 So, this afternoon we will present to you measurements that we did on gold, so we changed from uranium which was in the program to gold. The lecture that we give is practically the same. Just that the element that we measured was different, we were not completely ready with the analysis of our uranium data. So, I will present the results of the transmission measurements and afterwards Kim will go through the capture measurements and then this afternoon we will continue also with the EHS and we will use the data, some data that I will show you here and that you will be processing then with the EHS gold. So, just to remind you what Carlos already gave you in transmission what we do is we try to determine the transmission in order to get access to the total cross-section. So, it is a very simple formula that is also why it is almost one of the most accurate cross-section data that you can determine. So, what you need to have is to such that you can apply this formula is that your measurements are done in a good transmission geometry and that you can realize by properly collimating just before the sample, just when the neutrons are reaching the sample and by properly collimating the neutrons with the detector. So, this is again a view on where we have, here we have the sample changer and here we have places to put background filters. Now, very important is that we alternate sample in sample out measurements and I will come to that later on. So, we do every ten minutes about the sample out and then ten minutes of sample in measurement. Here, you see the detector which is a lithium glass interlator and packed in a plastic bag in order to avoid a background from the light. So, here you see a typical measurement of a sample out and you can notice here the dips here which are due to fixed filters which you place in the beam. So, we have a sodium filter and a cobalt filter which we continuously keep in the beam in order to control the background. So, this is when we do a sample out measurement now. Now, then we place a sample in the beam, in this case it's an aluminium and a gold metal foil of 3mm thick and then you see here the effect of the gold and you see all these resonance dips which are due to gold. Now, we were mostly interested in this region here since we want to determine from these measurements the total cross section in what we call the unresolved resonance region. So, in order to do that we need to have a signal which is background free and here I show you how we determine the background. So, the total background is given here with a red curve and you see that it hits all these resonances where the product of n-sigma total is so high that neutrons cannot go through the sample and that they in principle cannot reach the detector. So, neutrons which are in the beam can in principle not reach the detector there. So, therefore we can easily use these dips here to estimate our background. And this background is a combination of different components. We have of course the time independent components which are coming from cosmic rays from whatever or from any other radiation which is not directly related to the beam. Then we have a rather important component which is related to the neutrons which are captured in the moderator and you have an n-gamma reaction in hydrogen which emits a 2.2 Mv gamma line. And this is for us this gamma line, this 2.2 Mv gamma ray produces almost the same amplitude spectrum as a neutron that we detect. So, we cannot differentiate in amplitude. We cannot do a gamma n discrimination in our detector so we will always detect this gamma ray and the component here is represented by this green curve here. Then we have an additional component which is due to neutrons which go through the beam, which go through the sample and they come into our measurement station and then they are scattered through the walls etc. And this is also a time dependent component which is represented here by the brown curve. So, we have done a series of measurements to characterize the time behaviour of these components by putting a lot of black resonance filters in the beam and now we know how these time components or these decay constants of these exponentials, we know their magnitude, we know these time constants. Now what changes when we, this is now the background when the sample is in the beam. Now, we of course have also to do the same game when the sample is out of the beam. And now look on the right hand side here. Here you will see the background, this red line here represented here with a green line and you see that it's different. And that is due to the fact that the sample changes the background. When the sample is in the beam, your background is completely different, but not the shape. So, what we do then is if we have to fixed black resonance filters in the beam, we can always adjust these amplitudes. And so we have always a very good handle on the background and we can also account for the presence of filters or the presence of samples in the beam. So then, if we do a background correction, sample in on the sample in and a background correction on sample out, and we correct also for that time effects, then we just make the ratio of the two background corrected spectra and we have our transmission. Just a division and that you will do this afternoon also. Now we put in just a k-factor here. And this k-factor is one and we put an uncertainty of 3% on it. And this here accounts for systematic effects on our background correction. So where did we get this k-factor from? Again, that is done by a series of measurements with black resonance filters and then checking the difference between the measured points here and the red line. And then we can do statistics on them and from that we determine the 3%. Then we have an additional factor and that is the n here, which is again one. Since all the spectra which we use in this equation, they are normalized to the neutron output of our machine. We have somewhere on the roof a BF3 counter which gives us the intensity of the neutron production. Now we each time divide the spectra by the neutron intensity. Now of course there is a variation on this counter. This counter is also not 100% stable and to account for instabilities on the normalization to the neutron intensity, we put an n factor here but this one has an uncertainty of 0.25%. And why is this uncertainty so low? That is because we alternate. We do sample in, sample out. So practically we have only to account for short instabilities, short time instabilities. It's not long time instabilities but short time instabilities. So in principle the n here accounts for the short time instabilities of the neutron monitor. So this is summarized here. So now we can produce our experimental transmission and we can account for systematic effects on the background and we can account for systematic effects due to the normalization to the B intensity. So from that we have the transmission as function of time of light and then we use them for two types of analogies. So where we can still separate the resonances from each other, we do a resonance shape analysis. So this is the so-called resolved resonance region and then we also use this, in this part here we can't separate the resonances anymore. There we do average cross sections and we do an unresolved resonance analysis. So let me take this picture again. So if you have the width of a resonance and you have indicated here by capital gamma and you have the distance between two resonances, the resonance region is that region where the distance between resonances is larger than the width. Now in the resolved resonance region there the resolution of the spectrometer is smaller than the width of the resonances. So we can separate the resonances. In the unresolved resonance region the resonance structure is still there so the resonances are still separated from each other but we don't see it. But