 I work for the National Commission of Atomic Energy and for Instituto Balcedo in thermal scattering. So that is my first talk, what it's going to be about. First of all, I would like to show you where I'm coming from because it's too far away from here. Argentina is in South America, in the southern part of South America, in what is called Patagonia. So I have been traveling for more than 20 hours to be here today. First of all, related to Argentina, we have six research reactors that are working. We have the first research reactor in Latin America that is called RA1. Then we have two small reactors that are for academic uses. That one is in Córdoba University and the other one is in Rosario University. And then we have the RA3 that is the radioisotope producer that is located close to Buenos Aires near the airport. And that is the highest power research reactor we have. We also have a critical facility for the current reactor that is close to Bariloche. And inside the Bariloche Atomic Center, the place where I'm working, we have the RA6 reactor that is used for training the nuclear engineers. And also we have experimental facilities that are from Gamma, the NCT. We have a diffractometer and we also have a neutrography. And now we have under development and we have started building it a new reactor that is called RA10, that it will be close to RA3, that it has three main purposes. One of the purposes is the radioisotope production, then the irradiation of silicon, and also scattered experiments. This is the view of these new reactors. Here we can see the silicon facilities, then the awful irradiation test. And here we have a conutron source that will be providing these neutrons that we are going to use for scattering. And this information is explained in a poster we have outside and so then you are invited to see it. Apart from these research reactors, we also have three power plants that are working and one that is in thoughts only, but it is going to be constructed with agreement with the Chinese National Nuclear Cooperation. And also, apart from the nuclear power plants at the research reactor, we have an INVAP that is a company that belongs to the Argentinian government, designed together with the people of the National Commission of Energy for reactors that were sold around the world. These reactors are the Opal in Australia, in Egypt, in Peru and also in Algeria. So that is our nuclear situation today. That is what we have. So, in particular, myself, I work in the Neutron Physics Department at Centro Atomico Bariloche. This department was created by Héctor Altunez, who was working in General Atomics, and when he came back to Bariloche, he founded this department. The group was created towards a neutron source that is a linux that I will be talking about it in my next talk. It was a very small group, but now we are 23 people that we are working, counting researchers, technical staff and students. We are working on Neutron Physics, Applications to Contents Matter, Material Science and Nuclear Engineering. Also, at present, we are hardworking in the development of neutron scattering instruments for this new reactor I mentioned before. These reactors, just to remember, are similar to the Opal reactor that was built for Australia. So this is a subgroup of this big group I mentioned before. We are three people. We work in the development of thermal scattering kernels or thermal scattering libraries. And Rolando Granada, who is the head of that small group, he is the one that works in theory, Ignacio Marquez, who is working in the same thing, but with nuclear applications, and myself who I have been working in coal moderators, filters or light materials. So before starting with the thermal scattering theory, I think it's good to review some properties of the neutrons. We have to remember that neutrons can behave as particles and can behave as waves. So they are going to have properties from both, from particles and from waves. So as neutrons have no charge, they can penetrate deep in the matter. So they can avoid the Coulomb force, they can go in deep, and the interactions is between the neutron and the nucleus. If the material has a magnetic moment, as the neutron also has a magnetic moment, it can also happen a magnetic scattering. That is a very big advantage if you compare neutrons with X-rays or with electrons. They both have charge, so they interact with the cloud of the atom. So the interaction of neutrons is good because of the penetration. So if we consider the neutron as a particle, it will have a mass, it will have a velocity, it will have a momentum. We can connect these things with the energy and we can associate that with the energy that is related to a wave. A wave has a wavelength and a wave number. If we put all these things together, we can have a neutron with a certain energy, a certain velocity, a certain momentum, a certain temperature and a certain wavelength. The important thing to remember is that the higher the energy, the lower the wavelength. Another important thing, neutrons as free particles can live less than 15 minutes. That means that when we want to use neutrons as particles, we need to produce them in the moment. We cannot storage neutrons. So we need a nuclear reaction that can get neutrons out from the nucleus. There are two main nuclear reactions that can be used to produce neutrons. There is fission in a nuclear reactor or a spallation in a spallation source. By fission, we understand that the neutron strikes on a target. That target can be uranium-235. After that collisions, two other nucleus are formed together with energy and together to more neutrons between two and three neutrons. One of that neutrons can again collide to a new target and produce again two other nucleus, more neutrons and more energy. That is what we call the fission chain. Another option is the spallation. The spallation is produced with a high energy protons. The energy of this proton is close to one CAB. One