 Hello everyone, welcome to this lecture. Last lecture, we discussed the protections of nuclear reactions. We discussed the cross sections for neutron induced reactions and the charge particle induced reactions. In the case of neutron induced reactions, cross section decreases with increasing energy of the neutron, then in the intermediate region there are resonances. Whereas, in the case of charge particle induced reactions, cross section increases beyond a threshold value of ECM equal to Vc and after that it equals rising. We also saw how to determine the cross sections experimentally by measurement of excitation functions or even by measurement of particle spectra and emulation. Today, we will discuss the mechanism of different types of reactions and mostly I will be focusing on the dominant mechanism that is the compound nucleus reaction. So, just let us see in actual what are the different types of reactions that occur when the projectile bombards a target. So, I have given a schematic here. This is actually the time zone as a function of time how it is happening. So, the projectile is bombarding a target nucleus and many a times what will happen? In fact, it is always there a component of elastic scattering. Elastic scattering is nothing but a sort of a billiard ball collision between the two bodies a projectile and a target and then this in the elastic scattering I will be discussing very shortly what are the things that are conserved which are not conserved and so on. But this is actually not included in the nuclear reaction company and this elastic scattering is always there whenever a reaction is there. So, it can happen immediately that is what is I have to the initial stage that projectile just collides with the target and get under close elastic scattering. In fact, the prolonged scattering of the force scattering is also coming in the category of elastic scattering. Then we come to the intermediate zone where the projectile is now coming in close vicinity of the target nucleus and before that in fact, before it is completely using with the target there is a type of reactions called direct reactions that means their projectile and target projectile comes close to target nucleus and there is a transfer of few nucleons from projectile to target or vice versa. So, that happens at a much smaller time scale than the compound nuclear formation if you will discuss in length later on. And many a times they can form a compound nucleus the compound nucleus part we will discuss in detail in this lecture and the compound nucleus can again give rise to that projectile back. So, it is this is what is called the compound elastic scattering. The projectile it is like you know when it goes into the well of the nucleus and comes back with the same energy as it in turn. So, this is called the compound elastic scattering. There is a very small difference in the phenomena of elastic scattering and compound elastic scattering. And then the last stage is the compound nucleus formation that takes place after a lot of time. Now, the time scales you know in nuclear reactions will be for elastic scattering and direct reaction 10 power minus 22 seconds. For the compound nucleus formation 10 power minus 17 seconds. So, that is the time of time scale that you are talking about. So, when you say compound elastic scattering it has happened in the time scale of 10 power minus 17 seconds. So, the compound nucleus lifetime is the order of minus 17 seconds and in that lifetime it is all the projectile and target combined together on a mono nucleus equilibrium in all degrees of freedom. And then the subsequent de-excitation of the compound nucleus can take place by mission of particles, gamma rays and so on. So, that is what is called the final stage. So, on the way the projectile can have different types of reactions with the target nucleus namely elastic scattering, compound elastic scattering, direct reactions and the compound nucleus formation. These are the main types of reactions and the time scale is as you go from right left to right time scale of the reaction is increasing. You can also explain the different mechanisms that take place when a projectile bombards the target. And in fact, this is in the context of a projectile which is rather heavy compared to a neutron or proton and so on. So, when you say this is what I have drawn in the schematic is the target nucleus and the projectile is coming at different distance from the center of the target. So, we if you recall the previous lecture we defined the angular momentum involved in a nuclear reaction. And so, the angular momentum for the central collisions that means the impact parameter is 0. So, angular momentum if you recall is equal to b into p. In fact, parameter into the momentum. So, when the impact parameter is close to 0 here. So, this is what is the impact parameter. So, the central collisions means impact parameter is close to 0, for them the angular momentum is 0. So, it is here. So, what I have plotted also here the angular momentum dependent cross