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## Main Question or Discussion Point

The textbook says, "The cross section, [tex] \sigma [/tex], is the transition or reaction rate per scatterer in the target, per unit incident flux". It gives the formula

[tex] \sigma = transition \ rate \cdot \frac{1}{\# \ of \ scatterers \ in \ target} \cdot \frac{1}{unit \ incident \ flux} [/tex]

[tex] = \frac{transition \ prob.}{unit \ time} \cdot \frac{1}{\# \ of \ scatterers} \cdot \frac{1}{unit \ incident \ flux} [/tex]

It states, "Flux is defined as the number of particles crossing an area, A, in a certain amount of time, T". It gives the formula

[tex] flux = \frac{\# \ of \ particles}{AT} \cdot \frac{| \vec{v_1} |}{| \vec{v_1} |} = \frac{\# \ of \ particles \ | \vec{v_1} |}{V} [/tex]

It states that V is the volume containing the particles. It gives

[tex] flux = \frac{| \vec{v_1} |}{V} [/tex]

because in this case, they are considering only one particle. It then gives the cross section as

[tex] \sigma = \frac{transition\ probability}{unit\ time \times unit\ volume} \cdot 1 \cdot \frac{1}{| \vec{v_1} |} [/tex]

And I'm wondering, how all the sudden did volume get into the denominator? Something doesn't sound right.

BTW, this IS quantum mechanics, as the textbook is about to plug in the formulas from previously computed Feynman diagrams, which it has done a B- job of explaining so far. It's "Quantum Field Theory of Point Particles and Strings" by Hatfield.

[tex] \sigma = transition \ rate \cdot \frac{1}{\# \ of \ scatterers \ in \ target} \cdot \frac{1}{unit \ incident \ flux} [/tex]

[tex] = \frac{transition \ prob.}{unit \ time} \cdot \frac{1}{\# \ of \ scatterers} \cdot \frac{1}{unit \ incident \ flux} [/tex]

(7.132)

It states, "Flux is defined as the number of particles crossing an area, A, in a certain amount of time, T". It gives the formula

[tex] flux = \frac{\# \ of \ particles}{AT} \cdot \frac{| \vec{v_1} |}{| \vec{v_1} |} = \frac{\# \ of \ particles \ | \vec{v_1} |}{V} [/tex]

It states that V is the volume containing the particles. It gives

[tex] flux = \frac{| \vec{v_1} |}{V} [/tex]

(7.133)

because in this case, they are considering only one particle. It then gives the cross section as

[tex] \sigma = \frac{transition\ probability}{unit\ time \times unit\ volume} \cdot 1 \cdot \frac{1}{| \vec{v_1} |} [/tex]

(7.134)

And I'm wondering, how all the sudden did volume get into the denominator? Something doesn't sound right.

BTW, this IS quantum mechanics, as the textbook is about to plug in the formulas from previously computed Feynman diagrams, which it has done a B- job of explaining so far. It's "Quantum Field Theory of Point Particles and Strings" by Hatfield.

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