 Now, as I mentioned earlier that I will take a particular case since energy is well below the coulomb area, this back scattering can be called as the other put back scattering. Now, in the back scattering what you do is you have a target here and the beam is coming, this is beam and in back scattering you measure, you put the detector here, let us say this is detector, detector at a very backward angle. Now, this at backward angle there is a spectrum and if you choose the spectrum in such way that you take the end energies and maximum energy of the scattered particle, that means that a scattered particle is coming from the surface itself, it is the particle is not entering inside. So, the error due to uncertainty in the thickness of the thickness of the target will be minimized or equally almost like 0 and therefore, that is the advantage. So, the energy or the k value which we are determining. So, basically in by using whether the aluminum P gamma reaction or any neutron threshold experiment or by this back scattering experiment, we are measuring the k value and for k value we should know this precisely and other parameters like as we said that r value and because if the beam is coming, if suppose magnetic like this and if beam is, if it is following the center trajectory, then the radius of curvature is well defined, but if it is coming like this beam is diverging, heavily diverging then it may not be safe, it can. So, we have to well define the end. So, even if the beam is coming like this, we have to see that the only a very small portion of the beam is passing through that and that is so that the trajectory is central trajectory for which the radius of curvature is well known. So, this could error if your beam size is big, then that can introduce the error in the case of this. So, that can be taken care of by putting the well defined collimators. So, that is central only the central beam passes through the magnet and well defined and you can put another slit at the exit of the magnet. So, that to define very precisely the central trajectory, once you do that then all this is valid whatever I said and once that is there then central trajectory is known. So, r is fixed. So, k will be fixed for that magnet and the error coming out of due to this will be minimized. So, here we are doing the backscattering. So, in this case for example, as I said that I will give the example of the backscattering experiment to determine the k value in case of protea. So, we use the silicon surface barrier detector and we use several beams of for example, H1 hydrogen or proton, lithium 7, carbon 12 and fluorine 19 and also that was to and the several targets here they are mentioned and that was to get more data more data points in order to get more accuracy and the detector was mounted at 160 degree here in the case of and the direct beam of course is going to the faraday couple that is used for normalization and the measurement of to see that current is not fluctuating too much and that is done here in the case of this. So, this is a scattering chamber targets here and the beams here. Now, one of the example of this is a proton beam backscattered from the tantalum target tantalum 181 1 degree this can be shown. Now, as I mentioned that at the this is a scattered energy. So, a scattered energy at 160 degree highest energy will correspond to the particle which are scattered from the surface almost from the surface and therefore, target thickness is not coming to. So, any uncertainty in the target thickness or any impurity in the target will not be factored into this error in the measurement of k value and therefore, the energy of the particle. So, you can see that this is the spectrum one spectrum and different at different energies. So, you let us take this one spectrum at this energy C let us see at the 4.974 and this one or this is at 8 this is a different energy 4.58. So, this is almost like a delta function. That means, this is the very accurately we know the occur there is a procedure analysis procedure to find the exact energy scattered energy particle energy of a scattered particle at 160 degree and then of course, theoretically you can calculate the energy by this you can measure and this you can. So, using this expression you can calculate the and that is the matching with the detector energy obtained of the detector. So, this was the arrangement and the back is scattered particles were detected and they were analyzed and we found now the error in this kind of measurements can come due to the fact that when this is the magnet north and south here and is scattering chamber is put in the center of the magnet and the NMR bosom it are normally we cannot put it here. So, it is put slightly outside. Now, there is always a fringing field here the field will not be uniform in principle the field should be uniform if you want accurate measurements then in that case then the field should be better here at the center of it and this should be the uniform field, but since because of limitation the magnetic field is measured slightly outside and that is that magnetic field may not be equal to the central magnetic field. So, therefore, in order to reduce the error we have to find the calibration of magnetic field value at the center and this. So, this was done here the magnetic fields were measured at two places and the ratio of magnetic field B0 which is at the center here to the magnetic field outside which is outside where the NMR bosometer is put and the actual measurement of the field is done and that we saw that it should be ideally one if it is very close to it, but we saw that when the magnetic field is this magnetic field is slightly smaller than at towards the end. And therefore, in calculating the k value or the or the energy effectively we should take this factor into. So, we have to and that is because of that is because of because of fringing field fringing magnetic field however this has to be. So, if you want to decrease this magnetic field fringing then either the pole length has to be much bigger so that in that region of the ion beam the field is very uniform and this has to be taken care however in our case this magnetic field was not constant across entire pole pole this is called pole gap and this was not so but this correction was done. However, the general equation we have derived the simple equations and general equation will be slightly there which we take care of relativistic effect also and if you put that again the putting the constant into the expression and you find that the k values again the same and k is the units are tesla per nvv half to nv