there is still resonance fluctuations and that is very important to keep this in mind. So from the resolved resonance region what we do is we analyze single resonances and we try to determine the resonance parameters from a resonance shape analysis. And next week you will get some lectures on the R matrix theory. So what we do is we determine for example for this resonance here the 4.9EV resonance in gold from this transmission measurement we can determine both the neutron width which gives you the probability to form the compound nucleus and also is related to neutron scattering but we can also determine the radiation width even without doing a capture measurement since the radiation width comes from the shape from the width of this profile here. And this is so we determine from the transmission directly the neutron width and the capture width. We even don't need the capture measurement to get here the full resonance parameters. So in the unresolved resonance region here you see we can't separate them anymore the resonances so we cannot analyze for resonance parameters. So then what we do is we determine an average transmission and from this average transmission we determine average resonance parameters to reconstruct the cross-section. Now this is the equation for the transmission so the transmission is the exponential minus N the area density the amount the number of atoms per unit area multiplied by the total cross-section so if I calculate the average transmission that is given by this equation but the average transmission is not the exponential of N multiplied by the average cross-section or if you do a Taylor development of this one here and you average 10 then you get this expression. You see here that there is an additional term and if your cross-section is still varying if there are still fluctuations in your cross-section then the average transmission is not directly related to this term to the average cross-section. You need to correct for this additional contribution here and that is given here so the average transmission is not equal to this value here. OK so then the total cross-section cannot be calculated like this so here I give you if you would just take the logarithmic of the average transmission and divide by the area density that is not the average cross-section in the unresolved resonance region. So what we need to do is we need to correct for this and so what we do is this term here is nothing else than the average transmission divided by E minus N on the average total cross-section and that is given by this term so this accounts for still resonance fluctuations and these once we have this correction factor then we can calculate the average total cross-section. So and this correction factor can be calculated based on Monte Carlo calculation so what we do is we simulate a resonance structure based on prior information on prior average parameters so in principle we have to loop since we want to determine the average parameters but we need the average parameters to construct this correction factor so what we do is we build just a series of resonances and we reconstruct the cross-section and then we can recalculate then we can calculate this correction factor here but it's practically that is straightforward to do so once we have this correction factor so this is the one that you should not calculate this total cross-section but once we have this correction factor then we can calculate our average cross-section and you see that in this region here you would have a huge bias of about almost 10% so in your cross-section if you would not correct for this resonance fluctuations so that is a full bias it's not an uncertainty your correction is wrong your cross-section is then wrong but the further you go the less there are fluctuations in your cross-sections and then this this equation or the correction factor approaches once so this equation starts to be valid so yeah this is then the cross-section which we can get out so now we have to propagate of course the uncertainties so if we properly propagate these uncertainties which I said so decay 3% to end 0.25% and then the uncertainty on the area density of the sample which is about 0.22% we get a total cross-section average total cross-section as function of neutron energy in the unresolved resonance region with an uncertainty of about 1-2% now you can compare with data in the literature and you see that all these data that they agree very well so now we have of course to report this total cross-section and here I give you an example of how you can do it so we have the energy bins where we have calculated the average cross-section we report this correction factor that we applied and then of course we need also to report the covariance and for that we just use our HGS structure, our HGS formalism so we report the uncorrelated uncertainties and the correlated uncertainty components so in this case here this is the column with uncorrelated uncertainty components by just propagating the counting statistics due to the input spectra then we have the correlated component due to the K factor on the background very simple it's the partial derivative of the total cross-section here this equation versus K multiplied with the uncertainty of K then we have the uncertainty due to the normalization to the beam intensity which comes from the 0.25% of the stability of the beam monitor partial derivative of total cross-section with respect to N and its uncertainty and then the aerial density now you can easily verify where your biggest uncertainty component is coming from and so what we said is total cross-sections or transmission measurements provide you a very accurate experimental observable of 0.25% approximately that is the transmission but this 0.25% here is at the end the largest contribution to the uncertainty since practically the 0.25% is here on the average transmission but due to the fact that you have the aerial density included your total uncertainty here is dominated by this normalization and becomes about 1.5% on the total cross-section and that is due to the normalization to this 0.25% intensity but you see that with the AGS structure you can easily verify where your uncertainty components are coming from so the total cross-section the total uncertainty on the total cross-section here is nothing else than you just have to square all these terms and sum them and then you have the total uncertainty but you can also build the full covariance matrix so the S matrix in this case is 20 by 3 as a dimension of 20 by 3 so that is then the full reporting of the results now when you bring this data to XFAR you need also to provide all this information about your neutron source that we used to moderate the beam, the angle of our beam flight path with respect to the moderator, the filters that we used sample properties and detector properties so this all has to go also in XFAR and there is in the report we have there there is a template you just have to fill in the information that is related to your experiment so and that is what I wanted to say I want to make two remarks here so whenever you want to do measurements at our facility you can apply for access to our facility and you find information on our transnational access scheme on this website page we also have opportunities for students we provide financial support to participate in experimental programs and you can find information on that scheme here and then Tim will go now to the capture except if there are still questions so this year is basically this is a scheme to support it gives you travel support and accommodation support and it is meant for our master students our PhD students but we do not provide the PhD grant but if you are making a PhD and you think that it would be beneficial for you to add an experimental program to your PhD at our facility then we can provide you some financial support other questions?