section versus the angular momentum. And so, it is nothing but the 2L plus 1 sigma L 2L plus 1 and you can have the transmission coefficient also. So, this triangle is actually like 2L plus 1 until afterwards also. So, for the central collisions where the angular momentum is low the projectile will be fusing with the target or forming a compound nucleus formation. This is also called as the complete fusion. The projectile and target nuclei fuse together to form what is called as the compound nucleus. When you go to little bit away. So, it is either we go this way or this way it is symmetric. So, this is a impact parameter where they are just grazing. When we say grazing collisions means they just touch and go. So, during the touching process there could be a transfer of new nucleons from time to target or target to prototype. So, that is why this is why. Remember grazing collisions lead to transfer reactions. So, where they just come and touch each other and during that time scale there could be some transfer from one to other. So, they are at the higher. So, this is what in the higher impact parameter means. Transfer reactions taking place and then there are distant collisions which are beyond the physical boundary of the target. So, the distant collisions are like coulomb scattering. They come in the coulomb potential in the vicinity of each other's coulomb potential and escape. So, that is like you know rather for scattering and so on. So, the as we go away from the target center the angular momentum is increasing and so the different reactions are taking place that I have tried to explain. And so, the different cross sections for different processes compound nucleus and transfer reaction the coulomb scattering will not come in the category of nuclear reactions because they do not come in the vicinity of the nuclear potential of each other. The nuclear reactions take place when they come they experience the nuclear potential of each other. And so, if they only come in the coulomb potential of each other. So, we say they are not nuclear reactions. So, cross section sigma l versus l will take care of only the nuclear reactions like compound nucleus, direct transfer and so on. Okay, let us now see these reactions in more details. This is the first type of reaction though we will not call it as a you know the reaction cross section that does not include the elastic scattering also. But it is good to know exactly what are the different types of processes that are happening in the elastic scattering. So, in the elastic scattering as I have mentioned earlier, this is the projectile and this is the target. The projectile and target collide with each other and they go away from each other is retain their identity. So, they remain as a small a and capital. Secondly, the most important is that the kinetic energy is conserved. The kinetic energy is conserved means the projectile and target may have projectile may have some energy ea like for example, it could be zero. So, it can transfer some kinetic energy to the target nucleus. So, this is zero. Normally, when the target nucleus is stationary then ea is zero. Now, the projectile can transfer some part of its energy to the target nucleus. Both of the projectile and target are now having some kinetic energy which is that is what is happening. When your projectile is colliding with target then they go in different direction. So, some energy of projectile has been given to the target nucleus but it remains as kinetic energy. So, total kinetic energy of projectile and target after the scattering is same as that of the projectile. That is what we mean that the kinetic energy is conserved. So, it is only it can be transferred from projectile to target during the collision. But it does not it is not lost or it is not transformed to other type of energy like exhalation energy and so on. The important criteria in elastic scattering is that the kinetic energy is conserved. So, I have given a type given an example of neutrons when the neutrons are reducing their energy they are moderated. So, they collide with the target material like a and in the process neutron will give some kinetic energy to the target nucleus. So, the the final energy of neutron and target nucleus is equal to initial energy of neutron and if you recall the previous lectures then the energy of the target nucleus maximum energy that we get given to target nucleus can be given 4 m n m a e energy of neutron m n plus m a square. And so, for example, when a equal to 1 then e a equal to e n. That means, if the mass of the neutron and mass of the target nucleus is same like hydrogen proton then it can give all energy in one collision. So, proton that is why we say hydrogen is the best moderator in one collision all energy of neutron can be given to hydrogen. So, hydrogen hydrogenous material will reduce the energy of neutron fastest. So, that that is the reason why we say hydrogen is the best moderated. Moderator means we are trying to reduce the energy of neutron from whatever energy neutron has to