Recent Results on Nucleon Structure
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Lindau Nobel Laureate Meetings42 / 340
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00:00
Particle physicsAtomic nucleusCrystal structureNucleonCrystal structureColor chargeMeasuring instrumentElectric power distributionNeutronElectronCathode rayGaussian beamCollisionElectricityIntensity (physics)Series and parallel circuitsGentlemanFinger protocolTransfer functionMagnetic momentAngle of attackCrystal structureQuantumScatteringMassRoll formingComposite materialCartridge (firearms)RutschungElectronic componentYearField-effect transistorHot workingLinear particle acceleratorCross section (physics)Atomic form factorSizingSchubvektorsteuerungSteelAngeregter ZustandDayBook designScoutingSpare partMachine
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16:59
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25:29
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42:29
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VideoMaterialNanotechnologyElectric power distributionComputer animation
Transcript: English(auto-generated)
00:12
Dr. Mecka, Count Bernadotte, distinguished guests, ladies and gentlemen, and students,
00:22
I must admit that in this distinguished audience I feel very much like a student myself, but it is a great pleasure to be here to be able to talk to you. I want to talk today about a problem in which man has been interested for a long time,
00:47
namely the composition of matter. Professor Bohr has already, in his general remarks, foreshadowed many of the things that I want to say. Men have tried to understand for a very long
01:08
time what matter is made of, and Rutherford and Bohr and many others have given us a beautiful picture of the atom, and in recent years one has been getting a picture of the nucleus,
01:27
which lies at the center of the atom. But I don't want to talk about either of those subjects today. I would like to talk about what lies inside the nucleus, namely the individual
01:45
protons and neutrons. Now of course you will see from what I say that this is a very difficult problem, and we are really nowhere near a final answer. Perhaps the modest contribution,
02:04
in the words of Professor Bohr, that we have made is to show that the subject is complicated. In other words, that the proton and the neutron are probably some kinds of worlds in themselves,
02:24
and we are only at the beginning of an understanding of what they are really made of. Some of the things that I have just mentioned I will try to illustrate now in my talk.
02:43
The plan of my talk is to give you a kind of a general outline and try to present the main ideas first. The main ideas are really very few in number, and so I would like to try to suggest them to you. And then I will show you a series of slides,
03:12
which I hope will illustrate the points I am going to make at first. So that is the general procedure I plan to take. Unfortunately the blackboard, which I should like to use,
03:28
is very small. So I will just sketch a few things there, and fortunately I have some of the formulas reproduced on the slides so that you will be able to see them more easily.
03:43
I wonder if I may have some light ones. Yes, thank you. Now the general method that has been used is really just an extension of older methods, and the method is related very much to the idea of electron diffraction, say, in molecules. One uses a high-energy machine,
04:08
which is forcing electrons, in this case a linear accelerator. This is the work at Stanford that I am going to report on. The beam of electrons is, in a sense, diffracted
04:21
by the proton or the neutron, and it is that the beam of electrons is, as we say, scattered. And, for example, if one has an electron beam coming this way, let us say, with energy E, and it is scattered by a nucleon, some finite size, let us say a proton
04:47
or a neutron, then it is deviated, it is scattered, and we call this the angle of scattering. Now you tell about what was in this body by the angular distribution
05:07
of the scattered electrons. In other words, you put a measuring instrument here, and you measure how many electrons, let us say, in the E prime are scattered into this
05:22
spectrometer, and then you move this spectrometer around and find the angular distribution. This is the standard method of studying small objects. It turns out that this energy and this energy are related by something very close to the usual common
05:42
orbital, so that E prime over E for an elastic collision in which this body is not disturbed, is not broken up, is given by this expression. It is again on the slide where M is the mass
06:04
of this struck nucleon. So in an elastic collision, some of the energy is given to the projected, stays with the electron, and the spectrometer, you select the energy,
06:25
you select the electrons at this energy so that you know they would elasticly scatter. Now do this properly, angular distribution. Now using the Dirac theory, ideas about
06:49
quantum electrodynamics, Mott developed a formula for the scattering process, and the cross section, d sigma, d omega, which represents the intensity as a function angle,
07:08
was shown by Mott to be given by a formula like this for a point charge
07:30
was assumed to have no magnetic moment, so that it is simply an electrical point charge. The electron, which is being scattered, does have a magnetic moment and a spin,
07:43
and that is all included in this Mott formula. This is the rather introduced by relativity and the idea of a spin. If the object, let us say the object is still
08:00
an electrical one, if it's still an electrical one, then it can be shown that if the object has some finite size or has some component structure inside it, you can represent that structure by multiplying this cross section by a quantity called the form factor. As a form factor,
08:29
you multiply the square of the form factor. This quantity Q is the momentum transfer. If you have, and this is a finite representation of the scattering process,
08:42
here you have an electron, and here you have a nucleon, and there is a transfer here of photon Q. Now Q is actually given by, this is a very important quantity by this expression, produced the cross section by this quantity X squared.
