字幕表 動画を再生する 英語字幕をプリント The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. 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.