1 00:00:00,840 --> 00:00:03,180 The following content is provided under a Creative 2 00:00:03,180 --> 00:00:04,570 Commons license. 3 00:00:04,570 --> 00:00:06,780 Your support will help MIT OpenCourseWare 4 00:00:06,780 --> 00:00:10,870 continue to offer high-quality educational resources for free. 5 00:00:10,870 --> 00:00:13,440 To make a donation or to view additional materials 6 00:00:13,440 --> 00:00:17,400 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,400 --> 00:00:18,280 at ocw.mit.edu. 8 00:00:22,490 --> 00:00:25,280 MICHAEL SHORT: Today I want us to go more in-depth 9 00:00:25,280 --> 00:00:27,092 into the photon interactions with matter, 10 00:00:27,092 --> 00:00:29,300 and we're going to bring the theory back to something 11 00:00:29,300 --> 00:00:32,390 that we can actually start to use in doing 12 00:00:32,390 --> 00:00:33,440 shielding calculations. 13 00:00:33,440 --> 00:00:36,260 If you want to find out how much of this material 14 00:00:36,260 --> 00:00:38,720 do I need to shield this much gammas, 15 00:00:38,720 --> 00:00:40,795 we're going to answer that question today. 16 00:00:40,795 --> 00:00:42,170 First I want to start off, again, 17 00:00:42,170 --> 00:00:44,225 with Compton scattering because I messed up 18 00:00:44,225 --> 00:00:46,100 a couple of the energy things from last time. 19 00:00:46,100 --> 00:00:49,610 I got excited due to an energetic coincidence 20 00:00:49,610 --> 00:00:52,520 between the photo peak and the continent of our banana 21 00:00:52,520 --> 00:00:54,600 spectrum and one of the examples in the book. 22 00:00:54,600 --> 00:00:56,360 So I'm going to correct that now, 23 00:00:56,360 --> 00:00:58,813 and we'll go through in more mathematical detail 24 00:00:58,813 --> 00:01:00,230 why that wasn't the case, and what 25 00:01:00,230 --> 00:01:02,063 the actual quirk of physics is because there 26 00:01:02,063 --> 00:01:04,430 is a constant energy thing here that I 27 00:01:04,430 --> 00:01:06,650 want to highlight to you guys. 28 00:01:06,650 --> 00:01:08,640 So skipping ahead on the photoelectric effect, 29 00:01:08,640 --> 00:01:11,540 which I think was similar, to review Compton scattering. 30 00:01:11,540 --> 00:01:14,510 It's the same thing that we saw between two particles, 31 00:01:14,510 --> 00:01:16,610 except now one of them is a photon. 32 00:01:16,610 --> 00:01:19,370 And like I said, on the next homework, after quiz one, 33 00:01:19,370 --> 00:01:21,890 you guys will be doing the balance between energy 34 00:01:21,890 --> 00:01:24,953 and momentum, because the photons don't really have mass, 35 00:01:24,953 --> 00:01:26,870 in order to figure out what's the relationship 36 00:01:26,870 --> 00:01:29,900 between the incoming energy of the photon, 37 00:01:29,900 --> 00:01:32,060 the outgoing energy of the photon, 38 00:01:32,060 --> 00:01:33,785 and the recoil energy of the electron. 39 00:01:36,330 --> 00:01:37,830 And so these are the relationships 40 00:01:37,830 --> 00:01:39,190 we were showing last time. 41 00:01:39,190 --> 00:01:41,220 It is an interesting quirk of physics 42 00:01:41,220 --> 00:01:44,280 that the wavelength shift itself does not 43 00:01:44,280 --> 00:01:46,440 depend on the energy of the photon coming in. 44 00:01:46,440 --> 00:01:49,520 As you can see, it just depends on the angle that it scatters 45 00:01:49,520 --> 00:01:53,030 at and a bunch of constants, where that m right there stands 46 00:01:53,030 --> 00:01:55,080 for mass of the electron. 47 00:01:55,080 --> 00:01:58,050 Now that wavelength shift-- while that wavelength shift 48 00:01:58,050 --> 00:02:01,050 does not depend on the energy of the incoming photon-- 49 00:02:01,050 --> 00:02:02,670 the recoil energy does. 50 00:02:02,670 --> 00:02:06,690 You can see it depends on both the energy and the angle. 51 00:02:06,690 --> 00:02:11,920 And the incoming energy of the photon equals h nu. 52 00:02:11,920 --> 00:02:14,948 And to give that quick primer on photon things, 53 00:02:14,948 --> 00:02:16,990 I want to show you guys here why that's the case. 54 00:02:16,990 --> 00:02:20,110 So even if you have a constant wavelength shift 55 00:02:20,110 --> 00:02:24,180 that might give you a non-constant energy shift. 56 00:02:24,180 --> 00:02:26,310 So even though in this constant scattering formula, 57 00:02:26,310 --> 00:02:29,700 the wavelength shift only matters with the angle, 58 00:02:29,700 --> 00:02:31,440 the energy shift actually depends 59 00:02:31,440 --> 00:02:34,440 on the angle and the incoming energy of the photon. 60 00:02:34,440 --> 00:02:37,680 So now let's look at a couple of limiting cases. 61 00:02:37,680 --> 00:02:46,730 So as we have e of the photon equals h nu goes to 0, 62 00:02:46,730 --> 00:02:48,170 what does t approach? 63 00:02:48,170 --> 00:02:49,625 The recoil energy of the electron. 64 00:02:53,880 --> 00:02:55,500 Let's just do out the formula. 65 00:02:55,500 --> 00:02:58,440 This recoil energy equals h nu, which 66 00:02:58,440 --> 00:03:02,160 is the energy of the incoming gamma times 1 67 00:03:02,160 --> 00:03:11,640 minus cosine theta over mc squared over h nu plus 1 68 00:03:11,640 --> 00:03:14,700 minus cosine theta. 69 00:03:14,700 --> 00:03:18,954 As h nu approaches 0, what happens here? 70 00:03:18,954 --> 00:03:19,840 AUDIENCE: [INAUDIBLE] 71 00:03:19,840 --> 00:03:20,673 MICHAEL SHORT: Yeah. 72 00:03:20,673 --> 00:03:22,750 H nu goes to 0. 73 00:03:22,750 --> 00:03:27,260 This fraction goes to infinity. 74 00:03:27,260 --> 00:03:29,030 And this goes to 0. 75 00:03:29,030 --> 00:03:31,580 Hopefully that's an intuitive explanation. 76 00:03:31,580 --> 00:03:34,850 If the incoming photon has 0 energy, 77 00:03:34,850 --> 00:03:38,160 it can transfer 0 energy to the electron. 78 00:03:38,160 --> 00:03:39,410 Now the more interesting case. 79 00:03:39,410 --> 00:03:46,822 What happens now as e gamma approaches infinity, 80 00:03:46,822 --> 00:03:48,780 as the photon gets higher and higher in energy? 81 00:03:55,150 --> 00:03:56,772 AUDIENCE: T just approaches h nu. 82 00:03:56,772 --> 00:03:58,658 MICHAEL SHORT: T approaches almost h nu. 83 00:03:58,658 --> 00:04:00,950 I actually want to do a quick calculation without doing 84 00:04:00,950 --> 00:04:02,270 all the limit math. 85 00:04:02,270 --> 00:04:04,970 Let's say we had energy of the gamma 86 00:04:04,970 --> 00:04:10,922 was 1 GeV, an extremely high energy. 87 00:04:10,922 --> 00:04:12,380 So all we'd plug in-- and let's say 88 00:04:12,380 --> 00:04:14,660 we wanted to find out what's the maximum energy 89 00:04:14,660 --> 00:04:15,815 of this recoil electron. 90 00:04:15,815 --> 00:04:17,690 And this is something I want to ask you guys. 91 00:04:17,690 --> 00:04:18,398 I can't remember. 92 00:04:18,398 --> 00:04:24,950 Yesterday did we say that t is a maximum at theta 93 00:04:24,950 --> 00:04:26,810 equals pi or pi over 2? 94 00:04:26,810 --> 00:04:28,320 What did we say yesterday? 95 00:04:28,320 --> 00:04:29,240 AUDIENCE: Pi over 2. 96 00:04:29,240 --> 00:04:30,365 MICHAEL SHORT: Interesting. 97 00:04:30,365 --> 00:04:31,790 It's pi, actually. 98 00:04:31,790 --> 00:04:34,430 The case where you have the largest energy transfer-- 99 00:04:34,430 --> 00:04:36,440 and sorry for not catching that-- 100 00:04:36,440 --> 00:04:38,660 is just like in a nuclear collision, 101 00:04:38,660 --> 00:04:41,090 if the photon were to back scatter, 102 00:04:41,090 --> 00:04:43,580 it transfers the maximum energy to the electron. 103 00:04:43,580 --> 00:04:46,130 So the analogy here is, like, perfect. 104 00:04:46,130 --> 00:04:48,920 Between two particles hitting and between a photon 105 00:04:48,920 --> 00:04:52,160 and a particle hitting, the maximum energy 106 00:04:52,160 --> 00:04:54,780 is when theta equals pi. 107 00:04:54,780 --> 00:04:59,360 And let's actually plug that in to find out why. 108 00:04:59,360 --> 00:05:04,490 If we say t max equals h nu-- depends on the electron coming 109 00:05:04,490 --> 00:05:05,420 in-- 110 00:05:05,420 --> 00:05:12,350 1 minus cosine theta over mc squared over h nu plus 1 111 00:05:12,350 --> 00:05:15,340 minus cosine theta. 112 00:05:15,340 --> 00:05:20,760 At theta equals pi, cosine theta goes to minus 1, 113 00:05:20,760 --> 00:05:24,740 and so then that also goes to minus 1. 114 00:05:24,740 --> 00:05:34,738 And so this becomes 2h nu over mc squared over h nu plus 2. 115 00:05:34,738 --> 00:05:36,780 And so that without worrying about the numerator, 116 00:05:36,780 --> 00:05:40,380 especially in the limit of very high energy photons, 117 00:05:40,380 --> 00:05:44,310 you can see that that actually maximizes the recoil energy 118 00:05:44,310 --> 00:05:46,630 of the electron. 119 00:05:46,630 --> 00:05:49,630 The reason we're harping so much on this recoil energy 120 00:05:49,630 --> 00:05:52,990 of the electron is because that's what we measure. 121 00:05:52,990 --> 00:05:54,730 So when we look at our banana spectrum, 122 00:05:54,730 --> 00:05:58,300 you're not measuring the energy of the photon. 123 00:05:58,300 --> 00:06:00,130 You're measuring the recoil energy 124 00:06:00,130 --> 00:06:02,860 of the electron and the ionization cascade 125 00:06:02,860 --> 00:06:04,870 that happens as all those electrons smash 126 00:06:04,870 --> 00:06:07,750 into each other, creating electron whole pairs, which 127 00:06:07,750 --> 00:06:09,722 are counted as current. 