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Differential cross sections for reactive and non-reactive scattering of electronically excited Na from HF molecules
Volume 143,number 1
CHEMICALPHYSICSLETTERS
1 January 1988
DIFFERENTIAL CROSS SECTIONS FOR REACTIVE AND NON-REACTIVE SCATTERING OF ELECTRONICALLY EXCITED Na FROM HF MOLECULES R. DOREN, U. LACKSCHEWITZ, S. MILOSEVIC ‘, H. PANKNIN and N. SCHIRAWSKI Max-Planck-Institutftir Striimungsforschung,Blittingerstrasse 4-8, D-3400 GGttingen,Federal Republic of Germany Received 5 October 1987
We have measured the time- and angle-resolved cross section for Na( 3 *P) atoms interacting with HF molecules in a crossed beam experiment. The reactive and the non-reactive channel are separated by the time-of&@ technique. The results indicate (a) two potentials to be involved in the entrance channel with well depths of about 1I5 and 375-540 meV, (b) the product centerof-massdistributions to be characterizedby slightlyasymmetric backward/forwardscatteringwith an averageof I. 15 eV as internal energy in the NaF molecule.
1. Introduction Gradually the study of chemical reactions has passed from “broad band” chemistry to state specific initial state preparation and final state analysis. For the alkali-hydrogen halide systems this state specificity has been studied with respect to preparation of vibration, rotation and translation [ l-61. All these studies were restricted to alkali atoms in their electronic ground state. Recently some work has been published on a differential scattering experiment with electronically excited Na [ 71. Theoretical work on these and related systems including electronic excitation has also been reported [ B- 121. The
experiments with electronically excited Na rely on the use of narrow band cw dye lasers, in which respect they are with their application to chemistry a final step in a long series of similar investigations of non-reactive processes [ 13,141 and similar reactive work by Rettner and Zare [ 151. The report presented here belongs to the laser excited differential scattering experiments with crossed beams. We have chosen the Na-HF system basically because it is endothermic and for the given collision energies no ground state reaction occurs which has some advantage for the evaluation. In addition it may be a rea’ Permanent address: Institute of Physics,University of Zagreb, Zagreb,Yugoslavia.
sonably good candidate for an ab initio determination of the potential energy surface. Such work would be desirable since it can be read from our results that the system is definitely not compatible with simple approximations.
2. Experimental
The basic outline of the apparatus has been described previously [ 161 especially the particular technique of performing the pseudo-random chopping by modulation of the laser light for the excitation [ 171. Other parts have been rebuilt to meet the special needs of reactive scattering investigation, notably the beam sources. For Na we use a seeded beam oven similar to the one described in ref. [ 181, with He or Hz as carrier gas. This allows us to reach velocities up to 4000 m/s corresponding to Ecollx 1 eV. The HF source is a multichannel array for which the beam parameters have been measured by Loesch and co-workers [ 21. As a by-product of the laser crossing the scattering zone we use, alternatively with the excitation, the same laser beam reflected under 45 ’ and appropriately tuned to measure the velocity profile by Doppler excitation. Such measurents taken every now and then between the succesive TOF measurements, allow a check of long term drifts of the beam velocity. 45
Volume 143, number 1
CHEMICAL PHYSICS LETTERS
For detection we have applied positive surface ionization on rhenium, considering requirements on the ionization efficiency and residence time. ACcording to ref. [ 191 we can assume equal ionization efficiency for Na and NaF under our working conditions (wire temperature x 1650 K). The results presented below are obtained from two separate sets of data namely from a measurement of the total scattered intensity as a function of the angle- and the time-resolved measurements. We evaluate these data sets by (a) using the total measurements for calibration of the time-resolved ones, (b) performing a tit to the time-resolved data with two Gaussians to yield (after integration) the non-reactive and the reactive total cross section separately and (c) subtracting the best tit of the nonreactive contribution from the TOF spectra to yield the reactive contribution separately.