of these protons collides into a heavy metal target such as tungsten and a lot of things are produced, but in that lot of things we also have neutrons. The big difference between a neutron, a fission and a spallation is that about one useful neutron is produced in one fission and 25 neutrons are produced in one spallation. We can get more neutrons for a spallation source rather than with the fission. Another difference, a nuclear reactor gives a continuous beam of neutrons while the spallation neutron source are pulsed. Another big difference, fission neutrons have to be moderated. They have to be moderated because they are born as fast neutrons. So to increase the probability of producing a new fission with that fast neutron to be moderated, to be speeded down and to get neutrons with higher probability of producing a new energy, a new energy, a new fission. So in a fission, in a reactor, we need to moderate the neutrons. But the big difference with a spallation source is that the spallation cannot be self-sustaining, right? A fission reaction, yes. So these are the biggest difference. Another thing that we have to remember, in any neutron source spallation or fission, neutrons are born as fast neutrons. The typical energy of a fast neutron is close to 2 or 1 MED, right? That's neutrons. If you want to use them as a particle, a probe particle, if you want to do a scattering experiment, we need a thermal neutron. So we need a moderator to reduce the energy of that neutron, independently of the source we are using. So we let this neutron to collide with the atoms of the medium and we reduce the velocity. When neutrons have a high energy, they lose energy in collisions. They lose energy up to what moment? Up to the moment they get the equilibrium. The equilibrium means that the neutron has the same probability of giving energy to the medium than to gaining energy from the medium. That is called equilibrium. And that equilibrium is related to the temperature of the medium and that's why that kind of neutrons are called thermal neutrons, right? So that equilibrium depends on the temperature of the medium. So if we want to reduce even more the energy of that neutron, what we can do is to reduce the temperature of the moderator. So in that way we get what is called thermal neutron. This energy is associated to a room temperature neutron, right? If we put another moderator, a cold moderator, we can get what is called a cold neutron that has a typical energy close to one milli-electron volt. And even more, we can reduce that energy if we put an ultra cold moderator and we get what is called an ultra cold neutron. So this is a typical spectrum, just to remember, this is a typical spectrum in a nuclear reactor. Neutrons, as I have said, are born as fast, then start losing energy. They pass through a zone that is called a Pifermal zone where the spectrum is 1 over B and then they get the equilibrium and they reach this Maxwellian shape of the spectrum. The maximum of the Maxwellian here, this is related to the temperature of the system. The real spectrum is the convolution of all that three mathematical models that were put together. So if we want to start with scattering theory, we have a beam of neutrons that collide into a sample. Most of them are going to be transmitted. Some of them, few of them are going to be scattered. What we are going to study is what happens when an incident neutron scatters with a sample and goes to another way. So we have to define the incident flux is the numbers of neutrons that are crossing per unit of area and per unit of time. This is the beam intensity. And the first definition, the double differential cross-section. The double differential cross-section is a fraction of neutrons that are scattered per second into a solid angle in a fixed direction and with finite energies between a prime and a prime plus delta a. This is the definition. You can find all these definitions in books. This is very, what I'm going to talk about is very heavy, let's say. So I'm going to show you where you are going, where are you departing and where are you getting. In the middle, you will have to believe what is done because it's difficult, right? So this is the definition. Then this double differential cross-section can be integrated in energy, defined in energies. So we can define the differential cross-section that is the fraction of scattered neutrons per second into that solid angle until a fixed direction. And in the other way, the same way, we have the double differential cross-section and we integrate it in the final energy. Instead of doing that, what we can do is we can integrate in all the possible directions instead of integrating in energy and we get what is called the energy kernels. That is the same, it's the number of scattered neutrons per second and energy neutrons and its density is always defined in this interval to the final energies. And finally, if we do both things, we integrate in the final energy and also in the final angles, what we get is the total scattered cross-section that is the total number of scattered neutrons per second in any direction at with any energy. This cross-section, this total cross-section is a quantum property of the nucleus. It has nothing to do with the size, with the real size of the nucleus. But it's called cross-section because you can compare to the definition of cross-section in mechanical, in classical mechanical. The cross-section is the effective area presented by the nucleus to an incident neutron. This is the same concept, but the important thing is that it's not related with the size of the nucleus. It's a quantum mechanics magnitude and that's why we are going to go in-depth to quantum mechanics to analyze all the processes. So the first thing we are going to analyze is we have only one neutron and only one fixed nucleus. The first thing in what we have to think, remember that we are working with thermal neutrons. Thermal neutrons have a wavelength close to two Amstrons and we know that if the interaction of the neutron is with the nucleus, the force that is going to appear is the nuclear force. And we also know that the nuclear force are short-range forces. That short-range is close to one Fermi. One Fermi is 10 to the minus 15 meters. 