128 00:06:09,722 --> 00:06:11,680 If you guys remember from last class-- in fact, 129 00:06:11,680 --> 00:06:13,450 I'll just bring up the blackboard image 130 00:06:13,450 --> 00:06:14,950 because we can do that. 131 00:06:17,600 --> 00:06:20,500 So I took a picture of the board yesterday, 132 00:06:20,500 --> 00:06:22,300 photon interactions Part 1. 133 00:06:28,330 --> 00:06:28,960 There it is. 134 00:06:31,660 --> 00:06:34,540 We'll just use the screen as a bigger blackboard for now. 135 00:06:34,540 --> 00:06:36,280 So if you guys remember, let's say 136 00:06:36,280 --> 00:06:39,430 a gamma ray comes in and causes a Compton scatter 137 00:06:39,430 --> 00:06:42,250 event or a photoelectric emission, or whatever. 138 00:06:42,250 --> 00:06:43,960 It doesn't matter which process. 139 00:06:43,960 --> 00:06:46,870 And it liberates an electron, either by scattering off of it 140 00:06:46,870 --> 00:06:48,610 or just getting absorbed and ejecting it. 141 00:06:48,610 --> 00:06:51,010 Or it doesn't really matter how, but it creates 142 00:06:51,010 --> 00:06:52,870 this electron hole pair. 143 00:06:52,870 --> 00:06:56,650 That electron right here has this recoil energy, 144 00:06:56,650 --> 00:06:59,482 which depends on theta, the angle that it scatters 145 00:06:59,482 --> 00:07:00,190 and the incoming. 146 00:07:00,190 --> 00:07:02,620 Energy and that electron's going to keep 147 00:07:02,620 --> 00:07:04,750 moving in this material, knocking 148 00:07:04,750 --> 00:07:07,930 into other electrons very, very efficiently so 149 00:07:07,930 --> 00:07:11,170 that most of the energy of that electron recoil 150 00:07:11,170 --> 00:07:14,380 actually gets counted as other electrons being freed. 151 00:07:14,380 --> 00:07:15,940 We're going to go over on-- 152 00:07:15,940 --> 00:07:20,180 well, next Friday-- electron nuclear interactions, 153 00:07:20,180 --> 00:07:22,810 including what's the probability in energy transfer 154 00:07:22,810 --> 00:07:24,930 when electrons slam into each other 155 00:07:24,930 --> 00:07:27,520 or when ions slam into electrons or each other? 156 00:07:30,440 --> 00:07:34,570 So let me go back to the slides. 157 00:07:34,570 --> 00:07:40,900 And so this maximum, as this approaches infinity, 158 00:07:40,900 --> 00:07:50,290 this actually approaches a value of h nu minus .255 MeV 159 00:07:50,290 --> 00:07:53,840 Just to do the quick calculation to give a numerical example, 160 00:07:53,840 --> 00:07:57,940 if I plug in theta equals pi and h mu 161 00:07:57,940 --> 00:08:04,630 equals 1 gig electron volt, or 1,000 MeV. 162 00:08:04,630 --> 00:08:08,470 And can anyone remind me what is mass of the electron c squared? 163 00:08:12,228 --> 00:08:13,770 What's the rest mass of the electron? 164 00:08:13,770 --> 00:08:14,855 Sorry? 165 00:08:14,855 --> 00:08:15,730 AUDIENCE: [INAUDIBLE] 166 00:08:15,730 --> 00:08:17,190 MICHAEL SHORT: Right. 167 00:08:17,190 --> 00:08:20,730 While I'm usually against memorizing anything-- 168 00:08:20,730 --> 00:08:23,520 because that's what books and the internet are for-- 169 00:08:23,520 --> 00:08:26,130 this is one of those quantities that I 170 00:08:26,130 --> 00:08:28,740 want on the tip of your tongue as nuclear engineers. 171 00:08:28,740 --> 00:08:30,990 You should remember what the rest mass of the electron 172 00:08:30,990 --> 00:08:33,600 is because a lot of our quantities 173 00:08:33,600 --> 00:08:35,640 are calculated based upon it. 174 00:08:35,640 --> 00:08:37,980 For example, this ratio-- 175 00:08:37,980 --> 00:08:40,770 what was it, h nu over MeC squared-- 176 00:08:40,770 --> 00:08:43,020 gives you the energy the photon in terms 177 00:08:43,020 --> 00:08:45,450 of the number of electron rest masses, 178 00:08:45,450 --> 00:08:47,557 which is a useful quantity in itself. 179 00:08:47,557 --> 00:08:49,140 So why don't I plug all this stuff in. 180 00:08:49,140 --> 00:08:58,650 So we have .511 over 1,000 plus 2 flipped over the x-axis times 181 00:08:58,650 --> 00:09:02,070 2 times h nu. 182 00:09:02,070 --> 00:09:13,830 And we get-- so that t becomes 999.745 MeV. 183 00:09:13,830 --> 00:09:17,640 Interestingly enough, 1,000 MeV, our ingoing photon, 184 00:09:17,640 --> 00:09:25,630 minus that equals that right there. 185 00:09:25,630 --> 00:09:27,380 So that's the interesting quirk of physics 186 00:09:27,380 --> 00:09:31,460 is as the photon increases in energy, 187 00:09:31,460 --> 00:09:34,617 the maximum amount of energy that it can leave with-- 188 00:09:34,617 --> 00:09:36,200 or sorry, the minimum amount of energy 189 00:09:36,200 --> 00:09:39,290 the photon can leave with, or the maximum amount 190 00:09:39,290 --> 00:09:43,260 it can impart to an electron approaches 191 00:09:43,260 --> 00:09:46,580 .255 MeV or the photon energy minus that. 192 00:09:46,580 --> 00:09:48,330 What do you guys notice about that number? 193 00:09:52,274 --> 00:09:53,253 AUDIENCE: [INAUDIBLE] 194 00:09:53,253 --> 00:09:54,420 MICHAEL SHORT: That's right. 195 00:09:54,420 --> 00:09:57,510 It's exactly half the rest mass of the electron. 196 00:09:57,510 --> 00:10:01,620 So as your photons hit the GeV range and above, 197 00:10:01,620 --> 00:10:03,768 they can all leave with half the rest 198 00:10:03,768 --> 00:10:05,310 mass of the electron of energy, which 199 00:10:05,310 --> 00:10:08,850 means you have more and more energy able to be transferred 200 00:10:08,850 --> 00:10:11,820 in a given Compton scatter as the photon gets 201 00:10:11,820 --> 00:10:13,770 higher and higher in energy. 202 00:10:13,770 --> 00:10:17,490 So for the limit of low energy, the photons 203 00:10:17,490 --> 00:10:20,370 basically bounce off without transferring much energy 204 00:10:20,370 --> 00:10:21,360 at all. 205 00:10:21,360 --> 00:10:23,400 And the higher in energy the photon gets, 206 00:10:23,400 --> 00:10:27,970 the higher percentage of that maximum transfer can be. 207 00:10:27,970 --> 00:10:30,580 So that's what I wanted to clarify from last time. 208 00:10:30,580 --> 00:10:31,990 It was an interesting coincidence 209 00:10:31,990 --> 00:10:34,810 that our photo peak and our Compton edge 210 00:10:34,810 --> 00:10:37,480 were pretty close to that number apart. 211 00:10:37,480 --> 00:10:40,440 But one MeV isn't quite infinity. 212 00:10:40,440 --> 00:10:42,440 But it is pretty close. 213 00:10:42,440 --> 00:10:45,200 That difference right there, what does that come out to? 214 00:10:45,200 --> 00:10:50,430 Before I say something stupid, I'll just calculate it. 215 00:10:50,430 --> 00:10:52,410 1.241. 216 00:10:52,410 --> 00:10:56,290 It's like 0.218 MeV, so we're already most of the way there. 217 00:10:56,290 --> 00:10:58,140 So once you reach, like, 10 or 100 MeV, 218 00:10:58,140 --> 00:11:00,870 you're pretty much at that limit. 219 00:11:00,870 --> 00:11:03,050 And so what that tells you is that the distance 220 00:11:03,050 --> 00:11:06,500 between a photo peak and its corresponding Compton 221 00:11:06,500 --> 00:11:10,190 edge for high energy photons is going to be half the rest 222 00:11:10,190 --> 00:11:12,090 mass of the electron. 223 00:11:12,090 --> 00:11:14,400 Once you get to lower and lower energies, 224 00:11:14,400 --> 00:11:17,813 that distance will start to shrink. 225 00:11:17,813 --> 00:11:18,980 I'm sorry, other way around. 226 00:11:18,980 --> 00:11:21,260 That distance will start to grow. 227 00:11:21,260 --> 00:11:25,380 And I have a few examples I want to show you. 228 00:11:25,380 --> 00:11:27,410 But first, in order to understand these, 229 00:11:27,410 --> 00:11:29,160 now I want to get into the part I told you 230 00:11:29,160 --> 00:11:30,930 we'd get to yesterday, which is what's 231 00:11:30,930 --> 00:11:34,020 the probability that a Compton scatter happens 232 00:11:34,020 --> 00:11:35,520 at a certain angle? 233 00:11:35,520 --> 00:11:37,980 And this polar plot explains it pretty well. 234 00:11:37,980 --> 00:11:40,860 In the limit of really low photons, 235 00:11:40,860 --> 00:11:45,360 like .01 MeV or 10 keV photons, you 236 00:11:45,360 --> 00:11:48,600 can see that this forward scattering to an angle of 0, 237 00:11:48,600 --> 00:11:50,790 or back scattering to an angle of 180-- 238 00:11:50,790 --> 00:11:54,240 there's a 180 that's blocked by an axis right there-- 239 00:11:54,240 --> 00:11:56,250 they're almost the same. 240 00:11:56,250 --> 00:11:58,980 So forward and back scattering, there's 241 00:11:58,980 --> 00:12:02,920 not really that much of a big difference in probability. 242 00:12:02,920 --> 00:12:06,780 So if we were going to start graphing theta of this Compton 243 00:12:06,780 --> 00:12:09,570 scatter as a function of the-- 244 00:12:09,570 --> 00:12:12,330 going to introduce this new quantity, this angularly 245 00:12:12,330 --> 00:12:16,912 dependent cross-section. 246 00:12:16,912 --> 00:12:18,620 Before we were giving you cross- sections 247 00:12:18,620 --> 00:12:21,200 in the form of just sigmas, like sigma Compton. 248 00:12:23,828 --> 00:12:25,370 Now we're actually telling you what's 249 00:12:25,370 --> 00:12:28,970 the probability of that interaction happening 250 00:12:28,970 --> 00:12:30,953 in this certain angle? 251 00:12:30,953 --> 00:12:32,870 So it's called the differential cross-section, 252 00:12:32,870 --> 00:12:35,287 and you can have all sorts of differential cross-sections, 253 00:12:35,287 --> 00:12:37,820 like energy differential cross-sections, 254 00:12:37,820 --> 00:12:39,800 angle differential cross-sections, 255 00:12:39,800 --> 00:12:41,860 whatever have you. 256 00:12:41,860 --> 00:12:45,340 So if we try and graph what dpes the shape of this look like, 257 00:12:45,340 --> 00:12:48,310 this polar plot on a more understandable graph, 258 00:12:48,310 --> 00:12:51,350 we can see that the probability is pretty high. 259 00:12:51,350 --> 00:12:54,950 Let's just call that a relative probability of 1. 