Frame center-of-mass

H at m energy of 1.2 eV in the center-of-mass frame. By using an atomic orbital basis and a representation of the electronic state of the system in terms of a Thouless determinant and the protons as classical particles, the leading term of the electronic state of the reactants is... 

The mass weighted position of a single nucleus v in the center-of-mass frame of a molecule with N atomic nuclei at time points t is obtained from an END trajectory and can be expressed as... 

Figure 12. Diagram illustrating the difference between nearside scattering into positive deflection angles 0, and farside scattering into negative . The arrow (chains) represents the initial approach direction of the reagents in center-of-mass frame the gray rectangle represents the spread of impact parameters in the initial plane wave. Most of the 1-TS paths scatter into positive , and most of the 2-TS paths into negative 0.

To sum up, the basic idea of the Doppler-selected TOF technique is to cast the differential cross-section S ajdv3 in a Cartesian coordinate, and to combine three dispersion techniques with each independently applied along one of the three Cartesian axes. As both the Doppler-shift (vz) and ion velocity (vy) measurements are essentially in the center-of-mass frame, and the (i j-componcnl, associated with the center-of-mass velocity vector can be made small and be largely compensated for by a slight shift in the location of the slit, the measured quantity in the Doppler-selected TOF approach represents directly the center-of-mass differential cross-section in terms of per velocity volume element in a Cartesian coordinate, d3a/dvxdvydvz. As such, the transformation of the raw data to the desired doubly differential cross-section becomes exceedingly simple and direct, Eq. (11). 

Recently, the photodissociation process, HOD + hv — OD + H, has also been studied at the 121.6 nm using the experimental technique described above. Contributions from H2O were then subtracted from the results of the mixed sample. The experimental TOF spectra of the H atom from HOD were then converted into translational energy spectra in the center-of-mass frame. Figure 17 shows the translational energy spectra of the H-atom products at 121.6 nm excitation using two different polarization schemes... 

The Hamiltonian of helium, in the center of mass frame and under the action of an electromagnetic field polarized along the x axis, with field amplitude F and frequency w, reads, in atomic units,... 

Differential scattering cross sections may be specified in the laboratory frame or, alternatively, in the center of mass frame each may be transformed into the other by well-known relationships (Levine and Bernstein 1974). 

U = En(R) is t e potential for nuclear motion. This Hamiltonian can be written in the center-of-mass frame in the form... 

In this equation the angular velocity vector co is referred to the center of mass frame coordinate system and the s are the time derivatives of the internal coordinates. Moreover, the kinetic energy matrix coefficients may be expressed as... 

To illustrate the point, let us consider the collinear reaction AB + C— A + BC. It is known (c.f., Baer [1982]) that motion of the system in the center-of-mass frame is equivalent to motion of a single particle of mass... 

Fig. 1. Integral cross sections for the CID of Cr(CO)J with Xe at a pressure of 0.1 mTorr as a function of collision energy in the center-of-mass frame (lower x-axis) and laboratory frame (upper x-axis). The symbols represent the product cross sections Cr(CO)5 (open circles), Cr(CO)4 (solid triangles), Cr(CO)J (open squares), and Cr(CO)2 (solid diamonds). The solid line represents the total cross section. Adapted from [9]...

Fig. 5. Zero pressure extrapolated cross sections for the competitive collision-induced dissociation processes of (H20)Na+(NH3) with xenon in the threshold region as a function of kinetic energy in the center-of-mass frame (lower axis) and laboratory frame (upper axis). Solid lines show the best fits to the data using the model of Eq. (7) convoluted over the neutral and ion kinetic energies and the internal energies of the reactants, using common scaling factors. Dashed lines show the model cross sections in the absence of experimental energy broadening for reactants with an internal energy of 0 K. Adapted from [45]...

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