10 to the minus 15 is five orders of magnitude lower than the wavelength of a thermal neutron. That means that the wavelength of the neutrons see the nucleus as a point. So when the neutron is colliding, when the neutron is for the neutron, this is a point. That is what is called, that is catering as a point like. Also, as we are working with thermal neutrons, the energy of the neutrons, thermal neutrons have energies close to the milli-electron volts, 25 milli-electron volts. So the energy is too low to give energy to the system. So the catering is going to be elastic. So the catering of one neutron with one fixed nucleus is point-like and elastic. And that is the most important thing up to the moment. With this idea in mind, we can understand almost everything. So when we are working in quantum mechanics, we have a quantum mechanical system. What we have to do is to solve the Schrodinger equation. And to solve the Schrodinger equation, to solve the Schrodinger equation, what we need to know is which is the interaction potential that is taking place in that interaction. So the only thing we need to know is who or which is the potential. So we are going to do, first only for academic purposes, this simple calculation that is we suppose we are not going to perform all the calculation, but if we have an incident-way function that we suppose that is a plane wave, that is associated to the neutron that is colliding with that scattering point, when the scattering wave is a circular wave that has this shape. In this shape, what we can see is the presence of this parameter. This parameter is called scattering length. And this scattering length is a property of the nucleus. Right? If we use this parameter, if you use this information to solve the Schrodinger equation with the supposing that we are scattering with only one point, what we get after calculating, after integrating and after everything is that the total scattering is written as 4 pi with the scattering length with the square of the scattering length. That means that the scattering is isotropic. This is a constant which are the properties of this scattering length. The scattering length is a constant that depends on the nucleate and on the spin of the neutron nucleosystem. It is constant. That is really important. It doesn't depend on the angle. It can be a complex number and the imaginary part is related to resonances, to absorptions. It can be positive or it can be negative depending on the potential. It is attractive or repulsive. And the other important thing, there is no theory that can predict the values of this constant of the scattering length. These constants are tabulated, are determined experimentally and there is no way to find a model to adjust all the information about this scattering length. This is a good thing if you compare with X-rays. X-rays, we said before that the interaction was with the cloud of the atom. So it depends on the atomic number of the atoms. This parameter, the scattering length is analog to the form factor in X-rays. So for X-rays, the bigger the atomic number is, the bigger is the interaction. For neutrons, you don't know. You have to check in tables and to know how big is this parameter and that will give you good information about the scattering. Is it constant? No, because if you are working with fast neutrons, all this theory is not necessary. Because here, we are going to take into account that the neutron is so slow that it has time to see how molecules or how atoms are distributed in the sample. For fast neutrons, the interaction is totally different. This theory is only for thermal neutrons. Right? So now, we had before one nucleus and one neutron. Now, what we are going to have is one neutron that is scattering with a system. As I said before, we need to solve Schrodinger equation. So we have to think on states, initial states and final states. So we are going to call the initial state, the initial state of the neutron with the K, the final state with prime variables. The same name with the prime. The state of the scattering system with the lambda and the final state with the lambda prime. So we are going to look, we know from quantum mechanics that the differential cross-sections represents the addition of all the processes in which the state of the system goes from lambda to lambda prime and the state of the neutron goes from K to K prime. We are changing the system, the whole system from the initial state to the final state. Fortunately, we know that the differential cross-section is written in this way. This operator takes into account the number of transitions per second from the state, the initial state to the final state. Using the Fermi-Golden rule we are able to write that operator that takes the system to the initial state, to the final state. And independently of what is written here the important thing is that here we have a matrix element. That matrix element again is connected to the initial state with the final state through the interaction potential. We still don't know how it looks at potential. We are going to see that in two slides. But the thing is that the only thing that is here is the potential. So we can write this in a simple way. Here we have the information about the neutron and about the system on both sides of this matrix element and here we have information on the neutron. This is the differential cross-section. If we want to write the double differential cross-section we need to add information about the energy. We know the energy is conserved independently of what happens in the system. We know that the energy of the system plus the energy of the neutron before the scattering has to be equal to the