260 00:12:54,950 --> 00:12:57,740 And as we trace around this circle, 261 00:12:57,740 --> 00:13:01,380 that value gets lower and lower until we hit 90 degrees, 262 00:13:01,380 --> 00:13:05,400 or pi over 2, at which point it starts to pop back up 263 00:13:05,400 --> 00:13:07,710 almost to its original value. 264 00:13:07,710 --> 00:13:13,490 So this was for a 10 keV photon. 265 00:13:13,490 --> 00:13:16,010 Now let's take a different extreme example. 266 00:13:16,010 --> 00:13:18,870 We have a 3 MeV photon right here. 267 00:13:18,870 --> 00:13:22,650 And it's that long dashed curve, so that one here in the center. 268 00:13:22,650 --> 00:13:25,080 So we can see that the relative probability of 0 degrees 269 00:13:25,080 --> 00:13:26,580 is the same. 270 00:13:26,580 --> 00:13:28,230 And if we trace around to 180, we're 271 00:13:28,230 --> 00:13:32,220 almost at the origin, which tells us that, for 3 MeV, 272 00:13:32,220 --> 00:13:36,750 it starts off the same and quickly drops really far down. 273 00:13:39,490 --> 00:13:43,090 What that means is that what's called forward scattering 274 00:13:43,090 --> 00:13:44,245 is preferred. 275 00:13:50,280 --> 00:13:51,780 So up on this board, we were talking 276 00:13:51,780 --> 00:13:55,290 about what's the maximum energy that a photon can transfer, 277 00:13:55,290 --> 00:13:57,750 which is always in the back scattering case. 278 00:13:57,750 --> 00:14:00,630 The other part to note is that that back scattering 279 00:14:00,630 --> 00:14:03,780 probability gets lower and lower as the photon gets 280 00:14:03,780 --> 00:14:05,310 higher and higher in energy. 281 00:14:05,310 --> 00:14:06,600 Yeah. 282 00:14:06,600 --> 00:14:08,267 AUDIENCE: So it's that basically saying, 283 00:14:08,267 --> 00:14:10,245 since we said forward scattering [INAUDIBLE] 284 00:14:10,245 --> 00:14:11,998 as the energy gets higher, you just 285 00:14:11,998 --> 00:14:15,872 have a harder chance of it interacting. 286 00:14:15,872 --> 00:14:16,830 MICHAEL SHORT: Exactly. 287 00:14:16,830 --> 00:14:17,190 Yeah. 288 00:14:17,190 --> 00:14:18,815 The cross-section value, well, yeah, it 289 00:14:18,815 --> 00:14:21,480 goes down as you increase in energy. 290 00:14:21,480 --> 00:14:25,470 So a total forward scatter, if you had a true forward scatter 291 00:14:25,470 --> 00:14:30,810 where theta equals 0, I'll call that a miss. 292 00:14:30,810 --> 00:14:32,880 It means that, because we saw on this formula 293 00:14:32,880 --> 00:14:39,840 up here when theta equals 0, there is no energy transfer. 294 00:14:39,840 --> 00:14:41,040 Nothing. 295 00:14:41,040 --> 00:14:43,140 And so yeah, that would be to me like a miss. 296 00:14:43,140 --> 00:14:45,140 If that angles ever so slightly above 0, 297 00:14:45,140 --> 00:14:46,890 then there is some scattering, but there's 298 00:14:46,890 --> 00:14:48,990 very little energy transfer. 299 00:14:48,990 --> 00:14:51,690 But that smaller energy transfer becomes 300 00:14:51,690 --> 00:14:56,340 more likely when the photon goes higher in energy. 301 00:14:56,340 --> 00:14:59,250 These are these sorts of cause and effect relationships 302 00:14:59,250 --> 00:15:01,440 I want you guys to be able to reason out. 303 00:15:01,440 --> 00:15:04,680 If I were to give you a polar plot of this differential 304 00:15:04,680 --> 00:15:06,960 cross-section with angle and energy, 305 00:15:06,960 --> 00:15:10,020 I'd want you to be able to reproduce this and tell me 306 00:15:10,020 --> 00:15:12,070 what's really going on. 307 00:15:12,070 --> 00:15:14,410 If we fill in one of the ones in between-- 308 00:15:14,410 --> 00:15:20,260 let's go with 0.2 MeV, this sort of single dashed line-- 309 00:15:20,260 --> 00:15:22,990 you can see that the probability of back scattering 310 00:15:22,990 --> 00:15:27,250 is somewhere between the 3 MeV and the 10 keV. 311 00:15:27,250 --> 00:15:28,010 Yeah, Luke? 312 00:15:28,010 --> 00:15:30,880 AUDIENCE: Back scattering refers to the photon going back. 313 00:15:30,880 --> 00:15:32,047 MICHAEL SHORT: That's right. 314 00:15:32,047 --> 00:15:35,680 Back scattering refers to the photon going back, which means 315 00:15:35,680 --> 00:15:38,560 this situation, where the difference 316 00:15:38,560 --> 00:15:41,290 in angle between the incoming and outgoing photon 317 00:15:41,290 --> 00:15:44,470 is pi, 180 degrees, which means it just turns around and moves 318 00:15:44,470 --> 00:15:45,490 the other way. 319 00:15:45,490 --> 00:15:46,960 Right. 320 00:15:46,960 --> 00:15:51,760 So that dashed line right there would follow something 321 00:15:51,760 --> 00:15:54,310 like this at-- what did we say? 322 00:15:54,310 --> 00:15:55,720 0.2 MeV. 323 00:15:58,840 --> 00:16:01,480 The form, the full form of this cross-section right 324 00:16:01,480 --> 00:16:04,540 here is referred to as the Klein-Nishina cross-section. 325 00:16:04,540 --> 00:16:08,170 And it has been derived by quantum electro dynamics, which 326 00:16:08,170 --> 00:16:10,180 I will not derive for you now. 327 00:16:10,180 --> 00:16:11,800 But there are plenty of derivations 328 00:16:11,800 --> 00:16:14,088 online if that's your kind of thing. 329 00:16:14,088 --> 00:16:15,880 And I had to make a trade-off in this class 330 00:16:15,880 --> 00:16:18,760 of how deep do we go into each concept versus how 331 00:16:18,760 --> 00:16:20,660 many concepts do we teach? 332 00:16:20,660 --> 00:16:23,040 And I'm going for the latter because if there 333 00:16:23,040 --> 00:16:24,748 is any course that's supposed to give you 334 00:16:24,748 --> 00:16:26,470 an overview of nuclear, it's 22.01. 335 00:16:26,470 --> 00:16:30,060 There will be plenty of time for quantum in 22.02 and beyond, 336 00:16:30,060 --> 00:16:31,690 should you want. 337 00:16:31,690 --> 00:16:34,402 At any rate, this is the general form of it. 338 00:16:34,402 --> 00:16:35,860 And what this actually tells you is 339 00:16:35,860 --> 00:16:39,010 that as the energy of the photon increases, 340 00:16:39,010 --> 00:16:42,367 the effect of that angle will-- 341 00:16:42,367 --> 00:16:44,700 you guys'll have to work that out on a homework problem. 342 00:16:44,700 --> 00:16:45,630 I just remembered. 343 00:16:45,630 --> 00:16:47,130 I want to stop stealing your thunder 344 00:16:47,130 --> 00:16:48,547 and giving away half the homework. 345 00:16:48,547 --> 00:16:49,700 Yep. 346 00:16:49,700 --> 00:16:51,022 AUDIENCE: How does [INAUDIBLE]? 347 00:16:57,988 --> 00:16:58,780 MICHAEL SHORT: Yes. 348 00:16:58,780 --> 00:17:00,990 AUDIENCE: --the quantity D sigma D omega. 349 00:17:00,990 --> 00:17:02,850 MICHAEL SHORT: The quantity D sigma D 350 00:17:02,850 --> 00:17:07,810 omega says let's say you have a photon coming in at our x-axis. 351 00:17:07,810 --> 00:17:09,790 You've got an electron here. 352 00:17:09,790 --> 00:17:13,829 What's the probability that I'm going to scatter off 353 00:17:13,829 --> 00:17:17,369 into some small area d omega? 354 00:17:17,369 --> 00:17:25,250 So in some small d theta d phi, or some small sine theta, 355 00:17:25,250 --> 00:17:30,012 d theta d phi, into an element of solid angle. 356 00:17:30,012 --> 00:17:31,470 I should probably draw that smaller 357 00:17:31,470 --> 00:17:34,650 to be a little more differential looking. 358 00:17:34,650 --> 00:17:38,220 So gammas are going to scatter off in all directions. 359 00:17:38,220 --> 00:17:40,227 But this d sigma d omega tells you 360 00:17:40,227 --> 00:17:42,810 what's the probability that it goes through that little patch? 361 00:17:45,430 --> 00:17:52,370 AUDIENCE: And then that omega is also a function of [INAUDIBLE]?? 362 00:17:52,370 --> 00:17:57,970 MICHAEL SHORT: So that omega has some component of theta in it 363 00:17:57,970 --> 00:18:00,550 and some component of phi in it. 364 00:18:00,550 --> 00:18:02,050 Since it's a solid angle, it depends 365 00:18:02,050 --> 00:18:05,530 on both the angle of rotation and the angle of inclination, 366 00:18:05,530 --> 00:18:08,510 which we call theta and phi. 367 00:18:08,510 --> 00:18:10,930 Now to get from this to the regular cross-section you're 368 00:18:10,930 --> 00:18:17,710 used to, you can integrate over all angles omega 369 00:18:17,710 --> 00:18:20,592 of the differential cross-section, 370 00:18:20,592 --> 00:18:22,800 and you'll get the regular total cross-section, which 371 00:18:22,800 --> 00:18:25,530 is just what is the probability of Compton scattering, 372 00:18:25,530 --> 00:18:27,022 full stop. 373 00:18:27,022 --> 00:18:28,480 If you wanted to know, then, what's 374 00:18:28,480 --> 00:18:32,500 the probability of Compton scattering into this angle, 375 00:18:32,500 --> 00:18:33,850 it sounds kind of boring, right? 376 00:18:33,850 --> 00:18:35,500 Why do we care about the angle? 377 00:18:35,500 --> 00:18:36,708 Anyone bored yet? 378 00:18:36,708 --> 00:18:37,750 You can raise your hands. 379 00:18:37,750 --> 00:18:39,540 Be honest. 380 00:18:39,540 --> 00:18:40,230 Interesting. 381 00:18:40,230 --> 00:18:40,920 OK. 382 00:18:40,920 --> 00:18:44,340 Well, I'm going to tell you why it's not boring because I 383 00:18:44,340 --> 00:18:46,200 don't think you're honest. 