Good afternoon. My name is Jan Heise. I come from the Institute of Reference Materials and Measurements in Heel. It's one of the institutes of the Joint Research Centre of the European Commission. I graduated at the university in Ghent some time ago as a physics engineer, after which I did a PhD at the same university in experimental nuclear physics. I was mostly involved in proton and neutron scattering experiments studying nuclear-nucleon interaction. After that I switched to the neutron cross-section measurement business. In between I've been working for five years at the Belgian Nuclear Research Centre as a nuclear engineer working on the MIRA project. It's a project which is developing, or in the framework of which people are developing an accelerator-driven system. That's at SCK and MOL. In the meantime I've been back in Heel at IRMM for five years, I think. As a colleague of Peter Schillabakes and Carlos Paradella, who will also present something this afternoon. We're also working closely together with the Korea Atomic Energy Research Institute with our dear colleague Jung Il Kim. He will also present something. Good. I pronounce it right. Thanks. Basically we will be giving a series of lectures and exercises this afternoon, tomorrow afternoon and Friday afternoon. You will be seeing the four of us a couple of times. Mr. Kim is, as I said, from Korea. He works at the Korea Atomic Energy Research Institute in the Nuclear Data Centre. The three of us, we work at IRMM. As I said, IRMM is one of the institutes of the GRC. The GRC has different sites all over Europe. Quite a few of them are not that far from here, in Ispra, in northern Italy. But so we are in Belgium, in Heel. Now, this is the contents of what we would like to present the next coming days. I will not go through the whole schedule, but just to give you an idea, we will start with some principles of time-of-flight cross-section measurements. And then some evaluation of uncertainties and covariances. That's for this afternoon. And then tomorrow afternoon and Friday afternoon. There are some more lectures and exercises for scheduled. In this slide, we have tried to give you an overview of some interesting literature, which you might consider having a look at if you're interested by the subject. You will get the slide, so it's no use writing it down now, but just to be complete. And we also brought some materials, so you see the books here. Some of you have taken them already, if you haven't, feel free. Help yourself. So there's a number of reprints of articles, some overview reports. Quite interesting, since we will be doing exercises with AGS tomorrow and Friday. There's also a manual of the AGS code, so if at least you take one thing, I would consider taking that. Now, to start the subject, I will give a brief presentation on the principles of neutron time-of-flight cross-section measurements. Well, brief for the next half an hour or three quarters of an hour. And then Carlos will continue about transmission measurements and reaction cross-section measurements. When we are talking about neutron cross-section measurements, it's maybe a good idea to remind you of what we are talking about when we're speaking about neutron induced reactions. So when a neutron is interacting with a certain given nucleus, as a first step, a compound nucleus might be formed as a sort of intermediate state. And this compound nucleus, which is in an excited state, can de-excite through a number of channels. So either the neutron that was absorbed by the original nucleus can be emitted again and then we talk about elastic scattering. The neutron might be captured and then the nucleus will de-excite by emitting gamma radiation. In that case, we talk about radiative capture and gamma reactions. If it's a fissile nucleus, it might fission, it might break up into large chunks and then a number of neutrons, so that's neutron induced fission. The neutron might be re-emitted, but not with its original energy, but with a limited energy and then accompanied by gamma emission. So in that case, we are talking about inelastic scattering. And then any other number of neutron induced charged particle reactions might occur. So a proton might be emitted, a neutron, an alpha particle, triton, anything like that. So all these kinds of reactions are possible when neutrons are interacting with nuclei. And so we would like to study them and to do some measurements where we can study the probability for these interactions. Now the probability for such an interaction is given by a cross-section. And a cross-section is just a measure for the interaction probability between an incident particle and a target nucleus. So in this case, a neutron and a target nucleus. And here we've given an overview of a number of cross-sections as a function of incident-neutron energy. And so what you can directly see is that the interaction cross-section strongly varies as a function of neutron energy. So you see some 1 over v behavior in the low energy region for most nuclei, then a region where some sharp peaks in the interaction cross-section occur. So that's what we call the resonance region. And then going to higher neutron energies, we go back to a sort of continuum region. So there's a strong variation of the neutron cross-section as a function of neutron energy. You also see that the shape and the value or the amplitude of the cross-section also strongly depends on the type of nucleus that you're looking at. So it's very nucleus dependent and also strongly neutron energy dependent. Now if you want to study this neutron induced cross-section as a function of neutron energy, we will be needing dedicated facilities that are providing us with neutrons with which we can probe the different energy regions that we are interested in. Now why do we want to produce this nuclear data and how is it used? Well, you have experimental facilities producing or trying to map this cross-section behavior as a function of neutron energy. The results of these measurements are what we call