09:22
And this is the form factor, which gives you the diffraction structure that you see. For example, molecules, it is the same type of quantity that shows up in studies of a front over diffraction from slits in optics.
09:43
All right, now I introduce most of these quantities that I need. There is only one other thing to say here. And by the way, quantity excluding this X squared, sigma NS, that would include all of this. This will allow me to keep the next formula
10:06
simple. So it can introduce a bit of complexity in the problem. The proton is well known. It is not simply an electrically charged body. Now how do you take the proton and some kind
10:31
of magnetism, which is also able to scatter the electron? Not only does the simple Coulomb force scatter the electron, but the magnetic moment and the distribution of magnetic moment
10:44
inside the proton accounts for the scattering process. So when you describe a proton, you have to describe it in terms of, so to speak, its electrical behavior and its magnetic behavior. Now it's a little more complicated than that. In the Feynman diagram that I drew,
11:07
the proton is described not by one form factor, but by two form factors. This is called the
11:22
Dirac form factor, and this is called the Pauli form factor. This one is created with electrical form factor, and this one is a magnetic form factor. This refers to the distribution of anomalous magnetic moment in the proton. The proton has, as is well known,
11:42
a magnetic moment in nuclear magnetons given by a Dirac part and an anomalous Pauli part, and this describes how this moment behaves as a function of a momentum transfer, and this describes how that behaves. This I want to be able to tell you about k,
12:05
since it has a value 1.79 for the proton, and it has a minus 1.91 value for the neutron. In the case of the neutron, there is a zero here, a static value. You might say zero.
12:22
Now you notice that at this point, at this vertex, where the electron turns in a corner, I have not indicated any form factor of this number. Now it may very well be that there is some form factor there. In a way, that would indicate some breakdown in electrodynamics or
12:46
some change in the way calculations should be performed. As far as anybody knows, the latest experiments on the G minus 2 value of the new meson, all these things support
13:01
the idea that this electron vertex should just have a form factor of unity, at least as far as the small distances that are concerned in this problem, or at least when you stay within the range of the mental transfer that you're talking about. So I will assume that the
13:24
electron behavior is perfectly normal and goes with, you might say, an infinitely small distribution of electricity and magnetism. But on the other hand, the proton is thought to have a distribution both of its electrical charge and its magnetic moment. Now, by
13:45
standard methods, you can show that the cross-section, which is really an extension of the Mach formula, is given by the quantity which I had before, sigma NS times,
14:00
I think this is in the way here, it's going to be in the way anyway. This isn't very important because you will see it on the slide, but I simply want to indicate in this expression F1 and F2. So that, for example, if you measure
14:45
this cross-section and you make a plot in the F1-F2 plane, it's something like that, because this is, and it turns out to be, a glimpse. According to the ideas of quantum
15:04
electrodynamics, these quantities which describe the structure of a proton are thought to be functions only of the invariant momentum transfer, Q. If you use that idea, then you can find
15:21
F1 and F2, quite simply, because if you measure the cross-section at two values on the energy and angle, but both corresponding to the same value of Q, then you get another
15:41
ellipse of this kind, and the intersection will be the corresponding values of F1 and F2. That is a method essentially that we use. They're equivalent methods. You could plot this as a function of tangent squared theta over two, and then by, if you look at this formula,
16:02
you will see that by looking at the slope and the intercept, you can again find the values of F1 and F2. Now both of these methods are equivalent, and actually I will show how the results are obtained by both methods. All right, now suppose, by the way, this is
16:21
a formula called the Rosenblum formula and was developed in 1950. Now, suppose, very well, suppose that I use this and suppose that I find the form factors F1 and F2 for the proton by methods that I will describe to you in a little while, and find the corresponding
16:45
F1 and F2 for the neutral. Suppose I do this, and suppose I end up with four functions which describe the proton and the neutral. F1, let's say F1P, F2P, the proton form factors,
17:11
and these will be the neutral form factors, and all of these will be functions of the momentum transfer. Q is a problem because those are phenomenological descriptions of the proton
17:30
and the neutron over the details, but it turns out that you can use those functions in almost all cases that are known where you have problems that involve the proton and the
17:45