begin with and we are trying to thermalize. So, the number of collisions that they that is required to bring the neutron to thermal energy is called the how many collisions are there. So, that that number is much less for hydrogen. If you have a higher mass number material you will require more collisions. For hydrogen even one collision is sense. So, that is the way we explain the moderating power of the target material for neutrons. Next type of reaction is the elastic scattering. The elastic scattering again again says it is in the name itself reveals it is scattering. That means the projectile and target retain their identity like a plus a a dash plus a star. So, I have put a star because now the kinetic energy of projectile is not conserved. Some part of the kinetic energy of projectile is transferred to a target nucleus. So, the target can get excited. So, total kinetic energy before and after the scattering is not conserved now. So, some part of kinetic energy was transferred to target nucleus and its eccentricity energy and in fact, such reactions go the masses of the projectile the reactants products are same, but the target is not in a except suppose you have the target it is now excited state a plus a going to a. So, it is excited plus a dash. So, this much in the Q value of this reaction though it is the nucleus is same the mass in terms of the masses the Q value is 0, but this much energy is tied up. So, this is certain state of nucleus has an eccentricity energy and this much energy is required from the initial projectile energy. So, you can say the Q value is not constant the Q value is less than 0. So, Q value is also given as e a plus e a dash minus e a. So, now, this value is negative because some part of the energy of the projectile will be transferred to I will set this energy. In fact, there are applications inelastic scattering in the form of some ion beam reactions. This is called a particle induced gamma emission piggy. So, you can have expectation of a target nucleus and then this excited nucleus can emit a gamma ray and then gamma ray carry the signature of that nucleus. So, if you count the gamma rays these are prompt gamma rays emitted instantaneously. So, then this technique this is an ion beam analysis technique for material characterization. So, when you bombard the target nucleus with a projectile like proton. So, p p dash inelastic scattering of proton with target materials of aluminum, silicon, phosphorus and so on. Then the excited nuclei of aluminum, silicon and phosphorus they can they de excite by emission of its characteristic gamma rays and these gamma rays can be measured by the medium detector. And so, the intensity of the gamma rays is intensive the concentration of these elements. So, for the material characterization the elastic scattering is utilized in but as a form of ion beam analysis technique. So, this is a simple setup for piggy. We have a scattering chamber it can be having a diameter of 53 centimeter or even more than that under vacuum, take a minus 6 star or better. And we have a target nucleus target target material in the form of a foil or a pellet. And so, the projectile will be going in the in the forward direction, but this whenever there is a inelastic scattering then the gamma ray can be emitted in all directions and you put a detector at 90 degree goes in the forward direction. You cannot keep the detector because there will be a projectile beam will be passing through the 0 degree. So, you put a 90 degree the background is much less and you detect the gamma ray. So, you can put a HPG in at 90 degree to respect to the projectile beam and record the gamma spectrum. It is an online experiment while the beam is falling gamma rays are being measured you measure it for some time and then. So, you can you record the gamma spectrum of the products that are formed. So, this characteristic gamma rays tell you what are the elements it will take the peak area and you can use some standards you can find out the concentration of these elements in the material. So, impurities or even bulk material vectorization can be done in the beam in the last experiment. Then comes the direct reaction. The direct reaction happened in a very short time scale of the order of 10 power minus 22 seconds. Essentially, this time scale is because of the time that nucleus projectile will take to cross the nuclear diamonds. So, that happens in the region of 2 seconds. And so, the direct reactions means the they come in the potential nuclear potential contact with each other, but they do not amalgamate to form a compound nucleus. So, the energy is not equilibrated the mass is not equilibrated they just you know one step process you just knock out an electron a nucleon a proton or a neutron from the nucleus or it can strip its particles in a very short time scale. So, the type of reactions that are taking place are like this DP reaction. Neutron colliding with the target nucleus and the proton is coming out. So, neutron is stripped neutron is stripped of a neutron that