microscopic data and together with nuclear theory and integral data measurements, all these results are taken together and are used to produce what we call evaluations. So evaluations sort of try to give a summary, a consistent summary of all available experimental and theoretical knowledge to produce a library, a data file that is then used by industry, by regulatory bodies or by research laboratories for doing calculations on the design of new nuclear systems or for doing safety assessments of nuclear systems, things like that. Now basically it's a circle because quite often people who are working in practice with nuclear installations, they see that in practice calculations are not always corresponding to what they see in experiments or in the operation of nuclear facilities. So this often points to deficiencies or lack of data or faulty data in the evaluated data files and so this is often the trigger to start new measurements and then we are back at the beginning. Of course the kind of data that you need for a certain application strongly depends on the neutron energy spectrum of that specific application. So here on the left-hand side you see a typical neutron spectrum for a fast reactor so that's what we are talking about when people are studying generation 4 reactors or a neutron spectrum of a classical thermal reactor. Here on the right-hand side you see a typical spectrum for an accelerated driven system where that's driven by a proton beam of 600 MeV. So depending on the neutron spectrum of the application also different energy regions of the nuclear or the neutron induced reaction cross-section data will be important. Now how do we study these cross-sections as a function of neutron energy? Well as I said before depending on the energy region that you want to study you will need a dedicated or a different facility. Now to give you an idea of the facilities we have at our institute we have on one hand Chilina which is a neutron time of flight facility and which is producing neutrons, it's a white neutron source so it's producing neutrons from thermal energies up to a few MeV and neutron energies there are determined by the time of flight technique and I will come back to that later on. If we go to higher energies we are using a van der Graaf accelerator so it's an accelerator that is using charged particles to produce mono-energetic or quasi-mono-energetic neutrons through charged particle induced reactions. So let me first tell you a little bit more about that before going into the real time of flight business. This is an aerial picture of our institute in Chil and so here you see the van der Graaf building so the accelerator is positioned in the vertical direction in the tower you see on the picture so that's what it looks like on the inside. It's a 7 megavolt van der Graaf accelerator it's a DC machine or it can also deliver pulse beams with currents up to 50 microamps there are different beam lines and some rabbit systems for doing irradiations or activations. Now this kind of facility is producing quasi-mono-energetic neutrons by accelerating charged particles in the van der Graaf accelerator and then letting these charged particles impinge on certain targets so here we are showing the example of neutrons that are hitting a tritium target and then through this reaction both neutrons and alpha particles are produced. By choosing different targets and either protons or neutrons as charged particle by playing a bit with the energy of the incident particle and also by playing with the angle under which we observe the neutrons basically you can produce mono-energetic or quasi-mono-energetic neutron beams over a large range of different energies and so this next slide is trying to give an overview of that so depending on the incident particle and the target that you're using you can sort of cover different energy regions between 0 and slightly above 20 mega-electron volt. These different reactions allow you to cover different neutron energies but on top of that you can also play with the kinematics of the reaction since both the incident particles and the target nuclei that you typically use for these kinds of reactions are quite light kinematics can play a very important role so the neutron energy for the same reaction with the same incident beam energy might strongly vary depending on the angle under which you are looking so this is shown here in the figure for I don't know which doesn't really matter for which reaction in particular but if you're looking at 0 degrees you get a peak at the full energy and then if you look at larger angles you will see that the energy of your neutrons is getting smaller. That's what the mono energetic part of our activities is about so it's basically you scan point by point different neutron energies in the energy region that you're interested in. When we are talking about gelina as I said before it's a wide neutral source where it's producing a range of neutrons with different energies at the same time and let me go a bit more into detail in this so here you see the same aerial picture of our institute of IRMM with the gelina facility shown here now gelina stands for Heal Electron Linear Accelerator it's a post-wide neutron source so with neutrons producing neutrons between 10 mV and 20 mV and it's producing all these neutrons at the same time so how can you then do a measurement as a function of neutron energy? Well you determine the energy of the neutron that is causing the interaction at the moment of interaction and that's done by the time of flight technique so that's how we determine the neutron energy so the facility basically consists of a linear electron accelerator which is producing electrons up to 140 mV these electrons are hitting a target and in this target neutrons are produced and these neutrons we use to do our cross-section measurements as you see from the picture you see different flight paths along which the neutrons fly along these flight paths you have different cabins where we have setups to do total