energy of the system after the collision plus the energy of the neutron. That is always that way. So we can write, we can take profit of it and we can say that this differential cross-section can be with a delta function that takes this into account. We can construct the double differential cross-section. Okay? One important thing is that here we have defined this magnitude that is called, that is the difference between the initial energy state of the neutron and the final energy of the neutron. This is an energy transfer always talking about the neutron. One important thing is that we are going to be able to split the information on the particle and the information on the target and that's why neutrons are so good. Because we can separate totally the information about the sample. So now we have to think about that potential. The potential that we are going to use is the potential we always always happens that we don't know exactly which is the potential. We need to find a model. A good model that gives good results for this kind of catering is the Fermi pseudo-potential. This potential takes into account, depends only on the position of the nucleus and on the position of the neutron. Only depends in the difference, in the relative position of the particle of each atom on the sample. With that big supposition this is for each atom in the system we can get the total potential taking an addition of every interaction we can write the pseudo-potential, the Fermi pseudo-potential in this way. What we can see is that the dependence in the position is written as a delta function. It has to be with the neutron position and the position of each of the nucleus that belong to the system. And also, and very important here we have the scattering length of each of the nucleus that are present in the system. With this potential we can go and solve Schrodinger equation. Another important thing that we have to remember that is related to quantum mechanics is that in quantum mechanics we have magnitudes that are associated to operators that can commute or not. When that operators are not commuting the variables are called conjugate. Right? And we can go from one space to the other. We can jump from spaces of one variable to the other variable through the Fourier transformation. Right? So we can write the Fermi potential as a function of the position or using Fourier we can transform it to this variable that is there, this is associated to the moment, to the linear moment that is similar to the transfer of energy this is a moment transferred always related to the neutron. So in the same way we wrote the potential in space and we wrote the potential in the in the other space through Fourier. So suddenly we solve Schrodinger equation and we get this that is easily see that, no? Now it's not easy you can try to solve it honestly is only putting the potential in Schrodinger equation and to start solving it. But if you solve that what we get is this expression in the real case what you have to do is to take into account all the final states, states keeping one of the initial states fixed. So for one initial state you take into account all the final states and then when you get that for each initial state you do an average when you do that what you get is this equation that is called the master formula and it's the basis of the interpretation of all neutron experiments. So what we are going to do is to go inside this equation and to try to understand what is the meaning of each thing that appear inside. Any question up to the moment? So one thing that we have to remember is that the scattering elect is a characteristic of each nucleus of each isotope. Hydrogen and neuterions have different scattering lengths. Where can I know that? I go to a table right then we check that but each isotope has a different scattering length. So if we have a system we are going to have many scattering lengths that put all together will give one average scattering length for all the system and a standard deviation let's say related to that mean value right? So here it said each scatter has its own value on nucleus to another so here in this expression what we have to do is to write an average scattering length and an average v square right? So with this we are going to be able to split the scattering into two components one that is going to call coherence scattering and that another one that is going to be called incoherence scattering. The coherence scattering will be related to the mean value of the scattering lengths of the system incoherence scattering is going to be related to this difference that is related to the standard deviation right? The coherence scattering is associated to interference effects. The incoherence scattering has no interference effects. In the coherence scattering you will have a dependence in the direction of the Q vector. The Q vector remember that is the difference of the initial vector of the neutron and the final so you are going to have dependence on that in the coherence scattering and no dependence on that in the incoherence scattering. So the coherence scattering will notice the order or the structure of the material the incoherence scattering not So with this split we can what we can do is write, we can write the double differential cross sections into two components as I said before a coherent part an incoherent part we can also introduce these functions that are associated with the transformation in the, this is an energy space, remember that in quantum mechanics energy and time are related through the Fourier transform so we can define these functions that are called scattering laws one for the incoherence scattering and one for the coherent scattering that they are the transform of these functions that are called intermediate scattering functions all of these functions are relations almost the same, it depends on the variable right, so this correlation function scattering laws and the intermediate scattering functions contain