Molecular Beams and Collision Theory

At this point the author must take a stand. My love for physical chemistry s particular version of the reductionist endeavor leads me to beheve that chemistry can be reduced to physics. However, in spite of mounting evidence for biological reductionism, it is difficult for the author to conceive of himself as nothing more than a bag of particles. As such, the author must advocate biological hoHsm despite the burdensome paradox this presents. With these sentiments expressed, we proceed with physical chemistry. 

The observable quantity in molecular beam experiments is called the differential reaction cross section danj nr( jO,)/dQ, defined by [7] 

As such, the units of danj n v,n)/dQ are area per solid angle. Another important observable is the integral reaction cross section 7np,nr( ) which in subsequent chapters is simply referred to as the reaction cross section. This quantity is defined by 

Experimentalists measure integral reaction cross sections most directly in a bulb apparatus which does not detect the scattering angle dependence of product formation. A physical interpretation of the integral reaction cross section is the circular area centered at the target (i.e. one reactant collision partner) which, when crossed by the projectile (i.e. the other reactant collision partner), leads to a chemical reaction. 

To illustrate these definitions, we consider a collision between two hard spheres (HS) with radii ri and T2, yielding a total hard sphere radius r = ri -f T2. The HS differential reaction cross section is r /4, independent of scattering angle. The HS integral reaction cross section is Trr, consistent with circular area of radius 

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