cross-section measurements or partial cross-section measurements and so since we have different beam lines which can be used simultaneously gelina is typically a multi-user facility with a length ranging from 10 m up to 400 m so 400 m would be somewhere up here now how are the neutrons in gelina produced? what you see here is the final part, the last part of the beam line coming from the electron accelerator so this is the exit window the electrons when they exit they have an energy up to 140 mV and they hit uranium targets it's a rotating target it's rotating because if you would be hitting the electron beam continuously at the same part of the target it would just heat up and melt so that's why it's rotating it's also cooled by mercury and so the electrons are hitting the targets they are stopped in the stopping process due to the interaction of the electrons with the material a lot of branched trolling is produced and it's actually the branched trolling which is producing the neutrons by gamma-n reactions so gamma-n reactions and gamma-f photo-fission reactions in uranium targets so neutrons are flying in all kinds of directions they typically have an energy distribution which looks a little bit like a neutron a fission neutron spectrum with a high energy tail of course because the electrons have an energy up to 140 mV if you want to go down to lower energies to thermal energies we have to slow down the neutrons we have to moderate them and this moderation process is done by two moderators which you can see here on top and below the uranium disk these are irrelium containers filled with water so basically light material and by a number of collisions between the neutrons and the hydrogen molecules and the rest of the material but mainly the hydrogen and the moderators the neutrons will slow down and so you will soften your neutron spectrum so that's what you see here here on this plot on the right-hand side you see the flux as a function of neutron energy so the red curves show the fast spectrum the spectrum of the neutrons that are produced in the uranium targets and the blue spectrum is a spectrum that you get after moderating the spectrum with the containers on top and below of the spectrum now people often ask you can you switch between the two? yes we could but actually we do the two things together at the same time and we just switch between a moderated spectrum or a fast spectrum by putting shielding between the neutron producing targets and the entrance of the different flight paths so if at a certain flight path we want to do measurements with fast neutrons well we will make sure that we shield neutrons coming from the moderators because neutrons coming from the moderators will have a thermalized or a slowed down moderated spectrum and we will only be looking at neutrons coming directly from the uranium target so they are still having this fast spectrum shape and inversely we can also shield the neutrons coming from the uranium target itself and only look at neutrons coming from the moderators and then we will be looking at the moderated spectrum so here you see the shielding shielding which is with a hole in the middle letting through the fast neutrons or inversely just shielding in the middle which will block the fast neutrons before neutrons fly into the different beam lines now as I said before since we are producing neutrons with this whole spectrum quite simultaneously all the time we have to determine the neutron energy at the moment at which the neutron is interacting with the material that we are interested in and this is done by the time of flight technique so how does it work? well we have the target moderator assembly where the neutrons are produced and then at some distance L we have a sample that we want to study and some detector that will detect the neutron induced reaction that we are interested in now the pulsed electron beam will impinge on the target moderator assembly and produce a neutron beam it will produce a neutron pulse because it is the pulsed electron beam so it is very important that it is pulsed neutron will be generated will be created and will start flying at certain speeds to the sample if it interacts with the sample it might create some sort of reaction product or reaction radiation which is detected by the detector so if we determine the time at which the electron pulse is leaving the accelerator and we determine the time at which the neutron is interacting with the sample so basically the time at which we record an event in our detector the time of flight, the time the neutron needed to fly from the target, the neutron producing target to the sample that we wanted to study and so the time of flight gives us the speed because we know the distance it has travelled we know the time it has travelled and if we have the speed of the neutron we also have its energy so that is how the time of flight technique works now in practice it is a little bit more complicated than that because when the electron beam is sitting the target moderator assembly, as I said in the moderator you want to slow down the neutrons and so this is done by a number of collisions of the neutron with the material in the target moderator assembly so the neutron already travels a certain distance and it is already travelling for a certain time within the target moderator assembly before it is leaving the target moderator assembly and flying towards the sample so what we measure is the difference in time between the signal in the detector and electrons leaving the accelerator most of the time there is also an offset involved because just simply by electronics or different cable lengths especially if you are doing a measurement at 400 meter distance while the signal coming from the detector will have to travel 400 meters before you can compare it with the signal coming from your accelerator so that is something you have to take into account this offset you can determine by the gamma flash the gamma flash is a flash of gammas which is produced at the moment when your electron