Laboratory frame

FigureBl.5.10 Euler angles and reference frames for the discussion of molecular orientation laboratory frame (v, y, z) and molecular frame (x y, z).

Figure Bl.24.2. A schematic representation of an elastic collision between a particle of massM and energy Eq and a target atom of mass M2. After the collision the projectile and target atoms have energies of and 2 respectively. The angles 0 and ( ) are positive as shown. All quantities refer to tire laboratory frame of reference.

Theorists calculate cross sections in the CM frame while experimentalists usually measure cross sections in the laboratory frame of reference. The laboratory (Lab) system is the coordinate frame in which the target particle B is at rest before the collision i.e. Vg = 0. The centre of mass (CM) system (or barycentric system) is the coordinate frame in which the CM is at rest, i.e. v = 0. Since each scattering of projectile A into (v[i, (ji) is accompanied by a recoil of target B into (it - i[/, ([) + n) in the CM frame, the cross sections for scattering of A and B are related by... 

In Figure 2, we show the total differential cross-section for product molecules in the vibrational ground state (no charge bansfer) of the hydrogen molecule in collision with 30-eV protons in the laboratory frame. The experimental results that are in aibitrary units have been normalized to the END... 

Ecm energy (of collision) referred to the center of mass of the colliding particles Elab- energy (of collision) referred to a laboratory frame... 

The propagation of a shock wave from a detonating explosive or the shock wave induced upon impact of a flyer plate accelerated, via explosives or with a gun, result in nearly steady waves in materials. For steady waves a shock velocity U with respect to the laboratory frame can be defined. Conservation of mass, momentum, and energy across a shock front can then be expressed as... 

Very slow exchange. Slow exchange means that the lifetime ta = tb in each site is very long. Thus, a nucleus in site A precesses many times, at frequency (vq i a) in the rotating frame, before it leaves site A, and similarly for a nucleus in site B. Thus, there is time for absorption of energy from the radio-frequency field ffi, and resonance peaks appear at Va nd Vb in the laboratory frame. 

The way forward was proposed by Berne and Pechukas [11] many years later. Their important idea was to consider the overlap between two prolate ellipsoidal gaussian distributions. From the expression for this overlap they evaluated a range parameter which was taken to be the contact distance g and a strength parameter which was set equal to the well depth, e. If the orientations of the two rod-like molecules in the laboratory frame are represented by the unit vectors Ui and Uj and the orientation of the intermolecular vector by the unit vector f then the expression for the angular dependence of the contact distance is... 

These simple relations motivate a more formal approximation in which we first re-expand the interaction potential in a space-fixed ("laboratory-frame") coordinate system as... 

After the 90° pulse is applied, all the magnetization vectors for the different types of protons in a molecule will initially come to lie together along the y -axis. But during the subsequent time interval, the vectors will separate and move away from the y -axis according to their respective precessional frequencies. This movement now appears much slower than that apparent in the laboratory frame since only the difference between the... 

Laboratory frame The Cartesian coordinates (x, y, and z) are stationary with respect to the observer, in contrast to the rotating frame, in which they rotate at the spectrometer frequency. 

The quantities that are compared in Fig. 5.2 are mean square displacements, gi(t), of inner monomers in the laboratory frame and analogous quantities, g2 (t), in the center of the mass frame of each chain, the center of mass mean square displacement, g3(t), and mean square displacement of monomers at chain ends, (g4(t), gs(t). The precise definitions of these mean square displacements are as follows [12,20] ... 

This is most easily achieved by rotating the inner cylinder and keeping the outer fixed in the laboratory frame. Note, however, that this geometry leads to the formation of Taylor vortex motion if inertial effects become important (Reynolds number Re 1). Most rheo-NMR experiments are actually performed at low Re. In the cylindrical Couette, the natural coordinates are cylindrical polar (q, <(>, z) so the shear stress is denoted and is radially dependent as q 2. The strain rate across the gap is given by [2]... 

Fig. 21. The H atom product angular distribution in the laboratory frame for the...

Fig. 28. The D atom product angular distribution in the laboratory frame for the 0(1D) + D2 — OD + D reaction at two collision energies (a) 2.0 kcal/mol, and (b) 3.2 kcal/mol.

Laboratory frame model A means of visualising the processes taking place in an NMR experiment by observing these processes at a distance, i.e., with a static coordinate system. See Rotating frame model. 

ROESY Rotating-frame Overhauser effect spectroscopy. A variation (one and two dimensional) on the nuclear Overhauser experiment (NOE). The techniques have the advantage of being applicable for all sizes of molecule. See Laboratory frame model. 

The Hamiltonian describing the quadrupolar interaction in the laboratory frame (L), in the units of radians/s, can be written using the spherical tensor formalism as [1,6, 24]... 

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