3. Evaluation The total differential cross section shows two distinct features, which are due only to the non-reactive contribution. These are rainbow scattering and orbiting. For both a well depth E of the relevant potentials can be evaluated by e =@,E,,,/2
(1)
and t =Ecoll.orblO.g,
(2)
where eR is the rainbow angle, E,,, is the collision energy and Ecoll,orbis the collision energy at which orbiting is observed. To yield reliable values for the well depth both formulae need a study of the energy dependence of the cross section. For the rainbow angles the measurements at various energies can be combined to yield the e value. For the orbiting effect the energy dependence of the cross section is used to i.e. the energy, where this feature vandefine EcOll,Orb, ishes when going from a lower to a higher energy. Both these formulae are somewhat dependent on the model potential assumed [ 201 and accordingly these results are to be taken as estimates only. The TOF spectra presented below as a contour plot in the corresponding 8, v plane do not show for their reactive contribution a clear and easily interpreted 46
1 January 1988
pattern like backward or forward peaking. In the same way the individual TOF spectra are unspecific. This observation is in contrast to the above mentioned Na-HCl results [ 71. To proceed with our evaluation further it was necessary to obtain the center-of-mass distributions. For this we performed a forward convolution of model distributions with a conversion to TOF spectra, which are directly comparable to the measurements. We used the usual factorization of the double differential cross section in an angle- and an energy-dependent part as d2a -= dwdE
zP(E)
.
(3)
Considering in this report only one measured energy of the TOF spectra we did not use a cross section which depends on the incident energy. These simplications have their hazards but the results given below will justify their application. As external parameters of the convolution we used the experimentally determined velocity distributions (see above) and the value of 0.52 eV for the endothermicity of the ground state product [ 51. The energy distribution Z’(E) is counted as to refer to the internal energy of the product. This means that the corresponding energy range is given by the endothermicity and the maximum available energy in the collision E max=Ephoton+E~in,max-
(4)
For the latter this leads to a value of 2.5 eV. We should point out here that the assumed value of 0.4 eV for &in,maxis larger than the average kinetic energy of the measurement presented (0.3 eV). This discrepancy is to a certain extent artificial. It turned out that the results of the convolution were sensitive to the range of velocities allowed in the simulation. We had to make this to be defined by the 1Wlimits of the distributions of the velocities. On the other hand particles of these high velocities do not contribute substantially to the measured spectra. The result given for P(E) will therefore loose definiteness beyond 2.4 eV rapidly. 4. Results Fig. 1 shows one of the primary results, a TOF spectrum measured at a laboratory angle of 22”. The
Volume 143, number 1
CHEMICAL PHYSICS LETTERS
1 January 1988
VNa
20.0
40.0
80.0
80.0
100.0
Channel number Fig. I. Example of the time-of-flight spectrum measured for &,,,=0.3 eV at a laboratory angle of 22’. The width of time channel was 3 us. The best tit with two Gaussian functions is shown by lines.
collision energy in this example is 0.3 eV as throughout this section. The spectrum - one with decent signal-to-noise ratio - shows clearly the non-reactive and the reactive part separated. Together with the measured points we show a best fit to the experimental data based on the optimization of background and the parameters for two Gaussian functions. The best fit refers to the sum of these contributions. In the upper panel of fig. 2 we present as contour plot in the 8, o plane the sum of all measured data in their original form (reactive and non-reactive minus background). In the lower panel the reactive part is given, obtained by subtracting the non-reactive best fit and background from the measured data. The total cross section is dominated by the features of rainbow scattering, while the reactive part shows a broad distribution without clearly recognizable structure. Fig. 3 shows - as open squares - the results of a measurement of the total differential cross section, i.e. all scattered particles, non-reactive and reactive, without TOF analysis. This cross section shows as distinct features a rainbow maximum at 14” corresponding to 30” in the cm. frame and as verified by the most probable Newton diagram an orbiting maximum at 72”. It should be pointed out that these features are only due to the non-reactive contribution to the total differential cross section. Further measurements of these characteristic angles have been
VNa I
I
I
1000.0
I
2000.0
9000.0
Velocity (m/s) Fig. 2. The upper panel presents contour map in 0, v plane of total cross section in the measured region from 8” to 40” in the laboratory frame. In the lower panel only the reactive part is shown. Note that the intensity is given in a log scale.
performed at other collision energies. The classical rainbow angles (66% law) vary in inverse proportion with the energy and the common result of these measurements yields
20.0
40.0
Scattering
60.0
angle 0 lab.