beam is hitting your uranium target so as I said when the electrons are hitting uranium target they are slowed down you produce a lot of gamma strolling it is very instantaneous it is a flash that is produced at the moment when the electron pulse is hitting the target and of course you know that this is the moment where which also the neutrons were created you know the time of light of gamma of photons it is the speed of light so you can perfectly calibrate your timing or determine the time offset by looking at the moment in which you detect your gamma flash in your detector so that is that now we are still dealing with the measured time of light and not the real time of light because the real time of light is a time that the neutron needs to go from here to here but it is losing some time here and it might also lose some time in the target or in the detector so that is something we have to take into account we have to take into account the time the neutron is travelling in the moderate or in the neutron producing target before it starts flying towards our sample also the neutron might be travelling around in your sample that is something I think Carlos or Peter will discuss later today or tomorrow before the reaction product before the reaction takes place and before the reaction product is entering in your detector so that is also something that you have to take into account so the real the actual time of light will be an expression like this and this will give you the actual speeds of the neutron and thus the neutron energy that you want to determine now, as I said at Gelina with the time of light technique we are mostly interested in the cross section region where we are seeing very sharp peaks in the cross sections so what we call resonances so it is the resonance region now this is a theoretical shape of what you would expect for a typical resonance in iron 56 I think not 65 Peter? 56 we will change that there are a number of differences between what you would expect theoretically and what you will actually measure so one of the things that interferes is what we call Doppler broadening I will not go into too much detail but I will discuss it later on it is a broadening effect of the finite temperature of the sample that you are measuring so it is related to the thermal motion of the atoms or the molecules in the sample material that you are studying on top of that there is also some experimental resolution involved so something which is related to the limited experimentally or physically limited resolution of your time of light facility is the overall width of such a resonance will be determined by the resonance width which is physics by the experimental resolution which is detector physics or facility physics and by the Doppler broadening which is related to the temperature so typically you will get some shape like this which is the result of all these different effects and if you want to describe them accurately with nuclear theory and make a consistent set of neutron data you would like to get the parameters which correspond to the theory so you would like to extract the total resonance width or the resonance parameters the physical resonance parameters for this specific reaction for this specific nucleus at this energy and try to compensate or at least compensate for these effects now let me first discuss a bit the experimental resolution which is involved in time of light measurements so as I said before the time the actual time of light that you would like to measure is a combination of a number of things so it's a stop signal from your detector from your accelerator there is some offset there is a time that your neutron travels in the target moderator assembly time that it might travel in the sample and in the detector now if you manage to do this you can extract the speeds and now on this determination of the speed there will be a number of factors that are influencing the uncertainty on that so the relative uncertainty on your neutral speed is given by this expression so there is an expression or part of the expression depending on the uncertainty on the time and part of it depending on the uncertainty of the distance now how does this translate into an uncertainty on the neutron energy it's actually quite simple the relative uncertainty on the energy is given by this expression and for non relativistic energies this is basically a factor of 2 so this corresponds to the half mv squared thing that we are all very familiar with so if you want to look at the different factors that have an influence on the energy resolution actually we have to look at the different effects which have an influence on the time resolution and on the distance resolution in our time of light measurement now if you look at the uncertainty on the actual physical distance L between our target moderator assembly and the sample that we want to study I think that nowadays we can measure quite accurately and I think it's fair to say that we can do that with an uncertainty of the order of 1 mm but more importantly there are a number of effects that will influence the time resolution of your time of light measurement so each of these different terms that we have in the expression for time of light will play a role there is the uncertainty on the initial burst how short is your electron pulse that you use to produce your neutrons there is the uncertainty related to the time resolution of your detector and of the electronics that you use to treat your signal coming from your detector there is the uncertainty on the time that your neutron will pass in your target moderator system and then there is uncertainty on the time that your neutron will spend in the sample and possibly in the detector now if we start with the initial burst that's something that's depending on the facility for single burst machines we mostly can assume a Gaussian distribution and time for gelina this is of the order of 2 nanoseconds full with half maximum for orella which is a similar facility at Oak Ridge National Lab in