref. [ 1l] apparently Including the elastic scattering region as well. For reasons dlscussed in section 2 data evaluation in this range of E’,. energies is highly ambiguous. The pronounced and narrow forward peak at all values of the energy transfer appears to be most sigmficant, in particular so for &,brot = 3fiiw. Whde this findmg ISsuntlar to the Na*-H2 case [9], the clear backward peak seen presently was not observed there. It amounts to in between 8% and 30% of the forward maxunum increasing in height with the aoumt of energy transferred to the N2. The bond stretching attraction model for the E-VRT process as discussed III section 1 lends itself to a suggestive explanation of this behaviour. The backward peak indicates a tendency towards complex formation dunng the interaction process which becomes more important as larger stretching of the N, 332
Fg. 3. Double dtffercntnl qucnchmg cross section; multiphed m by mec.m. as D function of 17o m._ Pameter IS timjrot umts of Nz nbrattonal quanta 1. These anguku dutributions are normshzcd rektlve to ach other by mans of the ec m = 90” energy transfer spectrum of fig 1.
molecular bond is necessary before reaching the crossmg seam. This is equivalent to saying that it becomes more probable to channel energy into the molecular bond when the interaction time on the excited state PES is prolonged. The observed experimental trends become even more evident when the cross sections are multiplied by sin Ocm. as displayed in fig. 3. (In contrast to the previous procedure we have normahzed these distributions with respect to each other by means of the ec.,, = 90” energy transfer spectrum.) The plotted values (dlu/ #Lrn. dnc_m.Isin ecm. represent the contribution of each scattering angle and energy transfer to the total quenching cross section. In a classical trajectory picture each impact parameter b contributes to this expression as 2nb db dtI/db. The rationalization of the observed angular distribution for u’ = 2 and 3 is then analogue to that given for NaH2 [9]. The pronounced forward hump in the u’ = 3 excitation seen in fig. 3 is explained as a kind of glory behaviour due to positive and negative deflection angles contributing to scattering at small 0,,.. The angular distributions for higher &&rot = 4-6 ho exhibit much stronger contributions from intermediate
CHEhllCAL
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scattering angles and roughly resemble the behaviour of a classical collision complex, which would give a constant value as a function of scattering angle in this type of display. 3.3. Integrated cross sections For
prxtiwl
npphxtions
24 Scptcmber 1982
PHYSICS LEITERS
(see e.g. ref. [17] ) ZISweti
as for comparison with bulk measurements it appears useful to also report angular integrated energy transfer cross sections da/dE’,_ as a function of energy transfer. For this purpose we simply Integrate the normalized I@,_) distributions of fig. 3. The results are shown in fig. 4. Yet one more integration (over &A.) yields the total cross section which may be used to absolutely cahbrate fig. 4. As seen, the maxunum for the angular integrated cross sectlon IS found that an energy transfer of 4fio with approximately da/d&,,_ = 18 A*/eV. The maximum is in agreement ~th cell data for the inverse quenching process, i.e. the excitation of Na* by nbrationally excited N2 as adopted from Buck et al. [IS] _ Although a direct comparison with our data is some-
-r
what arbitrary
due to distinctively
different experimental
* the genera! tendencies agree quite well.
conditions
Both angular
integrated
results are sigmficantly
non-
with a prior translational dlstnbutlon of the Levine type [ 191. From fig. 4 we can also derive an average energy transfer (anbroI) = I .I3 eV or 5% of the total of 2.26 eV awlable which statistlcal
as seen by the comparison
emphasizes
even more the non-statistical
nature
of the
process as the prior translational energy distribution yields 67% average energy transfer.
4. Conclusions The pronounced structures observed in the present crossed beam study for this prototype non-adiabatic molecular process appear quite surprising in the light of earher theoretical quenching models. The new bond stretch attraction mechanism revealed by recent PES calculations [6-S] allows a qualitative discussion_ The remarkable features observed III the present work together wllh refmed studlcs of polarization dependences for this process [20] should serve as a crucial test to forthcoming theoretical efforts. Improved PES calculaions for the NaN, system with large scale Cl methods are on the way [2i 1. One may thus hope that an adequate scattering dynamical theory can be developed and may eventually lead to a full ab initio understanding for this type of elementary photochemlcal reactlon.
