Photon interaction cross section? What?

[Declan]

Photon interaction cross section? What?!?

Hey guys--

I'm practicing for the GRE, and I came across a question that has stuff that's not even in my textbook! I haven't found much from googling either.

Here is the question:

My instinct was to guess (C) because graphs I had seen of the Compton Effect had two peaks, representing the number of photons of a wavelength gotten at a certain angle. One peak stays the same, because they are ones that go really close to inner electrons and thus don't lose their energy, and the other peak moves based on the angle. So I thought curve 1 was the Compton Effect.

I also thought 3 was the Photoelectric because I know there is a linear relationship based on the frequency (K = h*freq - Workfunction). I couldn't find anything about the math involved in pair production, but I know that it doesn't start happening until the photon is of a certain energy (twice the electron rest energy), and energy means frequency here.

I am going insane...can someone enlighten me?

Thanks!

Answer:

Spoiler

(B). wtf.

edit: Here is what the only answer guide I could find said:

"Pair production only occurs above a certain energy on the order of MeV. Thus, all except choices
(B) and (C) remain."

Cool, I'm glad we agree.

"The photoelectric effect is dominant for low energies, so its cross-section must be line (1). Choose
choice (B)."

Huh?

 

[phyzguy]

As you said, pair production can't happen until E(gamma)>2 me = 2* 511 keV = 1.02 MeV. So you immediately know that curve 2 is pair production, narrowing it down to (B) and (C). I think the total cross section for photoelectric scattering ~ 1/E^3 for large energies, while the total cross section for Compton scattering ~ 1/Sqrt(E) for large energies, so the correct answer is (B). At least, that's what I think. Anyone else?

 

[Declan]

Well, so far we all agree about the first part. I really just need to know what "Photon interaction cross section" is. If I had to quickly guess, I'd say it's some some of flux of interacting photons. That makes sense for the Compton Effect, and pair production...but I can't really imagine what it means for the Photoelectric Effect. I mean...the crux of it is that it doesn't matter the intensity of the incident photon beam, but that they're of a certain energy (frequency), right?

 

[jtbell]

not even in my textbook!

This stuff is typically in intermediate-level "modern physics" textbooks. See for example p. 49 of Eisberg and Resnick, "Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles" which has a very similar diagram.

I really just need to know what "Photon interaction cross section" is.

"Cross section" is related to the probability that a photon interacts in a given way with matter. It depends on the type of interaction, the photon energy, and the type of material (lead, iron, whatever). In general, if a beam of N particles hits a "thin" target with thickness dx, the average number that interact in a particular way is given by

$$N \sigma n dx$$

where $\sigma$ is the cross section for that process, and n is the number of individual "targets" (atoms, nuclei or whatever is relevant) per m³ in the target material (sometimes called the number density of targets).

 

[Declan]

This stuff is typically in intermediate-level "modern physics" textbooks. See for example p. 49 of Eisberg and Resnick, "Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles" which has a very similar diagram.



"Cross section" is related to the probability that a photon interacts in a given way with matter. It depends on the type of interaction, the photon energy, and the type of material (lead, iron, whatever). In general, if a beam of N particles hits a "thin" target with thickness dx, the average number that interact in a particular way is given by

$$N \sigma n dx$$

where $\sigma$ is the cross section for that process, and n is the number of individual "targets" (atoms, nuclei or whatever is relevant) per m³ in the target material (sometimes called the number density of targets).

Yeah, I searched everywhere in Modern Physics, by Krane, couldn't find any mention of it! Unless it's called something else...

Anyway, so that seems to be pretty much what I suspected. Given some cross section, how many of the photons are interacting. But I still don't get it then...what does "dominant" mean in "the Photoelectric Effect is dominant at lower energies" ?

I trust them and I wouldn't deceive myself that I found some error which people way smarter than myself missed, but...what? So confused.

 

[jtbell]

what does "dominant" mean in "the Photoelectric Effect is dominant at lower energies" ?

It means the photoelectric effect is more likely than the Compton effect at lower energies. For any single photon, either effect is possible. The ratio of the probabilities equals the ratio of the cross sections. Which effect actually happens, is random, based on the probabilites.