neutron. In other words, you don't have to have a picture, a model, in other words, of the proton and the neutron. It's sufficient to have these phenomenological form factors. That is, of course, one way of looking at the problem, and you can say that as soon
18:02
as you determine these four functions, you're finished, at least the experimenter is finished. Of course, in some way, you want to find an explanation of why these behave in the way they do. I mean, as you will see later, if you plot Q squared this way,
18:22
let's say F1 looks like this and F2 looks like that, and it will be corresponding plots for the neutron. Why do they look this way? Always, this will ask the question, but I do want to, this will ask the question, well, what does the proton and neutron look
18:44
like at least in qualitative form in the form of a model? Now, some answers to those questions can be given, although for relativistic reasons, the idea of using a model is not a correct idea. However, it may lead, theoretically, to some new ideas about the understanding of the proton
19:07
and neutron, and perhaps for that reason, it's worth thinking about them. But in any case, one would like an explanation of the behavior of these form factors. I'm not a theoretical physicist, so I'm not going to be able to give you an airtight description of the theory
19:26
on this point on. But I would like to give you an experimentalist's view of this theoretical problem. Now, the theoreticians prefer to talk not about F1 and F2 or the corresponding
19:48
ones over here, but they prefer to talk about linear combinations of the form factors. For example, they like to talk about a scalar form factor, which is F1P plus F1N
20:08
divided by 2. And they like to talk about a vector form factor, which would be F1P minus F1N over 2. And they are correspondingly defined form factors in the case of the magnetic
20:25
distributions. Now, they have easier ways of talking about F1S and F1B than about these quantities themselves because they think of the nucleon as really one kind of body with
20:44
two orientations in the isotopic spin space, which correspond then to the proton and the spin. Let's say this one, for example, F1V. Now, the dispersion theory indicates, and
21:04
I believe that there are other ways of getting this same result. In fact, this result has even some intuitive appeal. When you look at the confinement diagram, which I drew already, this being the proton or the spin form, the dispersion theory experts write this form
21:28
factor typically as an integral for a certain function called the strength function, where in the integration, which refers by the virtual with the nucleon. This integral
22:00
comes from twice the mass of the pi meson squared, because this is the first thing that can happen to infinity. And this strength function describes how strong that particular interaction is for any value of the momentum transfer or for the virtual
22:22
process that occurs, even has some kind of intuitive understanding to it. Because if you transfer a proton with mass not zero, you won't have this kind. This is known
22:47
as the propagator. If the mass is zero, the propagator is one over q squared. And if there is a mass present, it's one over q squared plus n squared. So this has some kind of a significance, which finally ends up in giving you the form factor as a function
23:06
of q. You integrate over m, and then this appears, and this is a function of q. The interesting thing is this. Of course, if g, if this strength function has any form whatsoever, you can't tell much about the problem. But usually there are
23:25
always some kinds of simplifications that give you the first approximation of the problem. And you can see one approximation in this case. If this g function turned out to be a delta function, in other words,
23:42
a sharp p at a certain value of m, you could take this out of the integral, and you would get a simple result of a form one over q squared plus whatever appropriate value is corresponding to that resonance. Now, things will never be that simple. There will always be, if you plot g, let's say m squared,
24:08
there may be a resonance here, but actually there will always be some kind of a tail or some kind of a pre-structure in here. So the first primitive idea is simply to say that let us imagine this is a
24:23
delta function, and you approximate all the rest of this integral by saying, well, it gives you some constant. Now, if you do that, you get a result that looks like this. And this is the Clementine
24:41
Milly form factor. And using this Clementine Milly form factor for years in trying to understand the shape of our form factor curve, but we had no understanding of why we were doing it. And now using these ideas and using the fact that in fact resonances
25:05
have been discovered just in this nature, one has at least a kind of rough approximation to the answer. Now, these resonances are known and have been discovered in the last year or two in the rho resonance
25:22
and the omega resonance. This one corresponds, if I remember correctly, to about 780 MeV, and this one about 750 MeV. And this corresponds to, roughly speaking, a combination of three pi mesons in some kind of an expected state.