Fig. 3. Measured yields for total and for reactive scattering as a function of the scattering angle in the laboratory frame.
47
Volume 143, number 1
1 January 1988
CHEMICAL PHYSICS LETTERS
6,=115meV.
total cross section. We have performed such measurements which showed very weak variations with the polarization. Further studies of this subject are required to allow a final conclusion. In addition we show in fig. 3 the reactive contribution to the total differential cross section in the angular range, where it has been measured (up to 40”). These results are obtained from the original TOF spectra by subtracting the best fit of the nonreactive part and integrating the remainder. From the angle of the centroid (14 o) to larger angles it decreases monotonically. The reactive contribution to the total intensity varies between 20% and 50%. Finally we come to the measured TOF spectra for the reactive part of the cross section. The experimental results for some angles, obtained from the original spectra by subtracting the best fit of the nonreactive peak, and after some smoothing, are shown in the left-hand part of fig. 4. We notice in these results that the reactive scattering stretches out to quite large angles of observation. For the large angles one finds essentially widespread distributions with a weak maximum in the center. The most probable Newton diagram shows these maxima to belong to medium
(5)
For the orbiting effect the evaluation of the energy dependence is more complicated because of the necessity to observe a vanishing maximum. So far we can establish with certainty only an upper and lower limit for these values: 375
(6)
Similar features have been observed [ !I 11 and verified [ 181 with respect to the potentials of the Na(3P)-Hg system in our laboratory. According to these findings we may identify E, with a C-type and t,i with a II-type interaction. There is a question whether these features are rather the results of one double minimum potential especially in the light of the new ab initio results for the Na( 3P)-HCl potential surface [ 121. Our identification assuming two surfaces is based on the fact that the double minimum potentials usually show a more complicated multiple interference pattern than the one observed here [ 221, But quantitative calculations on this subject have not yet been performed. This question can be investigated by polarization measurements of the
__--------_____ -~~~_____~-~________.
_________----
r
10.0
*
f
15.0
3
I
20.0
I
~----------____________________.
. .._________------
t
25.0
I
I
10.0
Flight time (set)
I
I
15.0
I
I
20.0
I
I
I
25.0
90”
Fig. 4. Experimental time-of-flight spectra for the reactive part of cross section (left-hand part). Simulated TOF spectra (right-hand part).
48
CHEMICAL PHYSICS LETTERS
Volume 143, number 1
45.0
Scattering
80.0
135.0
angle c.m. (degr)
j ;....~
I January 1988
The angular part of the cross section may be characterized by slightly asymmetric forward/backward scattering with a width of 70” (fwhm) for the two peaks. Sideways scattering amounts to 10% of the forward maximum. The P(E) distribution is seen to have its maximum at Em,,= 1.65 eV and slightly asymmetric wings with AE,,2=0.4 eV for E-=cE,,,,, and AE,,, = 0.5 eV for E 3 Em,,, The uncertainty of the obtained distributions are indicated in fig. 5 by dotted lines. The boundary lines (dotted) represent c.m. cross sections which yield fits to the measured data of similar quality as those for the central (full) lines.