the US that's 4 nanoseconds for end of it's of the order of 8 nanoseconds for some facilities the original electron pulse or the original neutron pulse is not a single burst but it's a double pulse structure so this is a case for ISIS in the UK and J-Park in Japan and here you see a typical time shape of the original initial burst for ISIS so it's basically consisting of two bursts with 300 nanoseconds spacing in between so that's something that you have to take into account as a first step in your uncertainty in your resolution the second thing is the time resolution of your detector and the electronics now mostly you can also suppose that this is an uncertainty which follows a Gaussian distribution it strongly depends on the detector type so you have fast detectors and slower detectors the liquid scintillator typically has a resolution below 1 nanosecond it's quite similar for a lithium glass scintillator a Frisch grid ionization chamber depending on the gas that you're using and the size and geometry of the chamber but it's usually has an intrinsic time resolution of the order of a few tens of nanoseconds and a germanium detector typically has a time resolution of 10 nanoseconds now mostly the effects related to the initial burst and to the detector response are lumped together or put together in one normal distribution with a specific full width half maximum if you look at the next step there's a neutron transport in your target and a moderator and that's a bit more complicated that's less obvious so if we look at a probability distribution of the time that your neutron will travel inside your moderator as a function of neutron energy you get something like this for gelina and so you see four groups each curve corresponds to a different range in neutron energy and so the faster neutrons in the 100KV region they are not moderated too much so this means that they have not been traveling around in the moderator too long so you see that the time they spent in the target moderator assembly is quite small if you go to the other side of the spectrum the thermal region of course you start with neutrons in the MIV region so they have to do a lot of collisions in the moderator before they slow down and of course also the slower they are the more time they will spend the longer they will need to fly before they leave the moderator so you see that for the lower energy side you get a distribution of three times now this is a bit not very practical to work with since you see that there is a strong energy dependence in this probability function it is not so easy to find a consistent description for this so what we do is we work with something which is called the equivalent distance so we assume that we know the speed of the neutron and then we just transform the time it needs or it spends in the into a distance by multiplying the time with the speed you can do a mathematical transformation to transform this distribution to a distribution as a function of equivalent distance and then you end up with something like this so then you get a number of curves which are still depending on the neutron energy interval that you are looking at but you see that they are much closer together and it is also easier to interpolate in between these different curves to cover the different neutron energy regions so typically in the region between one and five electron volts this distribution and equivalent distance has a width of two centimeters if we plot this figure on the logarithmic scale you see that the tail is also varying according to the neutron energy region that we are looking at now to get some feeling or some more feeling about how this distribution is depending on the neutron energy we have made some plots where we show here on one hand in green the most probable the most probable length so it is the peak of the distribution for the different neutron energies so you see that it is the most probable distance that a neutron travels or equivalent distance that a neutron travels in a moderator target assembly does not very strongly as a function of neutron energy the most probable the average one which is the weighted average of the whole distribution you see that in a certain energy region it is not so depending on neutron energies but for higher neutron energies and for lower neutron energies there is a strong dependence on the neutron energy also if you look at the width of the distribution so if you look at the full width half maximum you see that it is quite flat down to low energy neutrons there the distribution gets much wider and if you look at the 2.35 sigma so which is the corresponding width for a Gaussian if you could fit it with a Gaussian you see that it is also strongly differs from the full width half maximum so it actually means that you have a very asymmetric shape of your resolution function and that this asymmetry is becoming more important for thermal neutrons now you can calculate all these things these resolution functions with Monte Carlo codes there is also a way to do it analytically so to split it up in different components there is a neutron production component so it is gamma N and gamma F reactions in the uranium so this part you can describe as an exponential decay the neutron moderation process you can describe with a chi-square distribution and a storage term so some of the neutrons might really travel around a long time in the moderator scattering around before they actually get out so this is called the Cole and Winsor function which is a theoretical approach or an analytical approach that is supplied at J-Park in Japan and something to take into account is that your resolution function will also your resolution function or your distribution will strongly depend on the neutron emission angle because if you are looking at a different angle with respect to the moderator your neutrons will on average have to pass a longer distance in the target moderator assembly so that is also something that you have to take into account in these analytical expressions now this