Z axis

In the active picture adopted here the (X,Y,Z) axis system remains fixed in space and a translational synnnetry operation changes the (X,Y,Z) coordinates of all nuclei and electrons in the molecule by constant amounts, (A X, A Y, A Z) say,... 

We consider rotations of the molecule about space-fixed axes in the active picture. Such a rotation causes the (x, y, z) axis system to rotate so that the Euler angles change... 

Initially, we neglect tenns depending on the electron spin and the nuclear spin / in the molecular Hamiltonian //. In this approximation, we can take the total angular momentum to be N(see (equation Al.4.1)) which results from the rotational motion of the nuclei and the orbital motion of the electrons. The components of. m the (X, Y, Z) axis system are given by ... 

Consider the case of two neutral, linear, dipolar molecules, such as HCN and KCl, in a coordinate system with its origin at the CM of molecule A and the z-axis aligned with the intemiolecular vector r pointing from the CM of A to the CM of B. The relative orientation of the two molecules is uniquely specified by their spherical polar angles 0, 03 and the difierence <]) = - <])3 between their azimuthal angles. The leading temi in the... 

A seoond interesting experiment is to begin with a pulse whieh is far below resonanee and slowly and oontimiously sweep the frequeney until the pulse is far above resonanee. At t = -oo tlie field veetor is pointing nearly along the -z-axis, and is therefore almost parallel to the state veetor. As the field veetor slowly moves from z = -1 to z = +1... 

Figure A3.1.3. The collision cylinder for collisions between particles with velocities v and v. The origin is placed at the centre of the particle with velocity v and the z-axis is in the direction of v - v. The spheres indicate tire range, a, of the intennolecular forces.

Figure A3.10.22 Relationship between seleetivity and surfaee stnieture forn-butane hydrogenolysis on iridium, (a) Illustrations of the Ir(l 10)-(1 x 2) and Ir(l 11) surfaees. The z-axis is perpendieular to the plane of the surfaee. (b) Seleetivity for C2Hg produetion (inol% total produets) for n-butane hydrogenolysis on both Ni single erystals and supported eatalysts at 475 K. The eflfeetive partiele size for the single erystal surfaees is based on the speeified geometrie shapes [43]. A Ir/Al203 nir/Si02.

The physical situation of interest m a scattering problem is pictured in figure A3.11.3. We assume that the initial particle velocity v is comcident with the z axis and that the particle starts at z = -co, witli x = b = impact parameter, andy = 0. In this case, L = pvh. Subsequently, the particle moves in the v, z plane in a trajectory that might be as pictured in figure A3.11.4 (liere shown for a hard sphere potential). There is a point of closest approach, i.e., r = (iimer turning point for r motions) where... 

The component of the DC quadnipolar potential in the z-axis direction is described by the following equation. 

The Bloch equation is simplified, and the experiment more readily understood, by transfonnation into a frame of reference rotating at the frequency ciDq=X Bq about die z-axis whereupon ... 

The effect of an MW pulse on the macroscopic magnetization can be described most easily using a coordinate system (x, y, z) which rotates with the frequency about tlie z-axis defined by the applied field B. 

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

Figure Bl.16.14. Top, the canonical axes for triplet naphthalene. The z-axis is directed out of the plane of the paper. Bottom, energy levels and relative populations during the CIDEP triplet mechanism process. See text...

A unifonn monoenergetic beam of test or projectile particles A with nnmber density and velocity is incident on a single field or target particle B of velocity Vg. The direction of the relative velocity m = v -Vg is along the Z-axis of a Cartesian TTZ frame of reference. The incident current (or intensity) is then = A v, which is tire number of test particles crossing unit area nonnal to the beam in unit time. The differential cross section for scattering of the test particles into unit solid angle dO = d(cos vji) d( ) abont the direction ( )) of the final relative motion is... 

Solution of this set for F R) represents tire adiabatic close-coupling method. The adiabatic states are nomrally detennined (via standard computational teclmiques of quanUim chemistry) relative to a set of axes (X, Y, Z ) with the Z- axis directed along the nuclear separation R. On transfomring to this set which rotates during the collision, then /(r, / ), for the diatomic A-B case, satisfies... 

Figure C 1.4.7. Spatial variation of the polarization from tire field resulting from two counteriDropagating, circularly polarized fields witli equal amplitude but polarized in opposite senses. Note tliat tire polarization remains linear but tliat tire axis rotates in tire x-y plane witli a helical pitch along tire z axis of lengtli X.

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