25:46
And this corresponds to two pi mesons. This one is very nearly like the delta function. This one is more spread out, but still fairly sharp. So therefore, there seems to be some pretty vague kind of explanation for these form factors.
26:04
However, I emphasize that these ideas are only in a primitive state now, and we cannot yet see all the implications that are involved. For example, if we investigate our form factors
26:21
and use the two known values of the resonances that have been found and that are known to apply to this problem, they have the right quantum numbers, in other words, we can't get a reproduction of our form factors. But if you modify the values of these answers slightly,
26:42
you can get a very good description. Now, how can you modify the values if they're given by nature? Well, the point is that, maybe the point is that one made the simple assumption that they were delta functions.
27:01
But in actuality, as Professor Heisenberg has already pointed out, these tails may contribute to the problem. And I understand that some recent calculations on Wong and Ball at La Jolla in California show that, in fact, the effective values are reduced by just about
27:26
the proper amount to account for the experimental results. I don't want to go through all the details, this isn't the proper place for it, but I have tried to give you a little bit of a picture of a theory.
27:43
Now, if you want to talk in terms of models, only to get some kind of an idea of what the proton and neutron look like, let's say in their outer clouds where the model ideas may not be too bad, one can make a Fourier inversion of the form factors
28:01
in a well-known way to get the charge distributions. And I will show a slide to that back towards the end. There is one other thing I would like to say. At the very end of my talk, I will show some quite new data which have not been analyzed as yet.
28:26
Well, they have been analyzed, but only very approximately. And this represents, I think, a new approach to the problem, which may be a considerable show-off to us. In the case of the deuteron, well, let me say,
28:41
when you study the neutron, you don't have a target where you have free neutrons. You can't get a problem with neutrons. So you have to use the neutrons moving around inside the deuteron. And, of course, then you have to have some theory for the deuteron.
29:01
Now, it turns out that the theory is pretty good for the neutron, and the part of it that you have to use is really quite good in these studies. Nevertheless, the neutron is a bound particle, and it's not the same as a free particle, such as a proton.
29:21
The question comes up, then, suppose that you perform the same kind of experiment that you do in the case of a free proton on either the proton or the neutron when they're bound inside the deuteron. Will you get the same form factors?
29:41
In other words, here I have a free proton, and here I have a proton inside the deuteron. Now, I perform similar experiments. Will I get from this second set the same form factors that I get from the first set? Well, the way in which you can perform that experiment is to take an electron beam,
30:03
and here you have a deuteron consisting of a proton and a neutron, and let the electron scatter this way and pick up the proton in coincidence with the electron. And then you know you have a particular event in which the electron struck a proton
30:21
except for exchange effects, and you're collecting the two at the same time, so you know you dealt with a very primitive type of phenomenon, the deuteron. Now, we have done such experiments, have just begun to do these experiments, and they mean looking at the deuteron in very close detail.
30:41
One would also like to do these experiments by taking the electron and looking at the neutron too, and that's a very difficult thing to do, at least with our apparatus, because of our bad B-cycle. Now, I will show you some of these results at the end of my talk, and an explanation of the results
31:01
are taking it too long, but I'll be glad to talk in private to anyone about these results. So I think now I'll try to go rapidly through a number of slides which will illustrate the things that I've been talking about. May I have the first slide, please?