neutron is captured by the nucleus like here 27 aluminum DP 28 aluminum. Similarly, alpha tritium alpha is stripped of one neutron tritium is going out neutron is using with the target alpha D a deuteron is going loose with target and the deuteron one deuteron goes out. So, like that this mostly you will find these reactions take place with the low jet nuclei like lithium, helium, tritium, deuteron and so one of the very interesting aspect of this direct reaction particularly here the transfer reaction is you have transferring a nuclear neutron from neutron to aluminum 27 which the energetics are quite different from if you consider a neutron captured by aluminum 27. When a neutron is captured by aluminum 27 then the energy that is released is binding energy of neutron in aluminum 28 7.7 ml. So, this is the mass of neutron plus mass of 27 aluminum minus mass of 28 aluminum. This is the energy released and this much energy will go in the excitation of aluminum 28. So, the de-excitation of aluminum 28 x from 7.7 ml will take place by the instead of gamma rays whereas by D p reaction you are not exciting this to at that high energy because the two value is different for this reaction. And so, if you consider the nucleus in a different excitation state neutron plus 27 aluminum 28 aluminum then you will find the in the case of neutron captured reaction you may populate it here. But in the case of D p reaction you may populate it here. And so, you see a different energy state populated in this kind of specific reaction. So, you can study the nuclear reactions at different energy state and different environment. Another type of reaction is pickup reactions that means a prototype picks up a nucleon like here a neutron, here a proton to neutron and so on. So, prototype picks up a particle a nucleon or a nucleon cluster from the target like here nitrogen 14 pd. So, proton is becoming neutron and escaping. So, it is picking up a neutron from nitrogen 14 and goes out as a neutron. So, these kinds of reactions are also direct reactions and they all take place at a much smaller time scale. So, I try to give a schematic of this neutron comes close to the target nucleus and then picks up a neutron from the target nucleus. And so, this is actually this is a stripping reaction not the pickup reaction. The neutron comes to the target nucleus gives a neutron to the target nucleus and proton is going out and the target plus neutron nucleus is going other direction. So, these are the kind of reactions you know where you populate the low lying states of the nuclei because their Q values are not very high and they infect the nuclear physics people who study such reactions. They study the spectroscopy of low lying states by using transfer reactions of stripping or pickup type. So, here the it is the momentum transfer. So, when you say a nuclear reactions you know the projectile and the projectile is wave you can rate e raised to psi is called e raised to i k x like plane wave. So, k is the momentum of the particle and so, when a like for example, here this GP reaction. So, the projectile is transferring a neutron to the target nucleus. So, the neutron momentum can be given in terms of proton momentum, the neutron momentum and the see like a vector a vector sum of proton and neutron momentum to give you the neutron moment. So, how much momentum is transferred to the target nucleus that is k n and that can be given in terms of. So, you can you know the momentum of the proton, you know the momentum of the neutron. So, you can tell what is the momentum transferred to the target nucleus and that momentum then you can transform to the angular momentum in terms of r cross p. So, p is k h cross and r maximum since they are peripheral collisions, they are surface of reaction. So, r can be replaced by the nuclear radius. So, the angular momentum transferred in these nuclear reactions are the neutron momentum and the radius of the target. So, they are the kind of reactions where you transfer some angular momentum and you can see those targets set in states having that kind of angular momentum. So, people are trying to see spectroscopy of low line states of target nuclei by means of these direct reactions. So, the nuclear physics community trying to study the spectroscopy of low line states utilize these beams of low jet, low charged particle like protons, neutrons so on to study the spectroscopy. Okay. So, now I will come to the last nuclear reaction mechanism and that is the most important one that is the compound nucleus reactions. In the compound nuclear reaction the projectile and target fuse together to form a compound nucleus C and this subsequently this will degrade by emission of particles or gamma ray. So, we can say this is a ejectile and this is the heavy residue. We will discuss the role of this subsequent. The important aspects of this are the projectile and target do their identity. That means the compound nucleus does not know what way it was formed. Kinetic energy is not conserved in the compound nucleus reactions. All