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  • MICHAEL SHORT: Anyway, today is going

  • to be a lot lighter than the past few days, which have been

  • heavy on theory and new stuff.

  • And I want to focus today on what can you

  • do with the photon and ion interactions with matter.

  • So we're going to go through a whole bunch

  • of different analytical and materials

  • characterization techniques that use the stuff that we've

  • been learning and see what you can actually do.

  • And I'll be drawing from examples

  • from the open literature, from textbooks,

  • and from my own work.

  • So stuff I was doing here on my PhD thesis

  • is actually a direct result of what do we do here in 22.01.

  • So a quick review just to get it all on the board of what

  • we've been looking at.

  • So I don't hit anyone on the way in.

  • We talked about different photon interactions, which include

  • the photoelectric effect.

  • Let's say this will be the energy

  • of the scattered whatever, and this will be its cross section.

  • We talked about Compton scattering.

  • We talked about pair production.

  • For the photoelectric effect, the energy of the photoelectron

  • comes off like the energy of the gamma

  • ray minus some very small difference, the binding

  • energy of the electron.

  • Let's just call it Eb.

  • And this effect starts when you hit what's

  • called the work function.

  • I'm just going to put this all up there,

  • so when we explain the analytical techniques,

  • we can point to different bits of this

  • and explain why we use these different things.

  • The cross-section, I made sure to keep this handy,

  • so I don't want to lose it.

  • Strongly proportional with z.

  • So the cross-section comes out of another line.

  • What was it proportional to?

  • Oh yeah, this is nuts.

  • It's like z to the fifth over energy to the 7/2,

  • which says that for higher z materials,

  • the photoelectron yield is much, much stronger,

  • and it's way more likely that way lower energy.

  • So you can imagine if you wanted to use

  • this in an analytical technique, and you

  • want to study which photoelectrons come from which

  • elements, you might think to use a low energy photon to excite

  • them, not a high energy photon, because like we had done

  • a couple of times before, if we draw

  • our energy versus major cross-section range,

  • we had a graph that looks something like this, where this

  • was the photoelectric effect.

  • This was Compton scattering.

  • This is pair production.

  • And so by knowing what energy--

  • oh, I'm sorry.

  • That's supposed to be z.

  • And this would give you the dominant process

  • that each the combination of energy and z.

  • So if you know what energy photons you've got

  • and what you're looking for, well, there you go.

  • Let's see.

  • What was the energy of the Compton electron?

  • Remember the wavelength formula.

  • It was like alpha 1 minus cosine theta over--

  • let's see.

  • Another 1 minus cosine theta.

  • In came the gamma ray energy.

  • What was the part that came beforehand?

  • That's why I have this here because I don't

  • want to write anything wrong.

  • It's good to have it all up there at once.

  • 1.

  • Yeah.

  • That's all I was missing.

  • Cool.

  • And the cross-section for Compton scattering

  • scaled something like z over energy, something pretty

  • simple, not nearly as strong as pair production

  • or photoelectric effect, so you can

  • think Compton scattering happens much more

  • dominantly at low z or the other two

  • don't really happen that much at low

  • z, whichever way you want to think of it.

  • And for pair production, you get a whole mess of stuff.

  • You get positrons coming out.

  • You get a bunch of 511 keV gamma rays

  • and all sorts of other things you can detect.

  • And the cross-section, this one's

  • got the funny scaling term.

  • This one, yeah.

  • It's like z squared log.

  • Energy over mec squared, so some z squared kind of dependence.

  • So let's keep those up for now.

  • Let's get the electron ones in.

  • AUDIENCE: [INAUDIBLE] mez squared?

  • MICHAEL SHORT: Was it z squared?

  • Let me check.

  • No, that's a c.

  • AUDIENCE: [INAUDIBLE]

  • MICHAEL SHORT: Yeah.

  • Yeah, just make sure that's clearly a c squared.

  • So now let's call it charged particle,

  • or just more generally ion electron interactions.

  • Since these are more fresh in our head,

  • what are the three ways in which charged

  • particles can interact with matter that we talked about?

  • Just rattle off any one of them.

  • AUDIENCE: Bremsstrahlung?

  • MICHAEL SHORT: Yeah, Bremsstrahlung or radiative.

  • What else?

  • AUDIENCE: [INAUDIBLE]

  • MICHAEL SHORT: Is what?

  • AUDIENCE: Ionization.

  • MICHAEL SHORT: Ionization.

  • Which we'll call inelastic collisions.

  • And?

  • AUDIENCE: Rutherford scattering.

  • MICHAEL SHORT: Yep, Rutherford scattering.

  • Which are kind of elastic or hard sphere collisions.

  • And if we had to make kind of a table of when

  • do we care about which effect, let's

  • say this was an ion or electron, scattering off

  • of either electrons or nuclei, in either elastic or inelastic

  • ways.