31:21
You can see on a large scale the Feynman diagram that I was drawing before. This is the electron line, and this is the proton line, or it could be a neutron, and this is the expression that comes into the real calculation that you must make.
31:40
This is F1, this is F2. May I have the next slide, please? Now, this is a diagram, a Feynman diagram, which shows a particular interaction in which the rho meson, the omega meson, is produced virtually, and this corresponds to one, it corresponds to that delta function
32:03
I drew in that strength function plot. This is just typical. You could have two lines here and have the rho meson. May I have the next slide, please? Now, here is the Rosenbluth scattering formula. I hope you can see it better than on the blackboard. All the figures aren't very much bigger.
32:23
Here is the momentum transfer. This shows the values for the proton. You can also apply this formula to helium-3. We have done experiments on helium-3. I cannot describe them here, in which you see the distribution of magnetism
32:42
in helium-3 and the distribution of electricity in helium-3, and they're both different. These are very interesting results. Again, I haven't the time to talk about them here, but I can discuss them in private. May I have the next slide? Now, this is just a simple diagram of the apparatus.
33:02
It shows that you have the beam coming in. You strike a target here, which can be liquid hydrogen or liquid deuterium, or it could be polyethylene-containing hydrogen or carbon. You have two spectrometers, one here and one here, a large one and a small one. You can pick out scattered electrons
33:21
going into this spectrometer and, for example, protons going into this spectrometer. You can do the two in coincidence, and this is how the coincidence experiments were done. May I have the next slide, please? This gives you an idea of the order of magnitude of the apparatus. Unfortunately, it is big and clumsy and hard to handle.
33:42
This is one of the spectrometers, and it weighs about 200 tons. It contains here a shield weighing about 40 tons, and inside this shield is a detector. In fact, there are a number of detectors in there, and I'll show you a picture of them in a moment.
34:00
Here is the smaller spectrometer. This weighs about 30 tons with a heavy shield up here, too. And here is the target. The electron beam comes from a long distance in front of this machine, and this is a Faraday cup. It's different from the usual idea of a Faraday cup since it weighs about 10 tons.
34:22
This spectrometer and this spectrometer both rotate around on this rail. Now the next slide, please. This one is upside down, I'm afraid, but it's all right. If you think of it, just turn it around. This is the liquid hydrogen liquid deuterium target,
34:45
and this is where the hydrogen goes, for example, and this is where the deuterium goes. Now when you put this, you see, there are very thin walls here. They're one mil of stainless steel, the walls on this target.
35:01
And when you put the chamber in vacuum and have the liquid hydrogen liquid deuterium in these target vessels, the walls bulge. And it's a fairly difficult matter to measure the thickness. And so we have put a wire on here which hangs down when you turn this around.
35:23
And then you can sight on the position of the wire by optical means and find the thickness of the target. This has turned out to be a rather difficult problem. It's a simple thing, but it's hard to do. But anyway, we have done it optically so far.
35:40
We're trying to develop a mechanical method of doing this at low temperatures. That's what makes it complicated. They have the next slide, please. Now this is the detector. This is a multi-channel detector. In most of our earlier work, we just used one counter. But now you see we're using ten.
36:00
There are ten counters here and ten full multipliers so that you get ten pieces of data at once. And this gives us a great increase in the potential accuracy of our results. We have not yet gotten that full accuracy, but we're on the way. And it's possible, of course, to think of 100 channels
36:22
by using semiconductor-type detectors. But we haven't done this yet. Now the next slide, please. Now this is a sample of all the data showing a hydrogen peak which one obtained from a polyethylene target. Here is the hydrogen peak.
36:41
I mean it's a polyethylene peak, but it contains hydrogen and carbon. And this is a background study made with carbon. And from the difference, you can get the hydrogen area and you get the hydrogen cross section. Now we have the next slide, please. Now this is a sample of our new results.
37:00
And you see our background is almost zero. In fact, the background here is coming in large part from the wire that we put on. It just so happens we put a thick wire on by mistake instead of a thin wire. And so about half of this background was due to the wire. And the other half was due to the thin steel walls.