5. Conclusion
1.0
Internal
tiergy
(e$O
Fig. 5. The center-of-mass distributions (doldw) and P(E) for the best fit to the measured TOF spectra with eq. (3) (full line). The dotted lines give limiting cases for which acceptable agreement with experimental results is obtained.
laboratory velocities of the product. At smaller angles - below 22 ’ - a second maximum belonging to high velocities is observed. The problem with these maxima is that they tend to be close to the (subtracted) non-reactive peak. A first guess would therefore discard this observation as an artefact stemming from the restricted possibilities of the leastsquares fit with two Gaussians, which may neglect possible inelasticity in the non-reactive part. We think that this reasoning must be rejected. At least if it were this influence it should become more pronounced for larger scattering angles in contrast to our observations. The right-hand side of fig. 4 shows our forward convolution of c.m. cross sections according to eq. ( 3). The above mentioned features are all seen to be reproduced by the fit. The most serious disagreement is found to be in the amplitude of the spectra for larger angles. The c.m. results for this fit are shown in fig. 5, in the upper panel dg/dw, and in the lower panel P(E) . The internal energy is measured to range between the ground state endothermicity of 0.5 eV [ 51 and E,,, in eq. (4).
The non-reactive contribution to the measured total differential cross sections for the interaction of Na(3P) with HF shows rainbow scattering and orbiting. Bot features are evaluated to yield well depths of 115 meV and 375-540 meV respectively. The forward convolution of reactive c.m. cross sections to simulate the observed TOF spectra are characterized by nearly symmetric forward/ backward (and some sideways scattering) in the angular part with half widths of 70” each. The internal energy is peaked at 1.65 eV with a nearly symmetric half width of 0.9 eV. For the interpretation of the measured data the DIPR model [ 23,241 appears to be very reasonable at a first glance. But one may exclude it due to the apparent complex formation which is not consistent with this model. The configuration of the intermediate is presently an open question. To study this problem work is in progress to calculate the Na( 3P)-HF potential energy surface and investigate the system with classical trajectories.
Acknowledgement
We wish to thank Professor Dr. H. Pauly for valuable discussions and continuous support of this work. The use of the computer facilities of the Gesellschaft fur wissenschaftliche Datenverarbeitung in Gbttingen is acknowledged. 49
Volume 143, number 1
CHEMICAL PHYSICS LETTERS
References [ 11 F. Heismann and H.J. Loesch, Chem. Phys. 64 (1982) 43. [2] M. Hoffmeister, L. Potthast and H.J. Loesch, Chem. Phys. 78 (1983) 369. [3] H.J. Loesch, Chem. Phys. 104 (1986) 213. (41 C.H. Becker, P. Casavecchia, P.W. Tiedemann, J.J. Valentini and Y.T. Lee, J. Chem. Phys. 73 (1980) 2833. [ 51F.E. Bartoszek, B.A. Blackwell, J.C. Polanyi and J.J. Sloan, J. Chem. Phys. 74 ( 1981) 3400. [6] B.A. Blackwell, J.C. Polanyi and J.J. Sloan, Chem. Phys. 30 (1978) 299. [7] M.F. Vernon, H. Schmidt, P.S. Weiss, M.H. Covinsky and Y.T. Lee, J. Chem. Phys. 84 (1986) 5580. [S] M.M.L. Chen and H.F. Schaefer III, J. Chem. Phys. 72 (1980) 4376. [9] M. Shapiro and Y.Zeiri, J. Chem. Phys. 70 (1979) 5264. [lo] N. Hijazi and J.C. Polanyi, Chem. Phys. 11 (1975) 1. [ 111 M. Baer, Mol. Phys. 26 (1973) 369. [ 121 M.M. Gallo and D.R. Yarkony, J. Chem. Phys. 86 (1987) 4990.