Acknowledgement Continuous sypport by the Deutsche Forschunggemeinschaft through Sonderforschungsbercich 161 is gratefully acknowledged. * WC have thcrcforc arlxtrardy normabzed rhc Buck data 10 our results for the maumum st u’ = 4. E&I&'-
Fig. 4. Angle mtcgmtcd quenchmg cross section (4) d&Ek_m. 3s 3 function of EL_m_ .. as evaluated for an cncrgy transfer ALT“&rot concspondmg lo u’ viirahonal quanta of Nz.Thcsc data for an imthl kinettc energy _- of 0.16 eV arc normahzcd to 3 to131 qucnchmg uoss scdlon of I7 A* 3s adopted from Barker and Weston [ 161. For comparnon uwcrse qucnchmg rates from Buck et PL [IS] (0) and a prior translational cncrgy dtiibutlon [ 191 are shown (-).
References [I ] S. Lemon1 and G.W. Flynn, Ann Rev. Phys. Chcm. 28 (1977) 261 [2[ W H. Brcckcnrldgc and H. Umcmoto, m: The dynamla of the cvclted state. cd. K. Lwlcy (Wdcy. New York, 1982)
333
Volume 91. number 5
CHCMICAL
PHYSICS LETTERS
13 I I.V. Hcrtcl, m The dynarnlcs of the cvcllcd stale, cd K. LawIcy (Wrlcy, New York, 1952). ]4] A. BJCIK and E.E. Ndatm. Chcm. Phys. Letters I (1967) 179 [S] E. Baucr, E-R. rrshcr and F.R. Glmorc, J. Chcm. Phys. 51 (1969)4173. [6] P. Botschwina. W. hlcycr, I V. Hcrtcl and W. Rcibnd. J Chcm Phys. 75 (1981) 5438. 171 P. Hab&z.Chcm. Phys. 54 (1980) 131. 181 W. Rcilmd, H.-U Trttcs, LV. Hcricl, V. Bona&-Koutcc~y and hl. Pcrsico. 1. Chcm. Phys , to be published. 191 W. Rclland, H.-U. T~ttcs snd I.V. Hcrtcl. Phys. Rev. Lctlcrs 48 (1982) 1389. lo] I.V. H&l. H. Hofmann and K A. Rat, J. Chem Phys. 71 (1979) 674. t 11 J A S~lvcr, N.C. BLlsand H. KWCI, J. Chcm. Phys. 7 I (1979) 3417.
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24 September 1982
[ 121 P. Archuzl and P. Hab&z, to bc pubhshcd. [ 131 G. Jamrcson, W. Rcdand, C.P. Schulz, H.-U. Trttcs and
[ 141
I.V. Hcrtel, J. Chcm. Phye. lo bc published. R. Diircn. H-0. Hoppc and H. Pauly, Phys. Rev. Lcttcrs
37 (1976) 743. [ 151 I.V. Hcr~cl and W. Stall, Advan. At. hfol. Phys. 13 (1978) 113. [ 161 J R. Barker and R.E. Weston. J. Chcm. Phys. 65 (1976) 1427. 1171 D.H Campbell and J.W.L. Lcw~s, Appl. Opt. 20 (1981) 4102. [ 181 U. Buck, E. Lcssncr and D. PUSI, J. Phys. 813 (1980) L 125 [ 191 A.D. Wdson and R-D. Lcvmc, Mol. Phys. 27 (1974) 1197. 1201 W. Relnd, G. Jamieson, H.-U. Tit& and 1-V. Hertcl, 2. Physrk A306 (1982), IO bc publihscd. 1211 V. Bonacr&KouIccky and D. Paplcrowska, pnvatc commurucahon.