37:23
But you see now, you can see this tail quite well. And so you have a nice idea of what the proton peak looks like. Now this should enable us to get results with much higher accuracy than we've had before. But as I say, we're only beginning these studies now. And I can't show you any real final results.
37:45
Now the next slide, please. Now with the old data, we got curves like this. This shows the cross section versus the energy at particular angles. We had results like this, this, and this. Now with the old data on the proton, we used polyethylene
38:04
and we obtained these curves. Now we're just starting to get new data with the liquid targets, which should be much better. And here is our first point. You see, it happens to fall right on the curve. But potentially, we can reduce the errors still further,
38:23
although we haven't done that yet. Now the next slide, please. Again, this shows results at other angles. The old results at 75 and 90 degrees and 135 degrees and 120. Now you notice the new liquid target gives results here
38:41
and here and here. So again, potentially, we'll be able to get very nice results. And more or less, they are in pretty good agreement with the old data. May I have the next slide, please? Now this represents purely old data.
39:02
And it shows a behavior which we have never understood out here, which may imply that there is something wrong with a Rosenbluth formula at very large momentum transfers. This is an open question at the moment.
39:20
And the Cornell group and other people are beginning to worry about this problem. And I don't think the answer is clear. But up to momentum transfers of about 25 family to the minus 2, the Rosenbluth formula is good. And I already talked about that region. May I have the next slide, please?
39:41
Now using data of that kind, you get these elliptical arcs and you can make intersections. And you find F1 and F2. Now there is a problem of other intersections because two ellipses intersected four points. And I haven't the time to go into that.
40:02
But in the case of the proton, there's no ambiguity. In the case of the neutron, there is some ambiguity. But we take the solution to the problem, which the theoreticians favor. They believe that one set is right. And that is the set we have chosen. May I have the next slide, please?
40:20
Now I also mentioned that you can use a straight line method in which you plot this cross-section essentially against tangent squared K over 2. And you get points like that. And from the slope and from the intercept, you can find F1 and F2. May I have the next slide, please?
40:42
More than a year ago, we found results for F1 and F2 for the proton that looked like this. I think our estimates of error were not large enough. And perhaps these lines indicating error limits
41:02
should be a little larger. But these are still pretty close to what we believe to be right. May I have the next slide, please? A more refined analysis of the same data shows that the region in which F1 and F2 can be looks like this and this.
41:23
This line and this line are the same ones that appeared on the previous slide. The scale has changed, but they're the same ones. And the error margins are indicated here. Now the new measurements with a liquid target fall right here and here.
41:42
So I think we're in the right neighborhood. And I'm sure that in the next year or so, these error bars will come down by perhaps a factor of 2 so that we will know the F1 and F2 behavior with more
42:01
accuracy than is indicated on this slide. May I have the next slide, please? Now I come to the deuteron and to the neutron. In the case of the neutron, as I said, you can't measure the form factors directly. You must use a theory. And furthermore, when you look at the neutron, when you look at the deuteron, which contains a neutron,
42:24
you see peaks like this. This is the elastic scattering peak that corresponds to this one when you consider the deuteron as a whole. Now when you break up the deuteron, you are essentially scattering from the proton and the neutron incoherently.
42:41
And therefore, the cross-section peak should be approximately at the position of the proton. And here is the proton peak, reduced scale by about a factor of 8 or so. And here is the deuteron peak. And you see, it does appear at the right place. And in fact, it shifted down just to energy
43:00
because of binding energy, as it should. If you measure the height of this peak from here to here and compare it with the area under the proton peak, you have a way of self-calibrating. And if you obtain the deuteron cross-section, then using a little bit of theory, you can get the cross-section for the neutron,
43:23
attracting, essentially, the proton cross-section. Now this is a very nice curve. It's a new one with a liquid deuterium target. And when you add the two backgrounds, and I can't explain all that you should do here, you get essentially zero.
43:41
So you have not only a method where you can use the peak, but you can also use the whole area of the curve. And this we have not yet done. But it should give an independent way of determining the neutron form factors. May I have the next slide, please? Now here is a similar curve, or points, rather,
44:01
for the neutron when plotted against engine squared theta over 2. And you see some old points here, open circles, and some new data here. They agree pretty well, but not perfectly. And in fact, there are some systematic differences.