50
1 January 1988
[ 131 A. Fischer and I.V. Hertel, Z. Physik A304 (1982) 103, and references therein. [ 141 R. Diiren and E. Hasselbrink, J. Chem. Phys. 85 (1986) 1880, and references therein. [ 151 C.T. Rettner and R.N. Zare, J. Chem. Phys. 77 (1982) 2416. [ 161 R. Dilren, W. Griiger, E. Hasselbrink and R. Liedtke, J. Chem. Phys. 74 (1981) 6806. [ 171R. D&en, W. Grijger and R. Liedtke, Rev. Sci. Instr. 56 (1985) 377. [ 181 L. Hilwel, J. Maier and H. Pauly, J. Chem. Phys. 76 (1982) 4961. [ 191 H. Kawano and F.M. Page, Intern. J. Mass Spectrom. Ion Phys. 50 (1983) 1. [20] H. Pauly, in: Atom-molecule collision theory, ed. R.B. Bernstein (Plenum Press, New York, 1979) p. 111. [ 211 R. Diiren, H.O. Hoppe and H. Tischer, Chem. Phys. Letters 64 (1979) 357. [ 221 J.N.L. O’Connor and D. Farrelly, J. Chem. Phys. 75 (198 1) 2831. [23] M.T. Marron, J. Chem. Phys. 58 (1973) 153. [24] M.G. Prisant, C.T. Rettner and R.N. Zare, J. Chem. Phys. 81 (1984) 2699.
CHEMICALPHYSICSLETTERS
1 January 1988
DIFFERENTIAL CROSS SECTIONS FOR REACTIVE AND NON-REACTIVE SCATTERING OF ELECTRONICALLY EXCITED Na FROM HF MOLECULES R. DOREN, U. LACKSCHEWITZ, S. MILOSEVIC ‘, H. PANKNIN and N. SCHIRAWSKI Max-Planck-Institutftir Striimungsforschung,Blittingerstrasse 4-8, D-3400 GGttingen,Federal Republic of Germany Received 5 October 1987
We have measured the time- and angle-resolved cross section for Na( 3 *P) atoms interacting with HF molecules in a crossed beam experiment. The reactive and the non-reactive channel are separated by the time-of&@ technique. The results indicate (a) two potentials to be involved in the entrance channel with well depths of about 1I5 and 375-540 meV, (b) the product centerof-massdistributions to be characterizedby slightlyasymmetric backward/forwardscatteringwith an averageof I. 15 eV as internal energy in the NaF molecule.
1. Introduction Gradually the study of chemical reactions has passed from “broad band” chemistry to state specific initial state preparation and final state analysis. For the alkali-hydrogen halide systems this state specificity has been studied with respect to preparation of vibration, rotation and translation [ l-61. All these studies were restricted to alkali atoms in their electronic ground state. Recently some work has been published on a differential scattering experiment with electronically excited Na [ 71. Theoretical work on these and related systems including electronic excitation has also been reported [ B- 121. The
experiments with electronically excited Na rely on the use of narrow band cw dye lasers, in which respect they are with their application to chemistry a final step in a long series of similar investigations of non-reactive processes [ 13,141 and similar reactive work by Rettner and Zare [ 151. The report presented here belongs to the laser excited differential scattering experiments with crossed beams. We have chosen the Na-HF system basically because it is endothermic and for the given collision energies no ground state reaction occurs which has some advantage for the evaluation. In addition it may be a rea’ Permanent address: Institute of Physics,University of Zagreb, Zagreb,Yugoslavia.
sonably good candidate for an ab initio determination of the potential energy surface. Such work would be desirable since it can be read from our results that the system is definitely not compatible with simple approximations.
2. Experimental
The basic outline of the apparatus has been described previously [ 161 especially the particular technique of performing the pseudo-random chopping by modulation of the laser light for the excitation [ 171. Other parts have been rebuilt to meet the special needs of reactive scattering investigation, notably the beam sources. For Na we use a seeded beam oven similar to the one described in ref. [ 181, with He or Hz as carrier gas. This allows us to reach velocities up to 4000 m/s corresponding to Ecollx 1 eV. The HF source is a multichannel array for which the beam parameters have been measured by Loesch and co-workers [ 21. As a by-product of the laser crossing the scattering zone we use, alternatively with the excitation, the same laser beam reflected under 45 ’ and appropriately tuned to measure the velocity profile by Doppler excitation. Such measurents taken every now and then between the succesive TOF measurements, allow a check of long term drifts of the beam velocity. 45
Volume 143, number 1
CHEMICAL PHYSICS LETTERS
For detection we have applied positive surface ionization on rhenium, considering requirements on the ionization efficiency and residence time. ACcording to ref. [ 191 we can assume equal ionization efficiency for Na and NaF under our working conditions (wire temperature x 1650 K). The results presented below are obtained from two separate sets of data namely from a measurement of the total scattered intensity as a function of the angle- and the time-resolved measurements. We evaluate these data sets by (a) using the total measurements for calibration of the time-resolved ones, (b) performing a tit to the time-resolved data with two Gaussians to yield (after integration) the non-reactive and the reactive total cross section separately and (c) subtracting the best tit of the nonreactive contribution from the TOF spectra to yield the reactive contribution separately.