the information on the structure in the coherent part and on the dynamics in the incoherence part of the sample, right this information is obtained in a direct way in the measurement of the double differential cross sections so the thing is up to the moment we thought of any system that goes through the potential from the initial stage to the final stage, we didn't care if it was a lattice or whatever, the best thing to do is the easy way to calculate is to suppose that we have a crystal we have a Bravais lattice right, in a Bravais lattice what we are going to suppose is that we have only one atom per unit cell that is the no base so we can call the position of each atom with the L this L vector and then we can allow each of that atom to move around the equilibrium position with this small perturbation to the system we can go to the previous expression and we can write the coherence scattering in this way and here important things start to appear writing these things, here we have you and me are operators that are related to the displacement of each atoms at time zero and in a future time and with the atom itself and with other atoms we have all that kind of correlations right so here in the double differential coherence scattering what we find is that all the information here from here to here is related to the sample the information about the neutron is only here this division is related to the neutron the other information is about the sample this information is also about the sample right this factor is a calculation that is related to the mean square displacement of each atom around its equilibrium position and this associated to that displacement is related to the temperature is strongly dependent on the temperature of the sample and this part is related to the creation of phonons phonons are the way to describe the normal modes of oscillation of the system the more normal modes of the systems are a way a behavior thing right so we need to invent or to create a pseudo particle the carrier of that wave that are called the phonons phonons are related to the collective movements of the sample right phonons are related to that collective movements are associated to solids but it can be used as is a Taylor expansion you can use in any system are associated in physics are associated to solids but it doesn't matter so we have here so we said we have something that this depends on the sample this depends on the neutrons this is information about the sample also is related to the temperature and this is related to the collective movements of the sample okay in the particular case that we don't have any transfer of energy from the neutron to the sample the scattering is going to be it's going to be elastic there will be no phonon creations right so this particular case of the coherent scattering we can calculate here in the double differential expression you can do this calculation and we get this expression this expression is maybe familiar to you because it's a Bragg scattering that applies not only for neutrons it applies to x-rays or to electrons it's the same expressions and the important thing here is to notice that there is a delta function this delta function means that this will be non-zero only in the cases that q that is the vector of the neutron the difference with the difference of the vectors of the neutron are equal to one of the reciprocal lattice vectors that is the definition of Bragg's scattering it only can be possible it can appear if we have an order system with this kind of thing then maybe you hear about in short orders in liquid you can have many things but in the general case the thing is that the elastic coherent differential cross-section depends on this delta function and also of course of the divide value function if you have a lattice that is not a Bragg lattice you are going to find an extra factor here that is called the form factor that takes into account that difference between being a Bragg lattice or not so as I said before the mean square displacements are associated to the oscillation modes we have the number of degrees of freedoms is equal to 10 to the 23 so instead of counting between each of that normal modes what we do is we use the density of states to describe all that normal modes that are characteristic of the sample so this density of states is a fraction of normal modes between this energy and energy plus a differential then if we write these normal modes with the density of states we can write the divide value factor in this way it doesn't matter the important thing is to remember that this divide value factor depends on that density of states in the same way we did that for coherent scattering we can do the same for incoherent scattering the big difference between coherent and incoherent scattering is the presence of the delta function for incoherent scattering we are not going to find that delta it's only for coherent scattering what we can find here is an expression that again depends on the divide value factor and again on the final creation in the special case that the scattering the scattering is elastic the expression the previous expression reduced a lot and we get a dependence only on the divide value factor what does it mean? it means that remember that the divide value factor we said that depends on the temperature of the system so at low temperatures these divide value factors goes to 1 so the lower the temperature the scattering, if this is close to 1 this is going to be constant so the scattering is going to be almost isotropic so the incoherent elastic scattering for low temperature samples is close to be isotropic so as I said before phonons can be written as a Taylor expansion of this expression right? in this expression we are going to have order 0 order 1, 2, etc so the first that is 1 is the elastic contribution the second is the first that is 1 phonon creation 2 phonon creation and so on why we write this? because in the master formula to put this