44:21
And we believe that the new data are better than the old, but we haven't yet proved this. May I have the next slide, please? Now, as a result of doing a lot of experimentation and a lot of analysis on the proton and the neutron,
44:40
you get these four form factors. There is a proton, F1, proton, F2. Here's what the neutron looks like. F2, N for the neutron, and this region for the F1 of the neutron. The neutron form factor appears to be very close to zero.
45:02
These are our early measurements. And these are some points based on elastic scattering of electrons from the deuteron as analyzed by Glendening and Kramer. And they seem to fit together, not perfectly, because in the early measurements we had this bump.
45:24
But on the whole, not badly, considering the size of the errors. The errors in F1N are, of course, very large, because it's a difficult thing to do. May I have the next slide, please? Now, here is an enlargement of the neutron form factors
45:41
that appeared in the bottom part of the last slide. And you see the same behavior. Now, our recent work by Urian and Hughes gives these points shown as crosses. And these were taped with a thin liquid target.
46:00
And you see they are tending to remove this bump and tending to give agreement with the elastic scattering data. So we believe, although obviously this work has to go on a long time before we will have good form factors, we believe that indeed the neutron form factors do lie in this region.
46:22
Now, an attempt at analysis has been made with these dashed curves. And there were also dashed curves in the case of the proton. Those are based on using these dispersion theory formulas and using resonance values found from the data.
46:41
May I have the next slide, please? As I said, you get two values of the resonances that are different from the known values. And that implies either that the effects of the tails have to be taken into account, or else there are other resonances that are contributing that we don't know about.
47:02
Now, if you want to make a rough model for yourself of the proton and neutron, this is what they would look like. These are qualitative and are not to be taken as indicating quantitative measurements. This is 4 pi r squared times the density in arbitrary units.
47:21
So if you have a finite density at the origin, you will get a zero. However, if you have a delta function at the origin, you can still get something, and that's indicated here. But the proton will look more or less like this. And this is in terms of 10 minus 13 centimeters.
47:41
And the neutron will look like that, with a positive part and a negative part and a negative delta function. Now, of course, these are very rough measurements. The errors here will be at least as large as that. And it may very well be that the neutron is identical to zero.
48:03
It could be consistent with these experiments that the neutron is identical. That gives you a charge distribution that is identical to zero. We don't think so, but it would still be, perhaps, consistent. May I have the next slide, please? Now here, just as a preview of what
48:23
we may be studying in the next few years, I would just like to show you a couple examples of coincidence techniques. Here is an electron in coincidence with a proton when you study free protons. In other words, liquid hydrogen.
48:40
And here is the coincidence peak that you see. It comes in exactly the right position, just where you place the spectrometer, and expect to find the peak for kinematic reasons. You find it exactly there. Now, when you go to the deuteron, may I have the next slide? Here is the deuteron.
49:01
This is a much harder experiment. You're knocking out the proton in the deuteron and also picking up the electron. And here is the peak that corresponds to the kinematics of a collision with a free proton. So it's just as if, in the deuteron, the proton were sitting still when you study this peak.
49:25
On the other hand, if you move one of the spectrometers, let's say the proton spectrometer, three degrees away from this position, you also find protons there. And that is because the protons were moving inside the deuteron, and the kinematics are slightly different.
49:40
And so you get another peak down here. And if you move six degrees off, you get still another peak there. So this gives you a detailed way of looking into the intricate things that are going on inside the deuteron. Now, we have some measurements of this cross-section. And to the first approximation, the bound proton
50:02
form factor is not the same as the free proton form factor. I think I understand the reasons why, but I have no quantitative data to support this at the moment. This would not influence any of the results I have shown already, but it gives you new information, I believe, on the exchange character
50:23
of the forces. I have tried to present a very complicated subject in a short talk, even though this has been pretty long. But I think you can see that the study of a small thing,
50:43
such as the proton in the front, will go on for a long time before one understands what's really there. Thank you.