3. Evaluation The total differential cross section shows two distinct features, which are due only to the non-reactive contribution. These are rainbow scattering and orbiting. For both a well depth E of the relevant potentials can be evaluated by e =@,E,,,/2
(1)
and t =Ecoll.orblO.g,
(2)
where eR is the rainbow angle, E,,, is the collision energy and Ecoll,orbis the collision energy at which orbiting is observed. To yield reliable values for the well depth both formulae need a study of the energy dependence of the cross section. For the rainbow angles the measurements at various energies can be combined to yield the e value. For the orbiting effect the energy dependence of the cross section is used to i.e. the energy, where this feature vandefine EcOll,Orb, ishes when going from a lower to a higher energy. Both these formulae are somewhat dependent on the model potential assumed [ 201 and accordingly these results are to be taken as estimates only. The TOF spectra presented below as a contour plot in the corresponding 8, v plane do not show for their reactive contribution a clear and easily interpreted 46
1 January 1988
pattern like backward or forward peaking. In the same way the individual TOF spectra are unspecific. This observation is in contrast to the above mentioned Na-HCl results [ 71. To proceed with our evaluation further it was necessary to obtain the center-of-mass distributions. For this we performed a forward convolution of model distributions with a conversion to TOF spectra, which are directly comparable to the measurements. We used the usual factorization of the double differential cross section in an angle- and an energy-dependent part as d2a -= dwdE
zP(E)
.
(3)
Considering in this report only one measured energy of the TOF spectra we did not use a cross section which depends on the incident energy. These simplications have their hazards but the results given below will justify their application. As external parameters of the convolution we used the experimentally determined velocity distributions (see above) and the value of 0.52 eV for the endothermicity of the ground state product [ 51. The energy distribution Z’(E) is counted as to refer to the internal energy of the product. This means that the corresponding energy range is given by the endothermicity and the maximum available energy in the collision E max=Ephoton+E~in,max-
(4)
For the latter this leads to a value of 2.5 eV. We should point out here that the assumed value of 0.4 eV for &in,maxis larger than the average kinetic energy of the measurement presented (0.3 eV). This discrepancy is to a certain extent artificial. It turned out that the results of the convolution were sensitive to the range of velocities allowed in the simulation. We had to make this to be defined by the 1Wlimits of the distributions of the velocities. On the other hand particles of these high velocities do not contribute substantially to the measured spectra. The result given for P(E) will therefore loose definiteness beyond 2.4 eV rapidly. 4. Results Fig. 1 shows one of the primary results, a TOF spectrum measured at a laboratory angle of 22”. The
Volume 143, number 1
CHEMICAL PHYSICS LETTERS
1 January 1988
VNa
20.0
40.0
80.0
80.0
100.0
Channel number Fig. I. Example of the time-of-flight spectrum measured for &,,,=0.3 eV at a laboratory angle of 22’. The width of time channel was 3 us. The best tit with two Gaussian functions is shown by lines.