Taylor expansion it is very complicated to calculate it by hand it is almost impossible the only case we can calculate by hand is 1 phonon so here we have the expression for the coherent elastic for only 1 phonon for the creation of 1 phonon this is the expression is easy but not that much so we calculate it for coherent and for incoherent another important thing is for incoherent in elastic of 1 phonon scattering here we get the density of states we mentioned before that it was a characteristic of the sample all the information of the dynamic of the system is included here this information what does the system do when a neutron gives energy to it we are going to see that in the but the important thing so it is that it is information of the dynamic of the scattering system so what we saw we saw that the scattering can be splitted into coherent and incoherent and both of them can also be splitted again into elastic and inelastic coherence has to do with interference aspects and incoherent has no interference in elastic scattering the neutron has the same energy at the beginning of the collision and after the collision it changes the direction but the energy is the same and in an inelastic scattering the neutron can lose or gain energy that is the big difference so the scattering the scattering cross section can be splitted in four terms scattering coherence no coherence inelastic coherence inelastic and incoherence inelastic or whatever they mix so we have four things we can split the cross section any questions up to the moment no questions so to sum up we see we have a neutron we have a sample we have an initial state we have a final state we connect the initial state with the final state through the pseudo Fermi potential equation and we can write the cross section of the system this only applies to thermal neutrons I was asked there if this applies to fast neutrons no, this is only for thermal neutrons why thermal neutrons? because thermal neutrons have energies or wavelengths close to the energies of the system we are colliding with this is only for thermal neutrons this is thermal scattering when we have a fast neutron the neutrons see the systems as if it were a gas so there is another theory and it is more easy to calculate so the calculation the analytical calculation of this expression is very difficult you cannot solve this by hand you need a code, you need a program to approximate you can calculate one phonon scattering but not more and normally one phonon is not the real case you have as much as you can so you can use the enjoy nuclear data processing system that is a commercial code that is used to generate the scattering law the kernels and the cross sections for any material at any temperature this code is designed to re-evaluate the data in the ENDF format and transform that information in the format for example if you need a cross section library for MCMP you can use the certain module to get the format that is convenient each module of the code performs a different task and communicates with the other module the idea of the initial code is to choose which other modules you need for each calculation this is the only commercial code that exists nowadays we have also GASCAT but it is not the more used in this moment but the enjoy is the only code that can be used you have to pay for it you have to have a license you cannot download it just use it you need a license but also it is the only one but it is a little restricted because it is not useful to calculate any cross section library in any temperature you have certain limitations for example you can calculate if you have other systems you cannot calculate for any Bravais lattice you have certain fixed lattice you also calculate under the incoherent approximation incoherent approximation is an approximation that gives you the calculation of the total inelastic cross section because the coherent part is difficult to calculate so directly it calculates the inelastic part of the scattering the total scattering cross section in this code you normally use alpha and beta variables that are the same variables we were using beta is related to the difference of the energy over Ca is Boltzmann constant t is the temperature of the system this is a dimensional variable to make calculation in an easier way the same for alpha alpha is related to the transfer of momentum and again is normalized with the temperature of the system in this way instead of calculating the s of q omega calculate the s alpha beta that is the way that thermal scattering is known what we need to feed the enjoy code well, we need information on the system remember we said that with the thermal scattering theory we were able to separate the information of the neutron to feed the enjoy nuclear data processing system what we need is information on the dynamics of the sample the dynamic is translated into this magnitude that is the frequency spectrum of density of states that in particular in the enjoy code is written in this way in the enjoy code you have to separate the frequency spectrum in two parts let's say in the continuous parts where you the old information related to rotations translate diffusion and all the things associated to collective movements are included in the continuous what is called the continuous parts then you have discrete oscillators for the vibration that are characteristics of the molecule this frequency spectrum spectrum can be calculated or can be generated in any way one way of getting this frequency spectrum is using molecular dynamics you can get the full frequency spectrum and you can calculate for whatever you want we have many other options but that is the most general and remember this is the way that enjoy writes the frequency spectrum is not the only way that it can be written for example we need a cross section library why we need a cross section library why are we trying to put this into enjoy normally when we want to calculate we use the MCMP code the MCMP code