384 00:18:46,200 --> 00:18:49,620 You can actually, if you know the angle at which a Compton 385 00:18:49,620 --> 00:18:50,880 photon scatters into-- 386 00:18:50,880 --> 00:18:53,640 actually I want to leave that stuff up-- 387 00:18:53,640 --> 00:18:56,760 there is a pretty much one to one relation 388 00:18:56,760 --> 00:19:00,570 between the energy and the angle of scattering, 389 00:19:00,570 --> 00:19:07,240 which means that let's say you have a cargo container. 390 00:19:07,240 --> 00:19:07,740 I'm sorry. 391 00:19:07,740 --> 00:19:09,600 You don't have a cargo container. 392 00:19:09,600 --> 00:19:15,570 You have a cargo ship full of tons and tons of these 393 00:19:15,570 --> 00:19:18,030 stacked up cargo containers. 394 00:19:18,030 --> 00:19:20,960 Has anyone actually ever seen one of these before? 395 00:19:20,960 --> 00:19:21,460 OK. 396 00:19:21,460 --> 00:19:23,980 In case not, I'm going to do something dangerous 397 00:19:23,980 --> 00:19:26,180 and go to the internet. 398 00:19:26,180 --> 00:19:28,030 And hopefully the search for cargo container 399 00:19:28,030 --> 00:19:30,820 doesn't come up with something disgusting. 400 00:19:30,820 --> 00:19:32,480 Oh, look at that. 401 00:19:32,480 --> 00:19:36,230 How about cargo container ship? 402 00:19:36,230 --> 00:19:37,120 Yeah. 403 00:19:37,120 --> 00:19:38,330 OK. 404 00:19:38,330 --> 00:19:41,000 You got one of these, right? 405 00:19:41,000 --> 00:19:43,340 And your detector goes off, and it just 406 00:19:43,340 --> 00:19:45,170 says there is something radioactive that 407 00:19:45,170 --> 00:19:46,520 shouldn't be here. 408 00:19:46,520 --> 00:19:48,110 How do you find out which container 409 00:19:48,110 --> 00:19:51,900 it's in without taking the ship apart? 410 00:19:51,900 --> 00:19:53,740 Interesting problem, huh? 411 00:19:53,740 --> 00:19:55,090 Do you just kind of look-- yeah? 412 00:19:55,090 --> 00:19:56,590 AUDIENCE: Do you kind of like shield 413 00:19:56,590 --> 00:19:58,336 certain angles [INAUDIBLE]? 414 00:20:00,950 --> 00:20:02,200 MICHAEL SHORT: That's one way. 415 00:20:02,200 --> 00:20:06,880 You could mask off the ship and move your detector around, 416 00:20:06,880 --> 00:20:09,070 and then do it for the other two dimensions. 417 00:20:09,070 --> 00:20:12,443 So that will get you there, but slowly. 418 00:20:12,443 --> 00:20:13,485 How do you do it quickly? 419 00:20:16,670 --> 00:20:20,240 Well, you do it with the Klein Nishina cross-section. 420 00:20:20,240 --> 00:20:23,060 If you know the relationship between the energy 421 00:20:23,060 --> 00:20:25,280 and the angle of a Compton scatter, 422 00:20:25,280 --> 00:20:30,630 you take two detectors, Detector 1, Detector 2, 423 00:20:30,630 --> 00:20:32,580 and you form what's called a Compton camera. 424 00:20:37,550 --> 00:20:40,220 This is awesome because with two detectors, 425 00:20:40,220 --> 00:20:44,390 you can pinpoint the location of a radiation source by knowing-- 426 00:20:44,390 --> 00:20:48,410 let's say you had a gamma ray that entered Detector 1. 427 00:20:48,410 --> 00:20:50,750 So you have your initial e gamma. 428 00:20:50,750 --> 00:20:52,160 And you get a spectrum. 429 00:20:52,160 --> 00:20:54,745 Let's draw a couple of spectra. 430 00:20:54,745 --> 00:20:56,120 I'm going to use different colors 431 00:20:56,120 --> 00:20:57,710 so I can make them bigger. 432 00:20:57,710 --> 00:21:03,420 This will be intensity and this will be energy. 433 00:21:03,420 --> 00:21:07,130 So we have our blue Detector 1, and we 434 00:21:07,130 --> 00:21:10,640 have some spectrum for Detector 1 435 00:21:10,640 --> 00:21:14,180 where we get the photo peak of the gamma at e gamma. 436 00:21:14,180 --> 00:21:18,350 And this time, you don't see every possible angle. 437 00:21:18,350 --> 00:21:23,935 You only see whatever angle you get that Compton scatter at. 438 00:21:23,935 --> 00:21:26,060 Or you might see a whole bunch of different angles. 439 00:21:26,060 --> 00:21:26,900 Never mind. 440 00:21:26,900 --> 00:21:29,250 So you're going to see the Compton 441 00:21:29,250 --> 00:21:31,700 edge in this whole continuum of things. 442 00:21:31,700 --> 00:21:34,100 And so you know that whatever energy this corresponds 443 00:21:34,100 --> 00:21:37,040 to means that theta equals pi. 444 00:21:37,040 --> 00:21:41,240 That energy corresponds to theta equals 0. 445 00:21:41,240 --> 00:21:45,440 And you know that there's a source somewhere in here. 446 00:21:45,440 --> 00:21:50,090 Now let's say that photon scatters out of Detector 1 447 00:21:50,090 --> 00:21:53,690 and into Detector 2. 448 00:21:53,690 --> 00:21:55,610 In this case, you've no longer just 449 00:21:55,610 --> 00:21:58,350 know that you have a source of some sort. 450 00:21:58,350 --> 00:22:00,740 You'll end up with a certain photo peak 451 00:22:00,740 --> 00:22:06,650 corresponding to this e gamma prime, the only energy 452 00:22:06,650 --> 00:22:09,780 that can Compton scatter in the direction from Detector 1 453 00:22:09,780 --> 00:22:12,710 to Detector 2, because you have now 454 00:22:12,710 --> 00:22:16,610 determined the angles between the line between the detectors 455 00:22:16,610 --> 00:22:18,540 and the detector at the source. 456 00:22:18,540 --> 00:22:25,770 So then you get a photo peak and the corresponding Compton edge 457 00:22:25,770 --> 00:22:28,180 for your e gamma prime. 458 00:22:28,180 --> 00:22:32,200 Your e gamma prime, that tells you the angle that it came off 459 00:22:32,200 --> 00:22:34,640 of for your first interaction. 460 00:22:34,640 --> 00:22:39,980 So that is your source angle. 461 00:22:39,980 --> 00:22:43,010 So what that means is that by using these two angles, 462 00:22:43,010 --> 00:22:48,930 you've now pinpointed your source to lie somewhere 463 00:22:48,930 --> 00:22:57,730 on these two cones projected back on one of the two points 464 00:22:57,730 --> 00:23:01,470 where those cones at that angle intersect. 465 00:23:01,470 --> 00:23:03,420 This is something I want you to try and think 466 00:23:03,420 --> 00:23:05,530 about and work out on your own. 467 00:23:05,530 --> 00:23:10,292 But it's really cool to explain this because with one detector, 468 00:23:10,292 --> 00:23:12,000 you know that there's a source somewhere, 469 00:23:12,000 --> 00:23:13,830 and you know generally where to point. 470 00:23:13,830 --> 00:23:17,100 With two detectors and energy resolution, 471 00:23:17,100 --> 00:23:20,400 the energy of the photo peak of the second event 472 00:23:20,400 --> 00:23:23,268 tells you what the angle of the first event was. 473 00:23:23,268 --> 00:23:24,810 And this way, if you know what source 474 00:23:24,810 --> 00:23:27,007 you're looking for from the first photo peak, 475 00:23:27,007 --> 00:23:28,590 and you know what angle you're looking 476 00:23:28,590 --> 00:23:32,190 for from the Compton scattered photons photo 477 00:23:32,190 --> 00:23:34,950 peak, because they have those, then you 478 00:23:34,950 --> 00:23:37,452 know not only what the source is, but where it is. 479 00:23:37,452 --> 00:23:38,910 And you know which container should 480 00:23:38,910 --> 00:23:41,115 take a part to start looking. 481 00:23:41,115 --> 00:23:43,240 So this is why we care about angle, because there's 482 00:23:43,240 --> 00:23:47,170 actual, real ways of using this to your advantage 483 00:23:47,170 --> 00:23:50,390 to solve some pretty insane problems, like which container 484 00:23:50,390 --> 00:23:52,500 would that be in. 485 00:23:52,500 --> 00:23:55,030 Who's starting to get the general idea behind a Compton 486 00:23:55,030 --> 00:23:58,858 camera, or who would like another explanation? 487 00:23:58,858 --> 00:24:00,713 Anyone? 488 00:24:00,713 --> 00:24:01,630 I asked two questions. 489 00:24:01,630 --> 00:24:03,682 So who would like another explanation? 490 00:24:03,682 --> 00:24:05,050 Yeah, OK. 491 00:24:05,050 --> 00:24:07,360 The idea here is with just one detector, 492 00:24:07,360 --> 00:24:09,742 all you know is whether or not there is a source. 493 00:24:09,742 --> 00:24:11,200 The only information you're getting 494 00:24:11,200 --> 00:24:14,920 is its photo peak and Compton edge and bowl. 495 00:24:14,920 --> 00:24:17,170 And so you know the identity of the source. 496 00:24:17,170 --> 00:24:19,180 Maybe it's cobalt 60 or something. 497 00:24:19,180 --> 00:24:20,950 But you don't know where it is. 498 00:24:20,950 --> 00:24:23,410 By making a second measurement, you 499 00:24:23,410 --> 00:24:26,590 can then determine where on the Compton 500 00:24:26,590 --> 00:24:29,860 spectrum of the first measurement 501 00:24:29,860 --> 00:24:31,660 does the photon lie. 502 00:24:31,660 --> 00:24:33,910 So by saying OK, the photo peak corresponds 503 00:24:33,910 --> 00:24:36,490 to this energy, which corresponds 504 00:24:36,490 --> 00:24:43,320 to some certain angle that this had to scatter off of. 505 00:24:43,320 --> 00:24:46,770 So then you know what this angle is. 506 00:24:46,770 --> 00:24:49,423 You've determined theta. 507 00:24:49,423 --> 00:24:51,340 AUDIENCE: Is that the same theta that you just 508 00:24:51,340 --> 00:24:53,248 drew as theta angle? 509 00:24:53,248 --> 00:24:54,040 MICHAEL SHORT: Yes. 510 00:24:54,040 --> 00:24:54,540 OK. 511 00:24:54,540 --> 00:24:56,985 Angle. 512 00:24:56,985 --> 00:24:58,360 You've then determined this angle 513 00:24:58,360 --> 00:25:00,970 because you know the incoming path of the photon, 514 00:25:00,970 --> 00:25:03,550 and you now know the outgoing path, 515 00:25:03,550 --> 00:25:05,740 which means you know angle. 