 Hello everyone. In this lecture, I will discuss the nuclear fusion process from the point of view of two aspects. One is the extension of periodic table, that means essentially synthesis of heavy elements. So, I will not give too much details, but we will explain the concepts behind what are the limitations in extension of periodic table, but that also involves a nuclear fusion process. And second is what are the research or what are the work going on producing electricity from nuclear fusion process. Okay. So, first let us discuss the extension of periodic table. You know that the elements up to 92 were available till 1930s. And after the discovery of nuclear fission, the attempts were made to synthesize heavy elements in actinium, plutonium by N gamma reaction followed by beta minus decay. And with the accelerators produced producing heavy ions charged particles, then by fusion reaction also heavy elements were being synthesized. And by this time elements up to 118 have been discovered. Majority of them, in fact, beyond under element 100, most of the elements have been synthesized by nuclear fusion, fusion of heavy projectiles with the heavy targets. And so, but there is a limitation. There are some inherent limitations in extending the periodic table that I tried to explain in this particular presentation. So, the limitation due to fission. As I discussed in the previous module, that facility parameter, if you have a facility parameter 0.6, that will correspond to a mass number of around 100 or so. You can see from here z square upon 50.13 into 8, you can calculate. So, these nuclei are as most, no, they are stable towards fission. They will not undergo fission. Whereas, if you see x equal to 0.8, so this comes to around californium or anstinium, fermium, gently close to 100. And these nuclei will have the fission barrier of the order of even around close to 1 MeV or so. So, the fission, so this is the spontaneous fission happening. They are having very short half-lives because they have a high fission probability. But if the facility parameter is 1, then there is no fission barrier. You can see here, there is no fission barrier for this nucleus. And so, you cannot produce this nuclei. The moment they are formed, they will undergo fission. For them, the fission barrier is 0. So, that is the limitation because of these instability towards fission of this heavy nuclei, it is very difficult to extend the periodic table. Another aspect, so the fission barrier decreases with the increased atomic number. And you can see how the facility parameter is changing for different nuclei. You can calculate from here. So, let us say z square upon 50 into, let us say 200 mass number. So, let us take 100 square upon 2. So, it will become 10,000. So, that means 10,000 upon 10,000, that is equal to 1. So, a nucleus of mass number 200 will have one facility. So, it is not survived. But if you make it 250, so it will become 125,000. If you put 12,500, then it will be close to 0.8. A facility will be close to 0.8. And so, it will have some finite fission barrier and therefore, it can survive fission. Another aspect is the angular momentum. Angular momentum is adding to disruption of the nucleus like coulombic repulsion. The coulombic repulsion is trying to separate the protons away and that is the negative, that is the factor which accelerates fission. Another thing is angular momentum. So, in a heavy ion reaction, when you bring in a heavy ion, it will bring in angular momentum. And the angular momentum will try to destabilize the nucleus. So, because of that, there is a one more term apart from surface energy. So, if you recall the expression, if you recall the this one for surface energy, coulomb energy, the angular momentum term also will be destabilizing the nucleus. So, the net result of surface energy, centrifugal energy and the coulomb energy will dictate the fission barrier. And so, because of these, for the same nucleus, if you have higher angular momentum, fission barrier will decrease. What I am showing here is you increase the angular momentum from 0 to 20, 40, 60, 80 h cross for this nucleus 153 terbium. The fission barrier for zero spin was around, this is 35 or so, 35 MeV and it is going down too close to let us say 5 MeV at angular momentum of 70 or so. So, you can see it is sharply declining fission barrier with increasing angular momentum. So, in heavy ion reactions, invariably you will have higher angular momentum. And so, there will be more unstable towards fission. What I am shown here is the profile, locus of the number angular momentum and mass number for nuclei having fission barrier 0. The angular momentum for which fission barrier become 0, you can see here for a mass number around 150, it can accommodate about 90 h cross of angular momentum. But for a nucleus of mass 300, it cannot accommodate even 5 h cross. So, that means what the fission barrier for the angular momentum for which fission barrier become 0, it is increasing and then it becoming decreasing. So, when you go to heavier elements close to 300, they will have nearly zero fission barrier. So, that is why you will find that their survival become very difficult. And so, it is that puts the limit on exchanging the priority. The third is the competition with particle evaporation limits the formation of heavy nuclear. So, fission competes with the particle evaporation and therefore, that puts a limitation on the survival of the heavy nuclear. So, there are different ways to reduce the particle evaporation by using what we call as the cold fusion. That means you produce a compound nucleus which have very low exquisite energy. There are different ways, but we will not go into details of those processes. I just wanted to give you a feel that why what are the limitations in extending the reality. Another thing is to entrance to fusion. There are other limitations that when two nuclei come together, then there are other factors which hinder fusion of nuclei. So, if you recall the previous lecture I have shown in the componentless mechanism that suppose a nucleus is coming close to another nucleus Z1, Z2. So, this is the R versus the potential and this is nuclear potential is like this. The Coulomb