the energy that most of the kinetic energy of the projectile will be converted into the excitation energy for the compound nucleus. The projectile and target nucleus used to form a compound nucleus. So, formation of compound nucleus in the first step it is a two step process. In the first step projectile target fuse together from a compound nucleus and second step the compound nucleus dexides by emission of particles and gamma rays. And the most important part is these two steps are independent of each other. So, whatever is the projectile excitation energy and angular momentum they decide how it will dexide. It does not depend upon how the weight projectile and target fuse together to form this compound nucleus. So, this is the important assumptions and they have been verified also subsequently. So, the compound nucleus this is your interest channel means A plus A is called the interest channel how it was formed. So, for the interest channel that means formation of compound nucleus from projectile and target we will call as the first part of the reaction and that is called the interest channel. Interest channel means how the retile return the target to form the compound nucleus and for that the Q value is mass of the projectile plus target minus the mass of the compound nucleus into you can say C square to write in terms of the delta M value in MV then we do not need to multiply by the C square. Secondly, the energy available in the center of mass system ECM is equal to volatile energy in the laboratory into mass of target upon mass of target plus projectile. So, it is the mass fraction of the target to total mass. Suppose the target is heavier then the majority of the energy of projectile goes to center of mass energy and a small fraction will go into the kinetic energy. So, what goes as the kinetic energy E A into MA upon MA plus MA this fraction is also called as the required energy. So, some part goes as the required energy some part goes as the ECM energy available in the center of mass system and that energy available in the center of mass system adds to the excess energy of the compound. So, the compound nucleus excess energy is equal to energy available in center of mass system ECM plus the Q value. And the another important property of compound nucleus is the angular momentum of the compound nucleus which is the projectile angular momentum plus target angular momentum and the orbital angular momentum that the projectile brings in the L value for a particular collision. So, these are the spins and this is the orbital angular momentum. They couple vectorially to give rise to a resultant angular momentum. So, the net deacceleration of the compound nucleus depends upon excelsic energy and the angular momentum. These are the two important properties of the compound nucleus that will govern how the nucleus will decay. The independent hypothesis I was talking about that means the formation of the compound nucleus and its decay these are two independent steps in the compound nuclear mechanism and this has been verified by one experiment of an Indian scientist S. M. Ghoshal way back in 1950. And very interesting experiment he carried out that is he formed a same compound nucleus zinc-64 by two different reactions alpha plus nickel-60, zinc-64, proton plus copper-63, zinc-64. And this compound nucleus is excited. This excited compound nucleus can meet a neutron, two neutrons or proton and neutron giving rise to different products zinc-63, zinc-62 and copper-63. So, what I have shown here on the left hand side in this graph is the variation of the cross section a particular product formed by two reactions. For example, this first reaction see let us see zinc-63 one end product. Zinc-63 here you can see nickel-60, alpha-end zinc-63, copper-63, p-end zinc-63. So, for nickel-63, for nickel-60 this is the reaction and for copper-63 this is the reaction. So, you can see here the both the ratio of the two the cross section for the two channels different interchannels are nearly constant. This is small difference in the cross section value actually may be due to angular momentum because it is very difficult to match ethyl energy and angular momentum. So, you can see the proton energy and alpha energy are matched. So, that means you will save ethyl energy but angular momentum could be slightly varying and that is why there could be small difference. But by and large you see other product copper-62, alpha-p-end and p-p-end both the reactions lead to similar cross section zinc-62. You can see the whether you form by nickel plus alpha or copper plus proton the cross sections for the individual products are nearly same. That was the experimental verification of the independent hypothesis that means whatever channel you use to form a compound nucleus then the extension of the compound nucleus is independent of that is what I try to explain using the experiment of S. N. Ghoshal for a compound nucleus process. I will stop here and take up the detailed mechanism of compound nucleus in the next part. Thank you.