Question about differential cross section

[Clara Chung]

Homework Statement:

Attached below

Relevant Equations:

Attached below

I have attached the two pages in my notes and I have the following question.
1. Where have the n_t*l gone in 9.9? (According to 9.5 why do they disappear?)
2. Why J_s=sigma_tot J_i? The dimension of flux is per m^2 and sigma is per area too, the dimension is not right...

 

[hutchphd]

View attachment 242124
View attachment 242125
I have attached the two pages in my notes and I have the following question.
1. Where have the n_t*l gone in 9.9? (According to 9.5 why do they disappear?)
2. Why J_s=sigma_tot J_i? The dimension of flux is per m^2 and sigma is per area too, the dimension is not right...

Looks like an error to me...

 

[jtbell]

Yes, insert $n_t l$ into (9.9) in such a way that the units are consistent on both sides.

A physical reality check: if $l = 0$ or $n_t = 0$, i.e. the target disappears completely, what should we expect $J_s$ to be, regardless of $J_i$?

 

[Clara Chung]

Yes, insert $n_t l$ into (9.9) in such a way that the units are consistent on both sides.

A physical reality check: if $l = 0$ or $n_t = 0$, i.e. the target disappears completely, what should we expect $J_s$ to be, regardless of $J_i$?

Yes, it should be zero :)