  • First of all, when do we actually

  • care about elastic scattering off

  • of electrons, which would be hard sphere collisions off

  • of electrons?

  • To help get you going, in an elastic collision,

  • the maximum energy transfer can be this formula gamma

  • times the incoming energy, where gamma

  • is 4 times the incoming mass times the mass of whatever

  • you're hitting over n plus big m squared.

  • Let's say if one of these masses was mass of an electron.

  • What is gamma approximately equal for most cases?

  • Well, let's say this was like electrons scattering off

  • of protons or vice versa.

  • How much energy could an electron

  • transfer to a proton in an elastic collision?

  • Basically zero.

  • The only time which this actually matters

  • is if it's an electron hitting another electron, in which case

  • you can have pretty significant energy transfer.

  • So I'd say for elastic collisions off of electrons,

  • you only care about those for other electrons.

  • And I'm going to put in low energy electrons.

  • Why do we only care about them for low energy electrons?

  • Or in other words, what are the other methods of stopping power

  • or interaction-- yeah, Chris.

  • AUDIENCE: [INAUDIBLE]

  • MICHAEL SHORT: Exactly.

  • Yep.

  • We already saw that Bremsstrahlung

  • the radiated power scales with something like z

  • squared over m squared.

  • So with a really small mass and a really high z

  • and also a higher energy, you end up

  • radiating most of that power away as Bremsstrahlung.

  • And there's not much of a chance of elastic collision.

  • So we only care about low energy electrons

  • when it comes to elastic collisions with electrons.

  • For inelastic collisions with electrons,

  • well, that's the hollow cylinder derivation

  • that we had done from before where

  • you have some particle with a mass m and a charge little ze,

  • getting slightly deflected by feeling the pull--

  • depending on what charge it is, it could be towards or away--

  • of that electron away from some impact parameter B.

  • So we care about this pretty much all the time.

  • Electrons and ions or stripped bare nuclei

  • actually matter in this case.

  • For elastic collisions off of nuclei,

  • this is what Rutherford scattering is.

  • It's a simple hard simple hard sphere collisions,

  • so this matters pretty much all the time.

  • What about inelastic collisions with nuclei?

  • What does an inelastic collision actually mean with a nucleus?

  • So fusion could be one of them, but let's go more generally.

  • We have some nuclear reaction, where it's the old thing

  • that I keep drawing all the time of some little nucleus striking

  • a large nucleus.

  • In an inelastic collision, this is

  • the case we haven't considered yet,

  • but I want to show you what actually happens.

  • In an inelastic collision, these two nuclei

  • join together to form what's called

  • a compound nucleus or CN, at which point

  • it breaks apart in some other way.

  • So there might be some different small particle

  • and some different large particle coming off.

  • But in an inelastic collision, it's

  • almost like the incoming particle is absorbed

  • and something else is readmitted.

  • It could be that same particle at a different energy,

  • and it could be a different energy altogether.

  • So yeah, I'd say fusion is an example.

  • It's kicked off by an inelastic collision,

  • because you've got to have some sort of absorption

  • event of the small nucleus by the big nucleus.

  • And then, maybe if it fuses and just stays that way,

  • it releases a ton of its binding energy,

  • well, that's pretty cool.

  • So these actually do matter, but not

  • for all energies in all cases.

  • So let's go back to the Janis database of cross-sections

  • to see when inelastic scattering actually matters.

  • Bring us back to normal size.

  • And we'll look at some of the cross-sections

  • to see when do we actually care about inelastic scattering?

  • So we haven't selected a database yet.

  • Let's say we're firing protons at things.

  • And pick a database that actually

  • has some elements listed.

  • Not a lot.

  • But iron, that works.

  • So we can look at the difference between the elastic scattering

  • cross-section and the anything cross-section.

  • So the red curve here--

  • can I make it thicker easily?

  • Probably.

  • Yeah, I can make it thicker pretty easily.

  • Easier to see.

  • Plots.

  • Wait.

  • That's not what I wanted.

  • I'm not going to mess around with this anymore.

  • Do you guys see the two lines?

  • OK, so this is the elastic scattering cross-section.

  • Kind of funny to see it negative.

  • But then there's the anything cross-section which

  • picks up at around 3 MeV or so.

  • And it usually takes somewhere between 1 and 10 MeV

  • for inelastic scattering to quote unquote turn on,

  • and that's because you have to be

  • able to excite the nucleus to some next energy level.

  • So sending in a proton at like 0.01 MeV

  • is not going to excite any of the internal particles

  • to a higher energy level.

  • So if you want to see some pretty interesting cases,

  • let's go to incident neutron data

  • where we have a ton of this data.

  • And I'll show you some examples.

  • We've got lots more data for neutrons.

  • So now we can look at some of these cross-sections.

  • Like this z n prime.

  • Let's take a look at what that looks like.

  • That means a neutron comes in.

  • Different neutron comes out.

  • Notice that the scale only starts at 862 keV.