516 00:25:05,740 --> 00:25:09,220 So if you know the line between these two detectors, 517 00:25:09,220 --> 00:25:13,480 and your photo pick lines up with your first Compton 518 00:25:13,480 --> 00:25:18,070 spectrum's angle, you then look at that angle back. 519 00:25:18,070 --> 00:25:21,040 You also have to sweep around in the other direction, which 520 00:25:21,040 --> 00:25:24,220 means you end up with a cone of possible locations. 521 00:25:24,220 --> 00:25:24,862 Yeah. 522 00:25:24,862 --> 00:25:26,612 AUDIENCE: How do you know that the photons 523 00:25:26,612 --> 00:25:30,172 that get to the second scatter from inside the first one? 524 00:25:30,172 --> 00:25:31,880 MICHAEL SHORT: There can be only a couple 525 00:25:31,880 --> 00:25:33,890 of things that could happen, right? 526 00:25:33,890 --> 00:25:35,650 You could have another direct photon just 527 00:25:35,650 --> 00:25:37,880 shoot into Detector 2, in which case 528 00:25:37,880 --> 00:25:41,420 you'll just get a little bit of photo peak. 529 00:25:41,420 --> 00:25:44,300 But we know to expect that, so we can ignore it. 530 00:25:44,300 --> 00:25:47,220 We're specifically looking for the photo peek 531 00:25:47,220 --> 00:25:48,940 coming from Detector 1. 532 00:25:48,940 --> 00:25:51,180 AUDIENCE: So they wouldn't just go in the air 533 00:25:51,180 --> 00:25:53,990 and do Compton scatter [INAUDIBLE]?? 534 00:25:53,990 --> 00:25:57,680 MICHAEL SHORT: They would, which gives the perfect pretext 535 00:25:57,680 --> 00:26:01,170 to bring up the cross-sections for these processes. 536 00:26:01,170 --> 00:26:04,010 So I'm going to skip ahead a little bit 537 00:26:04,010 --> 00:26:06,740 and start getting into what do the actual cross-sections look 538 00:26:06,740 --> 00:26:09,830 like for Compton scattering, photoelectric, and pair 539 00:26:09,830 --> 00:26:10,820 production? 540 00:26:10,820 --> 00:26:13,280 All of them have to do with the electron 541 00:26:13,280 --> 00:26:15,350 density of the material. 542 00:26:15,350 --> 00:26:17,510 The more electrons in the way, the more 543 00:26:17,510 --> 00:26:19,250 you get these events happening. 544 00:26:19,250 --> 00:26:22,040 So yes, you will get Compton scatters in the air 545 00:26:22,040 --> 00:26:25,250 because air contains electrons and they do Compton scatter. 546 00:26:25,250 --> 00:26:27,460 But air is not very dense, so you 547 00:26:27,460 --> 00:26:28,940 will get comparatively less. 548 00:26:28,940 --> 00:26:33,140 So let's say that adds a little bit of noise 549 00:26:33,140 --> 00:26:35,780 on the bottom, which is like any detector spectrum we've ever 550 00:26:35,780 --> 00:26:36,280 seen. 551 00:26:36,280 --> 00:26:39,020 There's always noise from all sorts of other processes 552 00:26:39,020 --> 00:26:41,030 we're not looking for. 553 00:26:41,030 --> 00:26:42,690 So now let's start to look at what 554 00:26:42,690 --> 00:26:46,407 the general energy and z ranges of each of these effects are. 555 00:26:46,407 --> 00:26:48,240 And we're going to recreate one of the plots 556 00:26:48,240 --> 00:26:52,350 that I showed you at the beginning of yesterday's class. 557 00:26:52,350 --> 00:26:56,100 So let's make a graph of energy of the photon 558 00:26:56,100 --> 00:26:58,260 and z of the material. 559 00:26:58,260 --> 00:27:01,650 And we want to try to map out where the following three 560 00:27:01,650 --> 00:27:03,030 processes are dominant. 561 00:27:03,030 --> 00:27:06,000 So tau, our photoelectric effect. 562 00:27:09,910 --> 00:27:14,830 C, which we'll call our Compton scattering. 563 00:27:14,830 --> 00:27:18,411 And kappa, which we'll call pair production. 564 00:27:21,360 --> 00:27:24,860 And these cross-sections do give us relative probabilities 565 00:27:24,860 --> 00:27:28,280 as a function of the energy of the photon and the medium 566 00:27:28,280 --> 00:27:30,830 they're going through, along with the actual density, 567 00:27:30,830 --> 00:27:33,060 that something's going to happen. 568 00:27:33,060 --> 00:27:35,110 So let's look at the form of these. 569 00:27:35,110 --> 00:27:38,420 The cross-section for the photoelectric effect scales 570 00:27:38,420 --> 00:27:40,840 with z to the 5th. 571 00:27:40,840 --> 00:27:42,430 Do you think that photoelectric effect 572 00:27:42,430 --> 00:27:47,124 will be more likely for low z or high z materials? 573 00:27:47,124 --> 00:27:48,110 AUDIENCE: High. 574 00:27:48,110 --> 00:27:49,735 MICHAEL SHORT: High z materials, right. 575 00:27:49,735 --> 00:27:52,730 So we know we're going to be in the top half area. 576 00:27:52,730 --> 00:27:56,575 And it scales with one over energy to the 7/2. 577 00:27:56,575 --> 00:27:57,950 So do you think this will be most 578 00:27:57,950 --> 00:28:00,410 likely with low or high energy? 579 00:28:03,320 --> 00:28:04,128 AUDIENCE: Low. 580 00:28:04,128 --> 00:28:05,420 MICHAEL SHORT: So lower energy. 581 00:28:05,420 --> 00:28:10,140 So we're going to fill in our photoelectric somewhat. 582 00:28:10,140 --> 00:28:11,280 Oh, I'm sorry. 583 00:28:11,280 --> 00:28:13,530 So we know it's going to be in this part of the z. 584 00:28:13,530 --> 00:28:15,947 We know it's going to be in this part of the energy curve. 585 00:28:15,947 --> 00:28:21,320 So let's fill in that area as photoelectric. 586 00:28:21,320 --> 00:28:24,450 Let's look at the other extreme, pair production. 587 00:28:24,450 --> 00:28:26,300 It scales with z squared, so is that 588 00:28:26,300 --> 00:28:28,130 going to be in the low or the high z area? 589 00:28:36,460 --> 00:28:37,450 AUDIENCE: [INAUDIBLE] 590 00:28:37,450 --> 00:28:38,610 MICHAEL SHORT: I think still high, 591 00:28:38,610 --> 00:28:40,440 just the bigger the z, the bigger the cross-section, 592 00:28:40,440 --> 00:28:41,100 right? 593 00:28:41,100 --> 00:28:42,540 So we know that pair production is 594 00:28:42,540 --> 00:28:44,220 going to be in the high z area. 595 00:28:44,220 --> 00:28:46,780 Now how about the energy? 596 00:28:46,780 --> 00:28:48,850 It scales with the log of energy, 597 00:28:48,850 --> 00:28:50,530 but the energy is on the top. 598 00:28:50,530 --> 00:28:54,740 So will a low or a high energy give you more pair production? 599 00:28:54,740 --> 00:28:55,240 High. 600 00:28:55,240 --> 00:28:59,110 So pair production is going to be here, 601 00:28:59,110 --> 00:29:04,440 leaving everything else for Compton scattering. 602 00:29:04,440 --> 00:29:09,020 And if we jump back to the start of last class, 603 00:29:09,020 --> 00:29:12,260 we've reproduced from the cross-sections the same sort 604 00:29:12,260 --> 00:29:16,210 of plot that we saw before just from looking 605 00:29:16,210 --> 00:29:20,450 at the relative probabilities of each effect, which 606 00:29:20,450 --> 00:29:22,160 I think it's pretty cool. 607 00:29:22,160 --> 00:29:26,100 We can now do that with some basic physics knowledge. 608 00:29:26,100 --> 00:29:29,070 Last thing I want to fill in for Compton scattering is that 609 00:29:29,070 --> 00:29:35,400 the Klein Nishina cross-section, which is your differential 610 00:29:35,400 --> 00:29:38,310 cross-section as a function of omega, 611 00:29:38,310 --> 00:29:44,520 combined with the probability that you scatter into a certain 612 00:29:44,520 --> 00:29:48,910 angle and a certain energy-- because there's a one-to-one 613 00:29:48,910 --> 00:29:50,530 relationship-- 614 00:29:50,530 --> 00:29:52,690 ends up giving you your d sigma c 615 00:29:52,690 --> 00:29:58,030 over de, which is your energy distribution of Compton recoil 616 00:29:58,030 --> 00:29:59,380 electrons. 617 00:29:59,380 --> 00:30:02,490 And that's directly what leads to the shape right here, 618 00:30:02,490 --> 00:30:05,650 where if you have, let's say, 0.51 MeV, 619 00:30:05,650 --> 00:30:08,810 relatively low energy, there's-- 620 00:30:08,810 --> 00:30:11,210 let's see. 621 00:30:11,210 --> 00:30:13,650 What do I want to say here? 622 00:30:13,650 --> 00:30:14,150 Yeah. 623 00:30:14,150 --> 00:30:17,240 So as you go up in higher and higher energy, 624 00:30:17,240 --> 00:30:19,340 you get fewer and fewer Compton electrons, 625 00:30:19,340 --> 00:30:22,190 because like Jared was saying, the probability 626 00:30:22,190 --> 00:30:23,870 of a Compton interaction does go down 627 00:30:23,870 --> 00:30:26,900 with increasing energy, as we kind of reasoned out. 628 00:30:26,900 --> 00:30:31,190 But in addition, you get relatively more 629 00:30:31,190 --> 00:30:34,880 of these back scattered ones, which is kind of interesting. 630 00:30:34,880 --> 00:30:36,308 I have to think about that one. 631 00:30:36,308 --> 00:30:38,100 But this is the typical shape that you tend 632 00:30:38,100 --> 00:30:40,680 to see for Compton scattering. 633 00:30:40,680 --> 00:30:43,560 For high energy photons, you get a Compton peak and then 634 00:30:43,560 --> 00:30:46,830 a very long, shallow tail. 635 00:30:46,830 --> 00:30:49,010 And as you go lower and lower energy, 636 00:30:49,010 --> 00:30:50,900 it starts to sort of bounce back up. 637 00:30:50,900 --> 00:30:52,650 And yeah, Luke? 638 00:30:52,650 --> 00:30:54,840 AUDIENCE: When Compton scattering happens, 639 00:30:54,840 --> 00:30:57,230 are the electrons being knocked off the atom? 640 00:30:57,230 --> 00:30:58,230 MICHAEL SHORT: Oh, yeah. 641 00:30:58,230 --> 00:30:58,772 AUDIENCE: OK. 642 00:30:58,772 --> 00:31:01,160 So how is that different from the photoelectric effect? 