Translational Distributions

In the best experiments the translational energy is directly determined by mechanically chopping the beam so that a short pulse of particles is admitted to the detector chamber. The product intensity is then measured as a function of the flight time from the chopper to the detector, thereby giving the velocity distribution. Earlier techniques used mechanical devices to identify and select products of a certain velocity. Translational energy distributions also have been obtained without direct measurement of 

The detector, which usually can be rotated to various scattering angles, must be able to differentiate among the species present. Surface-ionization detectors with efficiencies of approximately 10% are employed for reactions of metal atoms yielding metal halide products. Laser-induced fluorescence has proved to be an excellent detector for group Ilb halides and a few other systems. In general, products can be detected by electron-bombardment ionization with subsequent analysis by a mass spectrometer. Unfortunately, these mass spectrometer or universal detectors have a low detection efficiency ( 0.1%,) thus, beam machines with such detectors require several differentially pumped chambers to reduce the background pressure (of the mass of interest) in the detector to torr. Modulation tech- 

It is possible to obtain translational energies by measuring the widths of absorption or emission lines. This has been realized for reactions  

---

For smectic phases the defining characteristic is their layer structure with its one dimensional translational order parallel to the layer normal. At the single molecule level this order is completely defined by the singlet translational distribution function, p(z), which gives the probability of finding a molecule with its centre of mass at a distance, z, from the centre of one of the layers irrespective of its orientation [19]. Just as we have seen for the orientational order it is more convenient to characterise the translational order in terms of translational order parameters t which are the averages of the Chebychev polynomials, T (cos 2nzld)-, for example... 

Similar behaviour is found for the singlet translational distribution function, p z), in the two smectic phases. According to the McMillan theory... 

The correlation between the translational and orientational order is reflected by the mixed singlet orientational and translational distribution function P(z, cos ). The results for this are shown in Fig. 7 for the smectic A... 

The time-of-flight spectrum of the H-atom product from the H20 photodissociation at 157 nm was measured using the HRTOF technique described above. The experimental TOF spectrum is then converted into the total product translational distribution of the photodissociation products. Figure 5 shows the total product translational energy spectrum of H20 photodissociation at 157.6 nm in the molecular beam condition (with rotational temperature 10 K or less). Five vibrational features have been observed in each of this spectrum, which can be easily assigned to the vibrationally excited OH (v = 0 to 4) products from the photodissociation of H20 at 157.6 nm. In the experiment under the molecular beam condition, rotational structures with larger N quantum numbers are partially resolved. By integrating the whole area of each vibrational manifold, the OH vibrational state distribution from the H2O sample at 10 K can be obtained. In... 

This third primary process produced the hydroxymethyl radical which was needed to explain the third low energy peak in the translational energy distribution curve. From the areas associated with each of the peaks in the translational distribution curves they were able to determine that the relative quantum yields for each of these primary process were 9,4,1, and respectively, for reactions 19, 20, and 21. 

The reaction 140 has been studied by Margitan et al. (69) a molecular beam study of reaction 141 has been carried out by McDonald et al. (70). Note that for these reactions there is a direct transformation of the initial vibrational degree of freedom into a final translational degree of freedom and vice versa. For reaction 1A1 a peak in the translational distribution of the products has been obtained by the present method, in agreement with experimental data. 

The N2 rotational distribution also showed a sub-thermal distribution (Fig. 27) with a rotational temperature of 450 K, similar to the translational temperature. Despite the cold translational and rotational distributions, the vibrational co-ordinate is excited, with excess population in the high vibrational states. Remarkably, this result had been suggested previously on the basis of threshold ionisation measurements of N2 desorbed from Pd covered field ionisation tips [129]. Unlike the translational energy distributions observed for desorption from Ru(0001) [103], the energy release on Pd(l 1 0) does depend on the vibrational state, (E) decreasing rapidly for excited N2(u) states [127]. A cold translational distribution is indicative of desorption from a bound state, where cooling of the adsorbate hindered... 

The H + X2 reactions give non-linear surprisal plots for vibrational and translational energy disposal and are approximately quadratic in form. By including an additional minimal-momentum transfer or Frank—Condon-like constraint [250, 251], the translational distributions are reproduced by a surprisal that is Gaussian in momentum. A corresponding vibrational form can be derived [241]. 

Impact heating of large clusters was shown to be a method for achieving ultrafast heating in the literal sense. Already after two or three collisions the translational distribution is nearly thermal-like and this is particularly so for the atoms inside the cluster. At high velocities, energy which is sufficient to fully dissociate the cluster is provided on a time scale comparable to that of a molecular motion. As a result, the cliaster completely... 

The quantum yields found in this case for the production of I( E,/2)(63%) are in agreement with the findings of Ling and Wilson for the translational distribution peaks ( 60% and 40%), which were originally ascribed... 

The translational distribution /(E) can be Maxwellian with vibrational temperature only at relatively low translational energies ( < i ). At higher energies ( > E ),fjL 1, and the exponential decrease of f E) always corresponds to temperature To. The critical translational energy E T ) is... 

If fast atoms generated in exothermic processes react before Maxwellization, they are able to perturb translational distribution and accelerate the following reactions. A laser-chemical... 

Other translational distribution functions F can be defined e.g. Mazur and Rubin have used the Fourier transform of a Boltzmann energy distribution. The use of such distributions leads to quantities which are more directly related to experimental conditions. 

Bradley KS, Schatz GC (1997) A quasiclassical trajectory study of H + CO2 angular and translational distributions and OH angular momentum alignment. J Chem Phys 106 8464... 

The range in < y> corresponds to different methods of transforming the data from the laboratory to the center-of-mass coordinate system. Because iEy was utilized in fitting the scattering data, the new values for Dq(M-X) ° " also change the translational distribution functions. The preferred values for E of Bal, Cal, and Sri are those denoted as SRE in ref. 101b these are the lower limits quoted in the table (private communication from R. R. Herm, 1979). 

Simple surprisal plots of the M 4- CH3X translational distributions are nonlinear. The introduction of a momentum transfer constraint yields a model in which the surprisal is quadratic in the final momentum this model provides a better fit to the data. An impulsive photodissociation... 

Section 2.6.1) of the one-dimensional statistical distribution,J rather than use a surprisal analysis based upon the information theory prior distribution. We will follow this convention and, unless otherwise specified, the predicted statistical result for Et will refer to a one-dimensional translational distribution. 

---