collision energy in this example is 0.3 eV as throughout this section. The spectrum - one with decent signal-to-noise ratio - shows clearly the non-reactive and the reactive part separated. Together with the measured points we show a best fit to the experimental data based on the optimization of background and the parameters for two Gaussian functions. The best fit refers to the sum of these contributions. In the upper panel of fig. 2 we present as contour plot in the 8, o plane the sum of all measured data in their original form (reactive and non-reactive minus background). In the lower panel the reactive part is given, obtained by subtracting the non-reactive best fit and background from the measured data. The total cross section is dominated by the features of rainbow scattering, while the reactive part shows a broad distribution without clearly recognizable structure. Fig. 3 shows - as open squares - the results of a measurement of the total differential cross section, i.e. all scattered particles, non-reactive and reactive, without TOF analysis. This cross section shows as distinct features a rainbow maximum at 14” corresponding to 30” in the cm. frame and as verified by the most probable Newton diagram an orbiting maximum at 72”. It should be pointed out that these features are only due to the non-reactive contribution to the total differential cross section. Further measurements of these characteristic angles have been
VNa I
I
I
1000.0
I
2000.0
9000.0
Velocity (m/s) Fig. 2. The upper panel presents contour map in 0, v plane of total cross section in the measured region from 8” to 40” in the laboratory frame. In the lower panel only the reactive part is shown. Note that the intensity is given in a log scale.
performed at other collision energies. The classical rainbow angles (66% law) vary in inverse proportion with the energy and the common result of these measurements yields
20.0
40.0
Scattering
60.0
angle 0 lab.
Fig. 3. Measured yields for total and for reactive scattering as a function of the scattering angle in the laboratory frame.
47
Volume 143, number 1
1 January 1988
CHEMICAL PHYSICS LETTERS
6,=115meV.
total cross section. We have performed such measurements which showed very weak variations with the polarization. Further studies of this subject are required to allow a final conclusion. In addition we show in fig. 3 the reactive contribution to the total differential cross section in the angular range, where it has been measured (up to 40”). These results are obtained from the original TOF spectra by subtracting the best fit of the nonreactive part and integrating the remainder. From the angle of the centroid (14 o) to larger angles it decreases monotonically. The reactive contribution to the total intensity varies between 20% and 50%. Finally we come to the measured TOF spectra for the reactive part of the cross section. The experimental results for some angles, obtained from the original spectra by subtracting the best fit of the nonreactive peak, and after some smoothing, are shown in the left-hand part of fig. 4. We notice in these results that the reactive scattering stretches out to quite large angles of observation. For the large angles one finds essentially widespread distributions with a weak maximum in the center. The most probable Newton diagram shows these maxima to belong to medium
(5)
For the orbiting effect the evaluation of the energy dependence is more complicated because of the necessity to observe a vanishing maximum. So far we can establish with certainty only an upper and lower limit for these values: 375
(6)
Similar features have been observed [ !I 11 and verified [ 181 with respect to the potentials of the Na(3P)-Hg system in our laboratory. According to these findings we may identify E, with a C-type and t,i with a II-type interaction. There is a question whether these features are rather the results of one double minimum potential especially in the light of the new ab initio results for the Na( 3P)-HCl potential surface [ 121. Our identification assuming two surfaces is based on the fact that the double minimum potentials usually show a more complicated multiple interference pattern than the one observed here [ 221, But quantitative calculations on this subject have not yet been performed. This question can be investigated by polarization measurements of the
__--------_____ -~~~_____~-~________.
_________----
r
10.0
*
f
15.0
3
I
20.0
I
~----------____________________.
. .._________------
t
25.0
I
I
10.0
Flight time (set)
I
I
15.0
I
I
20.0
I
I
I
25.0
90”
Fig. 4. Experimental time-of-flight spectra for the reactive part of cross section (left-hand part). Simulated TOF spectra (right-hand part).
48
CHEMICAL PHYSICS LETTERS
Volume 143, number 1
45.0
Scattering
80.0
135.0
angle c.m. (degr)
j ;....~
I January 1988
The angular part of the cross section may be characterized by slightly asymmetric forward/backward scattering with a width of 70” (fwhm) for the two peaks. Sideways scattering amounts to 10% of the forward maximum. The P(E) distribution is seen to have its maximum at Em,,= 1.65 eV and slightly asymmetric wings with AE,,2=0.4 eV for E-=cE,,,,, and AE,,, = 0.5 eV for E 3 Em,,, The uncertainty of the obtained distributions are indicated in fig. 5 by dotted lines. The boundary lines (dotted) represent c.m. cross sections which yield fits to the measured data of similar quality as those for the central (full) lines.