643 00:31:01,160 --> 00:31:02,785 MICHAEL SHORT: The photoelectric effect 644 00:31:02,785 --> 00:31:04,920 is an absorption followed by an injection. 645 00:31:04,920 --> 00:31:08,250 In Compton scattering, the other photon is still intact. 646 00:31:08,250 --> 00:31:11,880 It just loses energy, gains wavelength. 647 00:31:11,880 --> 00:31:14,700 But the energy of Compton scattering is-- let's say, 648 00:31:14,700 --> 00:31:18,120 for MeV photons, it's on the order of hundreds of keV-- 649 00:31:18,120 --> 00:31:21,298 plenty to eject most of the electrons from an atom. 650 00:31:21,298 --> 00:31:22,840 So you always have to think about are 651 00:31:22,840 --> 00:31:24,250 you going to eject something? 652 00:31:24,250 --> 00:31:26,200 Are you above the work function? 653 00:31:26,200 --> 00:31:28,290 Work function for most atoms-- 654 00:31:28,290 --> 00:31:30,230 so we had a nice plot of that-- 655 00:31:30,230 --> 00:31:32,140 is in the eV range. 656 00:31:32,140 --> 00:31:34,300 So chances are, yeah, Compton scattering mostly 657 00:31:34,300 --> 00:31:36,280 is going to be ejecting electrons, too. 658 00:31:36,280 --> 00:31:38,350 That's the whole reason we can count them. 659 00:31:38,350 --> 00:31:40,450 If there wasn't an electron ejection, 660 00:31:40,450 --> 00:31:45,300 there would be no electron ionization cascade to count. 661 00:31:45,300 --> 00:31:47,880 So there's some sort of empirical or experimental proof 662 00:31:47,880 --> 00:31:49,670 that it does happen. 663 00:31:49,670 --> 00:31:52,130 And speaking of experimental proof, 664 00:31:52,130 --> 00:31:53,720 you can actually see that shape. 665 00:31:53,720 --> 00:31:57,470 In this case, this is a spectrum taken from two different gamma 666 00:31:57,470 --> 00:32:02,900 sources together, a-- what is it, 1.28 MeV and a 0.51 Mev. 667 00:32:02,900 --> 00:32:05,270 And you can see that the 1.28 MeV, first of all, 668 00:32:05,270 --> 00:32:07,730 has a way lower number of counts, 669 00:32:07,730 --> 00:32:09,650 showing that the cross-section does, 670 00:32:09,650 --> 00:32:12,500 indeed, decrease with higher energy. 671 00:32:12,500 --> 00:32:15,210 And it doesn't have-- well, you can't really even see-- 672 00:32:15,210 --> 00:32:18,620 but it does not curving back up, whereas this lower 673 00:32:18,620 --> 00:32:21,230 energy Compton photon is scattering 674 00:32:21,230 --> 00:32:23,630 more often because it's much higher, 675 00:32:23,630 --> 00:32:28,273 and it's got that bump back up at the really low energies. 676 00:32:28,273 --> 00:32:29,690 So it's kind of neat when the math 677 00:32:29,690 --> 00:32:33,230 that we're looking at, if I jump ahead to the cross-sections, 678 00:32:33,230 --> 00:32:36,770 you can see that you'd expect the Compton scattering 679 00:32:36,770 --> 00:32:38,800 to decrease with energy. 680 00:32:38,800 --> 00:32:42,650 And you look at an experimental plot of two different energies, 681 00:32:42,650 --> 00:32:45,000 and there you have it, higher energy, 682 00:32:45,000 --> 00:32:49,060 less total Compton scattering, but different shape. 683 00:32:51,890 --> 00:32:53,900 So any questions before I move on to how you can 684 00:32:53,900 --> 00:32:55,618 use them to design shielding? 685 00:33:01,970 --> 00:33:04,940 So what we're getting here, these cross-sections, 686 00:33:04,940 --> 00:33:07,220 are probably better known to some of you 687 00:33:07,220 --> 00:33:10,280 as mass attenuation coefficients, which 688 00:33:10,280 --> 00:33:14,600 are simpler ways of describing how many photons 689 00:33:14,600 --> 00:33:18,410 in a narrow beam would undergo some sort of process 690 00:33:18,410 --> 00:33:20,570 and be removed from the beam. 691 00:33:20,570 --> 00:33:22,670 And they get removed exponentially 692 00:33:22,670 --> 00:33:25,070 for the same sort of reason for pretty much everything 693 00:33:25,070 --> 00:33:27,710 in this class ends up being an exponential, doesn't it? 694 00:33:27,710 --> 00:33:33,080 Where if you have some intensity of photons 695 00:33:33,080 --> 00:33:35,300 or some change in intensity that's 696 00:33:35,300 --> 00:33:40,080 proportional to a change in x in the initial-- 697 00:33:40,080 --> 00:33:42,610 let's see-- and some-- 698 00:33:42,610 --> 00:33:45,460 what is it, concept of proportionality 699 00:33:45,460 --> 00:33:48,580 like the cross-section, or we'll call it now mu, 700 00:33:48,580 --> 00:33:50,890 this mass attenuation coefficient. 701 00:33:50,890 --> 00:33:53,140 The answer to that ends up being pretty much the same. 702 00:33:56,180 --> 00:33:58,520 And it's this simple exponential thing. 703 00:33:58,520 --> 00:34:00,035 And the nice thing is you don't have 704 00:34:00,035 --> 00:34:02,660 to calculate all these different cross-sections because they're 705 00:34:02,660 --> 00:34:05,330 tabulated for you by NIST. 706 00:34:05,330 --> 00:34:07,190 And that's one of the links on the website, 707 00:34:07,190 --> 00:34:09,815 on the learning modules website that I want to show to you guys 708 00:34:09,815 --> 00:34:10,639 now. 709 00:34:10,639 --> 00:34:14,090 You can actually look up these total summed cross-sections 710 00:34:14,090 --> 00:34:16,489 for gamma ray interactions as a function 711 00:34:16,489 --> 00:34:19,850 of energy versus their mass attenuation coefficient 712 00:34:19,850 --> 00:34:22,883 in centimeters squared per gram. 713 00:34:22,883 --> 00:34:24,300 The reason it's in that unit is it 714 00:34:24,300 --> 00:34:26,880 just tells you what the material does. 715 00:34:26,880 --> 00:34:29,330 It doesn't tell you how much you have in the way. 716 00:34:29,330 --> 00:34:33,409 And that's why I've rewritten this exponential attenuation 717 00:34:33,409 --> 00:34:36,260 formula with a rho on the bottom and a rho 718 00:34:36,260 --> 00:34:39,409 on the top, that rho being the density of the material 719 00:34:39,409 --> 00:34:42,590 because usually you can just say, it's like i naught e 720 00:34:42,590 --> 00:34:44,030 to the mu x. 721 00:34:44,030 --> 00:34:46,940 But these are the things that you'll look up in tables. 722 00:34:46,940 --> 00:34:49,370 And these rhos right here is whatever density 723 00:34:49,370 --> 00:34:51,239 you have of your material. 724 00:34:51,239 --> 00:34:54,710 So if you want to calculate how much better cold water is 725 00:34:54,710 --> 00:34:58,280 shielding than hot water because of its change in density, 726 00:34:58,280 --> 00:35:00,845 you can then look up the value for water, 727 00:35:00,845 --> 00:35:02,720 which I want to show you how to do right now. 728 00:35:06,460 --> 00:35:10,090 Back up to see the actual site. 729 00:35:10,090 --> 00:35:12,450 So if you guys looked right here, these-- 730 00:35:12,450 --> 00:35:13,350 what is it-- 731 00:35:13,350 --> 00:35:15,987 NIST tables of x-ray absorption coefficients. 732 00:35:15,987 --> 00:35:17,820 I'll show you how to read through this table 733 00:35:17,820 --> 00:35:20,640 now because you'll need it from everything from problem set 5 734 00:35:20,640 --> 00:35:21,930 to the rest of your life. 735 00:35:21,930 --> 00:35:24,750 This is one of those places you're going to go constantly 736 00:35:24,750 --> 00:35:27,570 looking for nuclear data. 737 00:35:27,570 --> 00:35:30,185 So you can either look at elemental media 738 00:35:30,185 --> 00:35:32,310 or compounds and mixtures, water being one of them. 739 00:35:34,960 --> 00:35:39,570 So let's go down to water, liquid. 740 00:35:39,570 --> 00:35:41,280 If you notice what's actually given here 741 00:35:41,280 --> 00:35:43,470 is this view over row. 742 00:35:43,470 --> 00:35:45,510 So the nasty, what is it, density 743 00:35:45,510 --> 00:35:48,820 specific mass attenuation coefficient. 744 00:35:48,820 --> 00:35:51,520 In other words, it's a cross-section, really. 745 00:35:51,520 --> 00:35:53,317 It's a microscopic cross-section. 746 00:35:53,317 --> 00:35:55,150 I don't know why, in a lot of these courses, 747 00:35:55,150 --> 00:35:57,730 they're introduced separately because they're the same thing. 748 00:35:57,730 --> 00:35:59,860 They're interaction probabilities. 749 00:35:59,860 --> 00:36:02,477 And then that other rho from the slides 750 00:36:02,477 --> 00:36:04,060 just tells you how much is in the way. 751 00:36:04,060 --> 00:36:06,460 That rho times x just tells you how much 752 00:36:06,460 --> 00:36:09,850 water's in the way in terms of how dense it is 753 00:36:09,850 --> 00:36:12,760 and how thick your water shield is. 754 00:36:12,760 --> 00:36:15,250 So using these tables, if you know, let's say, 755 00:36:15,250 --> 00:36:17,330 you're sending in one MeV photon, 756 00:36:17,330 --> 00:36:20,380 so we look up 10 to the 0 MeV-- 757 00:36:20,380 --> 00:36:23,080 you then have this value, this nice round value of 10 758 00:36:23,080 --> 00:36:27,120 to the minus 1 centimeters squared per gram. 759 00:36:27,120 --> 00:36:29,170 You then multiply by the density of the water 760 00:36:29,170 --> 00:36:32,230 that you have multiplied by the thickness of your water 761 00:36:32,230 --> 00:36:34,090 shielding, and you get the change 762 00:36:34,090 --> 00:36:36,570 in intensity of the photons. 763 00:36:36,570 --> 00:36:39,160 And let's do an example calculation just 764 00:36:39,160 --> 00:36:41,760 to make it a little more real. 765 00:36:41,760 --> 00:36:47,600 So let's say we have a beam of photons of intensity i naught. 766 00:36:47,600 --> 00:36:51,650 And we're sending it through a tank of water. 