here shows you a comparison between a probability distribution obtained by Monte Carlo and by Refit which is using an analytical expression but adjusted to experiment and you see that both are describing the shape in a rather good way I will not go too much into the details there now if we look at the resolution which is related to the photonuclear part of the neutron production process and we try to compare this for different facilities so we see that's for Gelina and for Oak Ridge it's an end-off you see it's given here on the same picture for Gelina the delta L is of the order of 2 cm for Aurelites also 2 cm for end-off it's 12 cm which is not surprising giving the fact that the target moderator assembly is quite large dimensions if you look at some other spallation sources like ISIS or J-Park you see that's depending on the facility and depending on the process that you use to produce the neutrons this resolution function might strongly vary and this is another picture showing the resolution function as equivalent distance as a function of neutron energy so for Gelina for end-off and for Lance which is a time-of-flight facility at Ozalamus if you want to have some more information about the different facilities we have included some references in the presentation so you can find some more details about that over there a final component into this equation that we showed before which might contribute to the experimental resolution is the neutron transport in the detector and as an example I can show you the response function which is a lithium-gloss detector so a lithium-gloss detector is a detector which is used to detect neutrons if you have a neutron beam which is impinging on the detector and the detector is basically a slab, a square slab in this case 1.6 millimeters and a thickness of a few millimeters probably one point that's probably 16 centimeters and you look at the contribution of the lithium-gloss scintillator to your resolution and you do the same thing you also describe it as an equivalent distance you get a distribution that looks more or less like this and that's not so surprising because if your neutron is impinging on your detector it might impinge somewhere in the beginning of the detector or it might intrude into the detector a little bit deeper and only interact with the detector further down the road so it's already normal that you get a distribution which corresponds to the physical width of your detector what you also see here is that the interaction probability is decreasing and it's not so surprising because that's a self-absorption effect all the neutrons that are interacting in the beginning of the detector cannot reach the end of the detector anymore so actually what you see here is the neutron absorption along the thickness of the detector and then there are some other effects which are related to neutron scattering in your detector before they are actually producing a signal that you can detect you also see a difference as a function of neutron energy so here again you will have to calculate this response function as a function of neutron energy in order to take it into account in the analysis of your data and to take it into account to be able to extract the physical information from your data to bring together what we've seen before so this is the expression we had before for delta v over v now what we can do is we can bring the L squared out of the square root and then you can write the same thing in this way now if we bring everything together that we've discussed so uncertainty on the initial bursts detection system, neutron transport and target and detectors which is described as an equivalent length we get this expression where the different components related to these four points are written down now we are using in our analysis a program called REFITS which is including a numerical and analytical response functions and a combination of both in order to a sort of deconvolution of the experimental effects in the data now it's important to realize that these different components will have different importance depending on the flight path length and also depending on the neutron energy region that you are looking at so if you just assume an uncertainty of two centimeters on your flight path length this will result in a flat uncertainty contribution which is apart from that neutron energy independence data T will have also an effect which is strongly varying with the neutron energy and so if you combine both you see that for lower neutron energies actually the time dependent or the uncertainty on your time component becomes quite unimportant there the resolution is mainly dominated by the uncertainty on your delta L so on the equivalent distance, traveling distance in your target in your detector intrinsically to the of the facility while for higher energies the time resolution will be the decisive factor I know but this delta L the two centimeters it's also it's the equivalent distance, traveling distance it's the uncertainty on the equivalent traveling distance in the target's moderator assembly so that's the delta L here so that's also something that's intrinsic to your facility so that's always there so just to illustrate that it doesn't make sense to worry too much about time resolution when you are in the electron volt region and everything which is linked to the uncertainty on the traveling distance is not so important anymore at high energy so that's something that you have to take into account some slides seems to have escaped but that's not so important I said before that the difference between what you do experimentally and the theoretical shape of a resonance is actually a combination of the theoretical shape of the experimental broadening and also of the doubler broadening and so as I said before the doubler broadening is related to the thermal movement of atoms, molecules in your sample due to the finite temperature of a sample so actually the cross-section is depending on the energy of the neutron but it's actually depending