half. Now, if you put all the constants for example, see when you are doing experiments you will like to quickly calculate the thing. So, if you put energy in nvv b in tesla are the radius of curvature in meters and c in coulomb m naught in kg per mu then k is equal to 4 into 10 power minus 7 times this root of m. So, this takes care of all the constants. So, as I mentioned earlier that we did not want to restrict to only one point one measurement. So, we did the measurements for several targets and several beams here you have seen you can see that we used proton lithium 7 carbon 12 at fluorine 19 beams and various targets and then we measured the measurement we measured the scattered protons and from that we calculated the k value and here the k value for various targets and projectile combination is shown you can see that this more or less constant and this is. So, this was one value obtained, but we wanted to make sure that this value is correct and therefore, most accurate as I said was is always a always a resonance expression and we should the resonant reaction and there you can locate the energy very nicely and this experiment was done over the elastic scattering of proton from the carbon 12 which is shown here and at that V value which correspond to certain energy this was the resonance we saw and corresponding to this this was fitted and then the energy was obtained. And we found that the energy or the k value obtained from these two methods are consistent they agree very well with the now so far I only talked about the aluminum P gamma that is one resonance and the other resonance I talked about in literature you will find that there are several resonances well defined resonances have been studied and not only resonances, but also the neutron threshold experiments have been done and some of them are listed these are these are the P gamma gamma resonances these are the targets and these are the exit nuclei which are and you can see that these are the reactions they here we have given the high energies and these are the resonance natural bits I think this is very important if you want more accuracy then you should choose a choose and a resonance which has very small natural bits then it can be much easier suppose you have a flat resonance very wide resonance of course the if it is flat it will not be called resonance but if you try to do it fitting becomes difficult and the extraction of energy value also becomes very the most widely reactions at low energy accelerators are this 27 aluminum P gamma going to silicon at 992 and that has a width of 0.1 k another reaction which is very widely used for determination of energy via calibration of magnetic field and hands k value is the proton the falling on lithium-7 emitting the neutrons that means neutron threshold experiment at 3 at 1.88 mV of course these resonances are available at various energies so even the accelerators up to 100 mV have been calculated have been energies have been have been determined using these resonances and not only these resonances even non-resonance experiments can be can be used for doing this but resonances are better and they they gain much better values of energy so this is the reference where this data is given and they have done a very nice experiments to measure the energies of the both P gamma and P and the actions and this data I think I have also listed here two three more references where you can find the resonances and the P neutron threshold experiments on various targets at slightly higher energies up to about 10 mV and these experiments these experiments also have been done in various accelerators and very accurate energy measurements have been done and the values have been found so at the end I would like to make remarks that in order to get accurate values of energy we should avoid resonance mixing say for example if you have two three resonances that they should not be very close to each other because then otherwise the determination of the energy will become so you should avoid close by resonances for example gamma from Algunium 27 P gamma silicon resonances are mixed with those of P P prime gamma so there may be some resonances using other reactions or the same target projectile combinations and if they are very close to each other then there will be error into it so we should try to avoid we should only choose the resonances which are well separated from other resonances or other and therefore in order to do the actual measurement this should be taken in. Other one is that you know this NMR Gauss-Wieter normally is kept outside the central project central portion of beam chamber because beam chamber inside is vacuum so you there are ways to put it inside but normally it is put outside in the magnet so field will be less than because of because of ranging field so field will be less than the central trajectory which is which is the field required for the calculation of the and hence we should be properly calibrate the magnetic field outside to the central because ultimately the central magnetic field corresponding to central trajectory only we have to use so there should be a very nice calibration that should be done. Choose the resonances which have a small natural width because if you have large width then uncertainty increases so we should have the resonances which are having very small width. Another thing which we have to take care is that impurities in the target should be minimized or at least we should know so that the correction can be made. So target inferiority target composition should be known prior to the experiment and they should be known otherwise the gammas or the other particles coming from other reaction from the other elements in the target they will interfere into it and that will be we have used backscattering method and there is an advantage and it gives better results is because this is independent of errors in the target sequence because at the backward angle we are measuring the backward angle counts backward angle particles and is not seeing the target thickness therefore the target thickness error in the energy will not be contributing and therefore the accuracy will be there because we are using from the falling as of the spectrum falling as corresponds to the backscattered particles from the surface. So these things should be taken into account if you want a very good value of the energy and of course here in the case of these measurements what we do is that we want to calibrate it in terms of k value of the magnet analyzing magnet and the accurate is the k value similar accuracy will be reflected. So thank you very much.