767 00:36:51,650 --> 00:36:54,680 And the question is, do you want to keep this water at 0 Celsius 768 00:36:54,680 --> 00:36:55,625 or at 100 Celsius? 769 00:37:01,480 --> 00:37:04,270 What's the difference in shielding between freezing 770 00:37:04,270 --> 00:37:06,250 and boiling liquid water? 771 00:37:06,250 --> 00:37:08,200 Well, we can look that up. 772 00:37:08,200 --> 00:37:10,820 And let's say we have to specify an energy of the photons. 773 00:37:10,820 --> 00:37:14,040 We'll call it 1 MeV photons. 774 00:37:14,040 --> 00:37:19,970 So we can look up and say at 10 to the 0 MeV, we go over. 775 00:37:19,970 --> 00:37:23,870 We get just about 0.1 mu over rho. 776 00:37:23,870 --> 00:37:32,930 So mu over rho equals 0.1 centimeters squared per gram. 777 00:37:32,930 --> 00:37:36,530 And now we can set up two equations, one for 0 Celsius 778 00:37:36,530 --> 00:37:38,850 and one for 100 Celsius. 779 00:37:38,850 --> 00:37:42,770 So we'll say i at 0 C equals i naught. 780 00:37:42,770 --> 00:37:49,880 E to the minus 0.1 times rho at 0 Celsius times x. 781 00:37:49,880 --> 00:37:53,140 Let's say we have, I don't know, 10 centimeters of water. 782 00:37:56,290 --> 00:37:58,170 So we'll just put a 10 in there. 783 00:37:58,170 --> 00:38:01,350 That works out pretty well. 784 00:38:01,350 --> 00:38:07,410 And then our i at 100C is the same i naught times e 785 00:38:07,410 --> 00:38:11,280 to the minus 0.1 times rho of water 786 00:38:11,280 --> 00:38:14,813 at 100 times 10 centimeters. 787 00:38:14,813 --> 00:38:16,230 And keep in mind here, I made sure 788 00:38:16,230 --> 00:38:20,700 that since my mu over rho units are in centimeters squared 789 00:38:20,700 --> 00:38:23,970 per gram, I'm putting in x as 10 centimeters 790 00:38:23,970 --> 00:38:27,635 because whatever is up here in the exponential has 791 00:38:27,635 --> 00:38:28,260 to be unitless. 792 00:38:31,110 --> 00:38:33,420 That's a good check to see why are my calculations off 793 00:38:33,420 --> 00:38:35,290 by a factor of a billion? 794 00:38:35,290 --> 00:38:38,500 Just check the units in the exponential. 795 00:38:38,500 --> 00:38:39,020 Yeah. 796 00:38:39,020 --> 00:38:42,620 AUDIENCE: Wouldn't the value of 0.1 change 797 00:38:42,620 --> 00:38:47,090 for your cross-section [INAUDIBLE]?? 798 00:38:47,090 --> 00:38:48,590 MICHAEL SHORT: The value of 0.1 will 799 00:38:48,590 --> 00:38:51,680 change depending on the energy of the incoming photons. 800 00:38:51,680 --> 00:38:53,340 AUDIENCE: I mean, for the density. 801 00:38:53,340 --> 00:38:53,850 MICHAEL SHORT: Nope. 802 00:38:53,850 --> 00:38:55,160 AUDIENCE: Density changes, right? 803 00:38:55,160 --> 00:38:56,452 MICHAEL SHORT: Density changes. 804 00:38:56,452 --> 00:38:59,400 And that's what we account for here with this rho. 805 00:38:59,400 --> 00:39:01,700 So next up we have to look up the densities of water 806 00:39:01,700 --> 00:39:04,470 at 0 and 100 Celsius because I don't actually know them. 807 00:39:09,280 --> 00:39:11,120 So density of water at 0C-- 808 00:39:11,120 --> 00:39:13,520 oh, surprise, surprise-- it's we'll 809 00:39:13,520 --> 00:39:17,102 call it 1 gram per centimeter cubed. 810 00:39:17,102 --> 00:39:18,060 Now what is it at 100C? 811 00:39:25,310 --> 00:39:28,540 Too close to tell. 812 00:39:28,540 --> 00:39:29,040 Actually. 813 00:39:29,040 --> 00:39:29,832 That's interesting. 814 00:39:29,832 --> 00:39:33,120 At 0 it's a little lower. 815 00:39:33,120 --> 00:39:35,492 AUDIENCE: No, I think that-- 816 00:39:35,492 --> 00:39:37,200 MICHAEL SHORT: I think that site's wrong. 817 00:39:37,200 --> 00:39:38,130 AUDIENCE: It's definitely lower at 100C. 818 00:39:38,130 --> 00:39:38,640 MICHAEL SHORT: Yeah. 819 00:39:38,640 --> 00:39:40,807 AUDIENCE: I don't think that second Google result is 820 00:39:40,807 --> 00:39:42,183 talking about 100 degrees C. 821 00:39:42,183 --> 00:39:44,100 MICHAEL SHORT: Let's look at some steam tables 822 00:39:44,100 --> 00:39:47,280 because this is a real place to look for them. 823 00:39:47,280 --> 00:39:49,200 So water is 100. 824 00:39:49,200 --> 00:39:52,020 Celsius atmosphere is-- 825 00:39:52,020 --> 00:39:53,020 OK, we'll just see that. 826 00:39:57,060 --> 00:39:59,100 I think they're down here. 827 00:39:59,100 --> 00:40:01,100 Oh, the chalk's not letting me use the touchpad. 828 00:40:01,100 --> 00:40:02,200 That's kind of cool. 829 00:40:02,200 --> 00:40:04,530 AUDIENCE: [INAUDIBLE] water at 100 degrees Celsius? 830 00:40:04,530 --> 00:40:07,190 MICHAEL SHORT: Oh, there we go. 831 00:40:07,190 --> 00:40:08,820 Yeah, I think I got it. 832 00:40:08,820 --> 00:40:10,570 So what's the density of saturated liquid? 833 00:40:10,570 --> 00:40:16,070 0.958. 834 00:40:16,070 --> 00:40:19,700 0.958 grams per centimeter cubed. 835 00:40:19,700 --> 00:40:21,900 Wow, I actually used the last corner today. 836 00:40:21,900 --> 00:40:23,060 Awesome. 837 00:40:23,060 --> 00:40:26,540 So you can actually, then, go ahead and calculate because-- 838 00:40:26,540 --> 00:40:28,460 I love how this worked out, right? 839 00:40:28,460 --> 00:40:30,230 0.1 in 10, cancel. 840 00:40:30,230 --> 00:40:32,360 0.1 in 10, cancel. 841 00:40:32,360 --> 00:40:36,680 So we'll just do e to the minus 1. 842 00:40:36,680 --> 00:40:45,920 And we get that this i is about 36.79% of the gammas 843 00:40:45,920 --> 00:40:48,500 will be transmitted through 10 centimeters of water. 844 00:40:48,500 --> 00:40:54,460 And here, e to the power of negative 958, 845 00:40:54,460 --> 00:40:59,830 we get 38.37% transmission. 846 00:40:59,830 --> 00:41:02,270 So actually, about 2% more of the gamma 847 00:41:02,270 --> 00:41:05,650 is will be transmitted if the water is hot. 848 00:41:05,650 --> 00:41:08,260 It's a neat little calculation that you can do. 849 00:41:08,260 --> 00:41:13,300 Now we've looked at a really fine, or very small 850 00:41:13,300 --> 00:41:14,950 magnitude example. 851 00:41:14,950 --> 00:41:16,570 Folks came to me yesterday saying 852 00:41:16,570 --> 00:41:20,500 we want to design a new type of medical x-ray apron 853 00:41:20,500 --> 00:41:22,840 because we're worried that people carrying around 854 00:41:22,840 --> 00:41:25,420 all this lead, their backs are hurting 855 00:41:25,420 --> 00:41:27,640 and it's making surgeons' lives difficult if they're 856 00:41:27,640 --> 00:41:29,410 doing radioactive procedures. 857 00:41:29,410 --> 00:41:32,350 Can we do any better? 858 00:41:32,350 --> 00:41:33,790 Can they do any better? 859 00:41:33,790 --> 00:41:35,790 What do you guys think? 860 00:41:35,790 --> 00:41:44,360 Can you beat physics when it comes to mass attenuation? 861 00:41:44,360 --> 00:41:46,700 It's going to be awfully difficult. 862 00:41:46,700 --> 00:41:50,930 And the best weapon you have is these mass attenuation 863 00:41:50,930 --> 00:41:53,990 coefficients to look at their relative values. 864 00:41:53,990 --> 00:41:57,480 Now these, again, are in centimeters squared per gram. 865 00:41:57,480 --> 00:42:00,590 So this actually ranks aluminum to uranium 866 00:42:00,590 --> 00:42:03,330 in a sort of like per atom basis. 867 00:42:03,330 --> 00:42:06,020 It has nothing to do with their higher densities, which 868 00:42:06,020 --> 00:42:07,580 only help things. 869 00:42:07,580 --> 00:42:09,110 This just tells you how effective 870 00:42:09,110 --> 00:42:12,080 each of these elements is relatively at blocking 871 00:42:12,080 --> 00:42:14,090 gammas of different energies. 872 00:42:14,090 --> 00:42:16,190 Then, to get the total amount of attenuation, 873 00:42:16,190 --> 00:42:17,990 you multiply by the density. 874 00:42:17,990 --> 00:42:19,660 Aluminum is pretty sparse. 875 00:42:19,660 --> 00:42:21,750 Lead and uranium are pretty dense. 876 00:42:21,750 --> 00:42:25,550 There's not too many ways around this problem. 877 00:42:25,550 --> 00:42:27,050 In fact, I wouldn't say that there's 878 00:42:27,050 --> 00:42:29,280 a way around this problem. 879 00:42:29,280 --> 00:42:32,640 The best thing you can do is look 880 00:42:32,640 --> 00:42:35,550 at the really only interesting features on these curves. 881 00:42:35,550 --> 00:42:38,060 Does anybody know why there's those jagged edges there? 882 00:42:42,960 --> 00:42:44,940 Well, let's take a look at some trends. 883 00:42:44,940 --> 00:42:50,030 For uranium, the jagged edge is at about 110 keV. 884 00:42:50,030 --> 00:42:52,680 For lead, it's like 80 keV. 885 00:42:52,680 --> 00:42:57,540 For tin, it's probably more like 50 keV. 886 00:42:57,540 --> 00:43:01,015 It's decreasing with z. 887 00:43:01,015 --> 00:43:02,640 Anyone remember what sort of magnitude? 888 00:43:02,640 --> 00:43:06,000 We've looked at things like this before. 889 00:43:06,000 --> 00:43:09,360 And if we're talking about photon electron interactions, 890 00:43:09,360 --> 00:43:12,020 what could be responsible for those sudden jagged edges? 891 00:43:22,330 --> 00:43:24,880 Well, we have talked before about all sorts 892 00:43:24,880 --> 00:43:27,310 of different decay methods, including 893 00:43:27,310 --> 00:43:31,090 those that can eject electrons from different energy shells. 894 00:43:31,090 --> 00:43:34,210 You're looking at the same electron energy shells. 895 00:43:34,210 --> 00:43:38,710 If you have a, let's say, photoelectric capable photon 896 00:43:38,710 --> 00:43:41,530 entering a calcium nucleus-- and let's go look 897 00:43:41,530 --> 00:43:44,370 at calcium as an example. 898 00:43:44,370 --> 00:43:47,110 So I'll go to the tables of coefficients. 