comes with libraries that are useful for fast neutrons or not so thermal neutrons the MCMP code includes the information not the isotopes but what is called the free gas library we need to know details on the structure of the sample so we need to use what I call the thermal libraries the thermal libraries are built using the enjoy and are built putting this information into this code so for example I will show you here when the RTRA10 reactor project started one of the main purposes was the silicon doping and people who were working on that need the cross section library of silicon need the thermal cross section library for silicon so we start working on that we fortunately we knew that that silicon that are to be radiated in the reactor are single crystals the good thing of single crystals is that they have only one main axis so the only way where you can get coherent scattering is if neutrons go exactly in the way of that principal axis so the coherent scattering can be you can suppose it is not there that is because it is a single crystal if we have a poly crystal we have a different cross section the cross section we calculate is not useful but for a single crystal we can suppose that only incoherence scattering is going to take place and we can work only on that and so it is good for that and that is what we did what we need was to know the frequency spectrum of the silicon the single crystal silicon so in the first place what we did is to start always when we start working on a new material what we do is we try to find in the bibliography the kind of information we have what we found is that in this reference we got this spectrum so we put this information into enjoy and we got it is not very clear we got this thermo library can be seen this thermo library the shape of this thermo library is inelastic all is inelastic and the cross section library that it was included in MCMP was this one so it's quite different so at first what we notice is that we don't know if the library we built was okay or not but what we notice is that we are going to find a difference in the calculation so for building that library what we did is we fed the enjoy and we got this one the pink one fortunately in that moment to get a single crystal silicon it was very difficult it was expensive but the most difficult thing was to get a provider of that crystal so we couldn't measure it but fortunately there were in the references we have information about a measurement that have already been done somewhere so this is the reference where we got the experimental data and fortunately what we got is this this is the calculation and this is the experiment right with that cross section we gave to the people that was working on that and they made this calculation they found that of course when silicon is irradiated they need to create in the silicon doping it consists in that you have a silicon single crystal by activation of one of the isotope of the silicon these silicon transmute into for photos and you get the how it's called the crystal you want right so what you need is to calculate how many photos were created that was done with MCMP with the reaction rate and the difference is here we found that it's not the same to use the cross section library that was included in MCMP we need to take into account the thermal scattering concrete example of things that we have been doing with this if you want more information about ENSHOI you can visit the idea of the talk was not related to ENSHOI I think that you can visit this website you have you have to pay for the code but you can learn how to use it for free so you can visit the page and you can learn when it is useful or not and which are the limitations also you are going to find information about the format of the libraries because one of the main characteristics of the ENSHOI code is that you can get the library in the format you need for MCMP you need the ace format for WIMS you need another format and etc. you get the format you need for each application and the last thing related to this is that the pictures were taken from this book that you maybe you may know this is a very friendly book to learn scattering so you can download it from the web also I have the PDF if you want is quite friendly to read so I think this is the last thing I don't know if you have any questions you should because no you mean about the total cross section the question is how to measure coherent and incoherent total cross section yes when you measure you cannot separate you measure you measure all together you need some to put information from outside the experiment the coherent and elastic and inelastic for example in the case of silicon when you have the single crystal you are measuring the total cross section but if you are measuring in a certain direction you are getting only one of the components because you only have coherent scattering in special cases always what you measure is that you can measure the double differential in another kind of experiment but the experiments we were using were total cross section experiment I will be talking about that in the following talk with enjoy you mean? no you can describe the branch edged from some materials because the enjoy code is a code that it was developed in the 60s so the calculations were slower than today and they were only for specific cases so you can predict a branch edged for carbon for example but not for any material I think in the way it is programmed not for silicon for example yeah yes no it depends because the S alpha beta are useful for calculations inside of a medium it doesn't take into account the optics of the neutron for that kind of things you use another code you are in the middle of a neutron field you are not following one neutron with the optics you can use the max test code for that and it has different libraries no more questions? good so after the break I will talk about our neutron source on our measurements so we can have the coffee