on the relative speed of the neutron and your sample nucleus so if the sample nucleus has a certain thermal motion the relative speed between your impinging neutron and the target nucleus might vary depending on the direction in which the atom is vibrating and so this effect will cause a broadening this gives you a theoretical description I will not go into the details of that but this is a picture, a plot that shows you the effect of this so at absolute zero temperature zero Kelvin a sharp peak or a resonance would look like that at room temperature by doubler broadening it's already broadened down to this blue level and if you go even to higher temperature it gets broadened even more so this is not only something which is interesting something to think about it's also very important for reactor applications because there often temperatures are reaching a few hundred degrees centigrade and so the doubler effect is something that's really influencing the way in which neutrons are interacting with material in your reactor in real life so if we come back to the theoretical capture yield that's what you would expect theoretically if you take into account the doubler broadening you get something like this if you then include the experimental resolution for instance at a 60 meter flight path you see that there is some broadening but it's quite limited because for a longer flight path you have a better time of flight resolution but if you go to shorter flight paths you see that also the experimental effects become very important so there is a big difference sometimes with what you see experimentally and actual physical width you would like to extract here is another example to illustrate that so it's a measurement a capture measurement on gold at the 12 meter flight path in this case at 12 meters you see that the experimental resolution is 2000 millilectron volts so about 2 electron volts the doubler broadening is a little bit less than 1 electron volt and the actual physical width is 120 millilectron volts so it's not straight forward to see the physical width in what you see experimentally if you move to a longer flight path and since the flight path length is in the denominator of this equation going to a longer flight path will increase or will improve the resolution so if you go to a 30 meter flight path you see that this already is drastically improving so the doubler depending due to doubler and the natural width stays the same but by reducing the experimental width you already see that you get a much better separation of your peaks here this works quite fine if you look at the same reaction but at a different neutron energy you see that here it doesn't help you a lot to go to a shorter flight path because here your experimental resolution improves from 200 millilectron volt to 80 millilectron volts but since the doubler broadening is causing a broadening of 300 millilectron volt it doesn't really help a lot so in summary I would like to say that the full width have maximum so the resolution of what you measure is combination of the total resonance with the doubler broadening and the experimental resolution and quite often one of these two is dominating what you see so it's not straight forward to extract the total width from the shape of your resonance and in practice it's quite often just the resonance area which is the effective experimental observable that you get from your experiment that's what I had to say thank you if you have any questions maybe you are switching between what you are doing what kind of shielding we are not actually switching we are a multi-user facility on one flight path we look at the moderated and on the other we look at the fast spectrum and we are using lead and copper as a shielding material so it's large blocks I think it's about 25 centimeters thick and it's normally enough to shield the neutrals that you're not interested in if I think at the moment one, two well not at the moment because the facility is down now one, two one, two, three, four, five six, seven, eight I think nine nine at this moment so we are doing nine experiments at the same time yeah now you're exaggerating Carlos more questions? no, no, typically I didn't mention that typically it's 800 hertz so 800 pulses per second but we can actually vary it down to as low as we want but every now and then we also do 50 hertz measurements because I didn't mention it explicitly but I think that Ralf mentioned it's this wraparound or this overlap so you get overlap of neutrons from the previous burst into the next burst you will discuss this then I'll learn our say nothing so which one did you and this one we were discussing this with each other yesterday and we should ask our colleague he's more informed but I don't know if you have anything sensitive to say about this it looks a bit I was also a bit surprised to see it so you also see that if you look at the original shape you also see that for the fast neutrons it has a very distinctive distinctive shape so there has to be some effect that you also see you also see it here that there is some special feature for the higher energy part so we have to check with maybe Stefan knows if you're asking if you want to measure the construction of the high energy neutrons that means the detector is so far with the compared to the neutral source so the plug is very low and normally the construction with the high energy neutrons is also low so how much time do you need to take for a measurement that's a good question that's true so that's the advantage of being a multi-user facility at some flight paths which you really dedicate for this kind of experiments you can just continue doing the experiment for a few months and other people can do other experiments at the same time which take less time so we have a 400 meter flight path but this is not used very frequently exactly because it would take an enormous amount of time to get sufficient statistics there they used to do it in the past apparently in the past people had more time than nowadays