899 00:43:47,110 --> 00:43:51,240 I'm going to back up to elemental media. 900 00:43:51,240 --> 00:43:54,130 And I'm going to go to calcium for a simple example. 901 00:43:54,130 --> 00:43:57,490 Calcium has got this jagged edge right here. 902 00:43:57,490 --> 00:44:04,290 And if we draw a line down, it is precisely 4 keV. 903 00:44:04,290 --> 00:44:08,370 4 keV, I bet, is going to be the k edge 904 00:44:08,370 --> 00:44:12,600 energy, the energy of the most inner bound calcium electron. 905 00:44:12,600 --> 00:44:14,550 To find out, we can go to the other NIST page 906 00:44:14,550 --> 00:44:18,480 that I linked you guys to, the NIST X-ray Transition Energy 907 00:44:18,480 --> 00:44:20,040 Table. 908 00:44:20,040 --> 00:44:21,325 And let's look at calcium. 909 00:44:24,550 --> 00:44:27,760 Wow, this really doesn't work with chalk on your fingers. 910 00:44:27,760 --> 00:44:31,170 And let's look at the k edge to check. 911 00:44:31,170 --> 00:44:32,160 Lo and behold. 912 00:44:32,160 --> 00:44:35,700 4.05 keV. 913 00:44:35,700 --> 00:44:40,740 So what you're seeing here is the photoelectric peak k edge 914 00:44:40,740 --> 00:44:41,850 absorption. 915 00:44:41,850 --> 00:44:45,480 What this says is at energies below 4 keV, 916 00:44:45,480 --> 00:44:48,450 you can't inject the innermost electron. 917 00:44:48,450 --> 00:44:50,430 You just don't have enough energy. 918 00:44:50,430 --> 00:44:53,790 As soon as you hit 4 keV, those inner shell electrons 919 00:44:53,790 --> 00:44:55,470 become accessible to you. 920 00:44:55,470 --> 00:44:57,840 So the cross-section suddenly jumps up 921 00:44:57,840 --> 00:44:59,910 because you have more electrons that you 922 00:44:59,910 --> 00:45:02,220 can inject photoelectrically. 923 00:45:02,220 --> 00:45:05,640 Beyond 100 keV or so, there's no more jagged edges 924 00:45:05,640 --> 00:45:09,960 because any photon above 100 keV can access pretty much 925 00:45:09,960 --> 00:45:12,570 any electron in any element, except maybe 926 00:45:12,570 --> 00:45:16,250 the super heavy ones, and we don't have data for them yet. 927 00:45:16,250 --> 00:45:18,140 So then you might ask, well, there's going 928 00:45:18,140 --> 00:45:20,660 to be an L edge for calcium. 929 00:45:20,660 --> 00:45:23,130 Where would that be? 930 00:45:23,130 --> 00:45:25,260 Probably off this chart. 931 00:45:25,260 --> 00:45:27,300 But you can look up where it would be. 932 00:45:27,300 --> 00:45:28,510 So we'll go to the NIST-- 933 00:45:28,510 --> 00:45:29,010 yeah. 934 00:45:29,010 --> 00:45:30,450 So you had the right idea, Dan. 935 00:45:30,450 --> 00:45:31,470 To the left, right? 936 00:45:31,470 --> 00:45:32,770 Yeah. 937 00:45:32,770 --> 00:45:33,970 Exactly. 938 00:45:33,970 --> 00:45:36,770 So now let's look up the L edge. 939 00:45:36,770 --> 00:45:39,020 So if I were to ask you-- wow, it really 940 00:45:39,020 --> 00:45:41,160 doesn't work with chalk. 941 00:45:41,160 --> 00:45:44,440 OK, that's better. 942 00:45:44,440 --> 00:45:51,130 So the L1 edge is down at 438 eV, which is indeed 943 00:45:51,130 --> 00:45:52,630 off the scale for this graph. 944 00:45:52,630 --> 00:45:54,940 This bottoms out at 1 keV. 945 00:45:54,940 --> 00:45:57,790 But if I were to ask you to draw the full mass attenuation 946 00:45:57,790 --> 00:46:01,180 coefficient for uranium, I'd expect 947 00:46:01,180 --> 00:46:04,840 to see a k edge, an L edge, an m edge, and an n edge 948 00:46:04,840 --> 00:46:08,050 corresponding to shell levels 1, 2, 3, and 4. 949 00:46:08,050 --> 00:46:09,940 And where do you get that data? 950 00:46:09,940 --> 00:46:13,240 You get it from here, from this NIST databases. 951 00:46:13,240 --> 00:46:16,600 Or you calculate it one at a time using 952 00:46:16,600 --> 00:46:30,850 that Rydberg formula, where that n final goes to infinity. 953 00:46:30,850 --> 00:46:32,978 So you can either calculate them if you don't know. 954 00:46:32,978 --> 00:46:34,770 Or if NIST doesn't have them in the table-- 955 00:46:34,770 --> 00:46:38,440 and I don't think they have the n edge-- 956 00:46:38,440 --> 00:46:40,090 wow, they go all the way up to fermium. 957 00:46:40,090 --> 00:46:42,060 Let's do uranium. 958 00:46:42,060 --> 00:46:43,620 What do they go to? 959 00:46:43,620 --> 00:46:44,120 Yep. 960 00:46:44,120 --> 00:46:46,340 They don't have the m or the n edge. 961 00:46:46,340 --> 00:46:50,270 But you do know how to calculate them, is with that formula. 962 00:46:50,270 --> 00:46:54,200 And so if we were to construct any old mass-- 963 00:46:54,200 --> 00:46:56,030 what is it, mass coefficient-- good, 964 00:46:56,030 --> 00:46:58,175 we have a little space left. 965 00:46:58,175 --> 00:46:59,800 It's going to look generally like this. 966 00:46:59,800 --> 00:47:03,500 There's going to be a photoelectric region. 967 00:47:03,500 --> 00:47:05,000 Let's say that's going to correspond 968 00:47:05,000 --> 00:47:07,370 to our photoelectric cross-section, which goes 969 00:47:07,370 --> 00:47:09,560 way up with lower energies. 970 00:47:09,560 --> 00:47:14,070 There's going to be a pair production part, which 971 00:47:14,070 --> 00:47:16,290 goes up with higher energies. 972 00:47:16,290 --> 00:47:20,130 And there's going to be this kind of decreasing Compton 973 00:47:20,130 --> 00:47:21,720 cross-section. 974 00:47:21,720 --> 00:47:24,820 And if you kind of dance these curves, 975 00:47:24,820 --> 00:47:27,040 you end up with a shape like that, 976 00:47:27,040 --> 00:47:29,980 which is just like all the other mass attenuation coefficients 977 00:47:29,980 --> 00:47:30,813 that you see. 978 00:47:30,813 --> 00:47:32,230 So this is why they take the shape 979 00:47:32,230 --> 00:47:35,080 that they do if you add up the cross-sections 980 00:47:35,080 --> 00:47:39,850 for photoelectric effect, Compton scattering, and pair 981 00:47:39,850 --> 00:47:43,090 production, and you just kind of bounce on top of those, 982 00:47:43,090 --> 00:47:45,953 you end up with the mass attenuation coefficient. 983 00:47:45,953 --> 00:47:47,370 And the part that's not shown here 984 00:47:47,370 --> 00:47:50,490 is that this photoelectric effect 985 00:47:50,490 --> 00:47:52,050 will have some jagged edges whenever 986 00:47:52,050 --> 00:47:55,282 you hit an electron energy transition level. 987 00:47:58,230 --> 00:48:00,110 So it's five of. 988 00:48:00,110 --> 00:48:02,910 Want to see if you guys have any questions on photon 989 00:48:02,910 --> 00:48:04,580 interactions with matter. 990 00:48:07,160 --> 00:48:08,910 I know it's a lot to throw at you at once, 991 00:48:08,910 --> 00:48:11,700 but I'm going to be giving you guys lots to calculate, to try 992 00:48:11,700 --> 00:48:14,640 it out and to learn what's going on from a more hands 993 00:48:14,640 --> 00:48:17,230 on point of view. 994 00:48:17,230 --> 00:48:17,730 Yeah. 995 00:48:17,730 --> 00:48:21,200 AUDIENCE: So you can't, I guess, beat physics 996 00:48:21,200 --> 00:48:24,520 by increasing density of materials. 997 00:48:24,520 --> 00:48:26,985 Is there a way to slow down gammas? 998 00:48:26,985 --> 00:48:29,100 MICHAEL SHORT: Is there a way to slow down gammas? 999 00:48:29,100 --> 00:48:31,497 AUDIENCE: Besides relying on [INAUDIBLE]?? 1000 00:48:31,497 --> 00:48:32,330 MICHAEL SHORT: Yeah. 1001 00:48:32,330 --> 00:48:34,550 So the question is, can you slow down gammas 1002 00:48:34,550 --> 00:48:37,848 without putting stuff in the way? 1003 00:48:37,848 --> 00:48:39,140 Well, then, what are you doing? 1004 00:48:39,140 --> 00:48:41,680 You've got a vacuum, right? 1005 00:48:41,680 --> 00:48:44,140 So-- hmm. 1006 00:48:44,140 --> 00:48:47,390 That's probably a deeper question than I think. 1007 00:48:47,390 --> 00:48:50,300 So gammas, for example, do have indices 1008 00:48:50,300 --> 00:48:52,460 of refraction and materials. 1009 00:48:52,460 --> 00:48:53,480 Gammas are just photons. 1010 00:48:53,480 --> 00:48:55,130 They're just really high energy. 1011 00:48:55,130 --> 00:48:57,170 And they do have indices of refraction 1012 00:48:57,170 --> 00:48:59,300 that are usually around one part per million, 1013 00:48:59,300 --> 00:49:02,420 or like 1.000001 or so. 1014 00:49:02,420 --> 00:49:04,850 So you can refract or bend gamma. 1015 00:49:04,850 --> 00:49:07,110 Just not very well. 1016 00:49:07,110 --> 00:49:08,860 So the question is, could you do something 1017 00:49:08,860 --> 00:49:12,380 to stop the gammas that were maybe 10 feet away? 1018 00:49:12,380 --> 00:49:14,447 The answer is physics. 1019 00:49:14,447 --> 00:49:15,280 Not much you can do. 1020 00:49:18,130 --> 00:49:20,160 But if they're, like, planetary levels away, 1021 00:49:20,160 --> 00:49:22,380 it's possible that you could bend them away from an object, 1022 00:49:22,380 --> 00:49:24,713 just like you can bend visible light away from something 1023 00:49:24,713 --> 00:49:26,220 closer up because it's got a much 1024 00:49:26,220 --> 00:49:27,785 higher index of refraction. 1025 00:49:30,700 --> 00:49:31,495 Pretty crazy stuff. 1026 00:49:31,495 --> 00:49:34,120 Did you ever think of gamma ray as having indices of refraction 1027 00:49:34,120 --> 00:49:36,890 and behaving like regular light? 1028 00:49:36,890 --> 00:49:38,570 It's just regular light. 1029 00:49:38,570 --> 00:49:41,968 It's just really high energy light. 1030 00:49:41,968 --> 00:49:44,010 So any other questions on the photon interactions 1031 00:49:44,010 --> 00:49:45,010 with matter? 1032 00:49:48,910 --> 00:49:50,460 Cool.