5. Conclusion
1.0
Internal
tiergy
(e$O
Fig. 5. The center-of-mass distributions (doldw) and P(E) for the best fit to the measured TOF spectra with eq. (3) (full line). The dotted lines give limiting cases for which acceptable agreement with experimental results is obtained.
laboratory velocities of the product. At smaller angles - below 22 ’ - a second maximum belonging to high velocities is observed. The problem with these maxima is that they tend to be close to the (subtracted) non-reactive peak. A first guess would therefore discard this observation as an artefact stemming from the restricted possibilities of the leastsquares fit with two Gaussians, which may neglect possible inelasticity in the non-reactive part. We think that this reasoning must be rejected. At least if it were this influence it should become more pronounced for larger scattering angles in contrast to our observations. The right-hand side of fig. 4 shows our forward convolution of c.m. cross sections according to eq. ( 3). The above mentioned features are all seen to be reproduced by the fit. The most serious disagreement is found to be in the amplitude of the spectra for larger angles. The c.m. results for this fit are shown in fig. 5, in the upper panel dg/dw, and in the lower panel P(E) . The internal energy is measured to range between the ground state endothermicity of 0.5 eV [ 51 and E,,, in eq. (4).
The non-reactive contribution to the measured total differential cross sections for the interaction of Na(3P) with HF shows rainbow scattering and orbiting. Bot features are evaluated to yield well depths of 115 meV and 375-540 meV respectively. The forward convolution of reactive c.m. cross sections to simulate the observed TOF spectra are characterized by nearly symmetric forward/ backward (and some sideways scattering) in the angular part with half widths of 70” each. The internal energy is peaked at 1.65 eV with a nearly symmetric half width of 0.9 eV. For the interpretation of the measured data the DIPR model [ 23,241 appears to be very reasonable at a first glance. But one may exclude it due to the apparent complex formation which is not consistent with this model. The configuration of the intermediate is presently an open question. To study this problem work is in progress to calculate the Na( 3P)-HF potential energy surface and investigate the system with classical trajectories.
Acknowledgement
We wish to thank Professor Dr. H. Pauly for valuable discussions and continuous support of this work. The use of the computer facilities of the Gesellschaft fur wissenschaftliche Datenverarbeitung in Gbttingen is acknowledged. 49
Volume 143, number 1
CHEMICAL PHYSICS LETTERS
References [ 11 F. Heismann and H.J. Loesch, Chem. Phys. 64 (1982) 43. [2] M. Hoffmeister, L. Potthast and H.J. Loesch, Chem. Phys. 78 (1983) 369. [3] H.J. Loesch, Chem. Phys. 104 (1986) 213. (41 C.H. Becker, P. Casavecchia, P.W. Tiedemann, J.J. Valentini and Y.T. Lee, J. Chem. Phys. 73 (1980) 2833. [ 51F.E. Bartoszek, B.A. Blackwell, J.C. Polanyi and J.J. Sloan, J. Chem. Phys. 74 ( 1981) 3400. [6] B.A. Blackwell, J.C. Polanyi and J.J. Sloan, Chem. Phys. 30 (1978) 299. [7] M.F. Vernon, H. Schmidt, P.S. Weiss, M.H. Covinsky and Y.T. Lee, J. Chem. Phys. 84 (1986) 5580. [S] M.M.L. Chen and H.F. Schaefer III, J. Chem. Phys. 72 (1980) 4376. [9] M. Shapiro and Y.Zeiri, J. Chem. Phys. 70 (1979) 5264. [lo] N. Hijazi and J.C. Polanyi, Chem. Phys. 11 (1975) 1. [ 111 M. Baer, Mol. Phys. 26 (1973) 369. [ 121 M.M. Gallo and D.R. Yarkony, J. Chem. Phys. 86 (1987) 4990.
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