potential is like this and the sum total of that will be so, this is the fusion barrier. Once you bring in angular momentum, then angular momentum also is a repulsive barrier and so, that will reduce the pockets. So, the special barrier will decrease and a time will come, but higher angular momentum the this pocket there is a pocket being formed in fusion a pocket will vanish. This is what I have tried to show here that for argon plus 197 gold, the nuclear potential and the Coulomb potential will give rise to this pocket. This is the pocket in the fusion barrier. For heavier projectile like xenon plus gold target is same, but the projectile is now increased you will see here that the Coulomb barrier is here, nuclear potential is here and the fusion profile has become very shallow. That means this pocket starts vanishing and once this pocket starts vanishing the compound nucleus formation becomes difficult. So, the two nuclei cannot come close enough to fuse and form a mononuclease called compound nucleus. So, you can see here 54 plus 79. If you want to go to heavier elements, you have to have heavier projectiles trying to fuse with the so, there are the nucleus community is trying to study what are the factors that will limit the formation of heavier elements. So, there is a effective facility parameter they call just squared by A effective they say that if it is less than 48. So, again it is nothing but this it is like a Coulombic energy of a dinuclear system. If it is less than 48 then you may be having a pocket if it is more than 48 then you may not have the pocket. So, you can see here for argon plus gold it is 31, but xenon plus gold it is 50. So, that is how this is one of the limitations in fusion of projectile in target to achieve synthesis of heavier elements. So, the nuclear chemistry fraternity has been engaged in synthesizing heavier elements that there are predictions based on cell model calculations that nuclei having atomic number 114 and neutron 184 are expected to have heavy along half lives that is what is called super heavy elements. The super heavy elements around this region have may have a long half life. So, people have tried to in fact separate them from the natural resources from the earth crust wherever there is a large deposits of uranium, thorium people have tried to separate some elements resembling their lighter homologs, but so far there has been no success in the process people have been trying to synthesize them by fusion reactions. So, as I was mentioning the hot fusion to take lighter projectile and heavier target nuclei or cold fusion to take heavier projectile and not so heavier targets. So, by cold fusion reaction you will see you try to produce a compound nucleus which is not very hot in terms of excretion energy and so by these processes people have tried to synthesize heavy elements and because of that the half lives are very long very short, but still attempts are going on to synthesize heavier elements. So, you can see here the periodic table has been extended to mass 118 and these experiments take a very very long time. In fact, even to synthesize elements these elements rutherfordium, dubonium, cyborgium which the chemistry had been also studied element 104, 5 and 6. A lot of chemistry had been studied even there the production rates are one atom per hour or so as you go to higher and higher like this highest elements production rate may be one atom per month or so. You can see here the kind of experiments people are doing and then they have to get an unambiguous signature of that it is that Z and A. So, the atomic number the mass number of that particular isotope has to be established to claim it that they have discovered a particular the new element. So, what they do actually they when this heavy element isotope is produced they will undergo alpha decay and the alpha decay energies are monitored for the lighter part lower daughter products the alpha decay energies are known and so that is how they correlate that this daughter is growing from this parent. So, this is the atomic number and mass number of this particular heavy isotope. So, element up to 118 so the super heavy element as we are calling N equal to 114 Z equal to 114 N equal to 184 is close to that region the people have achieved, but the half-lives are not long enough half-lives are very short they are in millisecond microsecond range. So, still people may be searching for the super heavy elements with long half-life, but the experiments in accelerators to synthesize elements beyond 118 that is for 119 they are not going going on they are planned in in Japan and USA. Now, in fact, the different countries actually are pulling their resources to plan such mega experiment to synthesize heavy elements. So, to conclude the part of nuclear fusion in producing heavy elements I would like to say that there are experiments going on using nuclear fusion reactions wherein you try to understand what are the factors that limit the extension of periodic table. People have tried to produce heavy nuclei by hot fusion reaction or cold fusion reaction. This cold fusion is not the type of cold fusion which were in between it came in the news that fusion of hydrogen isotopes to give neutron. This is the fusion of heavy nuclei but with to give lower oxygen energy to compound nucleus. So, you want to survive the fission. So, you produce compound nucleus with low oxygen energy so that it can survive fission. Now, I will come to the next part how to produce power from nuclear fusion and what is the status as of now. So, the fusion of two light nuclei to form a heavy nucleus to release large amount of energy is similar to fission process and fission process has been already realized to produce electricity because we can control the reactor very easily but in the case of nuclear fusion process that still is yet to become a reality. So, let us discuss this nuclear fusion the fusion of lighter isotopes. So, here we have the different types of nuclear fusion reaction. So, fusion of deuterium plus deuterium giving rise to helium-3 and neutron a q value is 3.2 MeV fusion of deuterium and tritium to give rise to helium plus neutron q value is 17.6 MeV and fusion of lithium with hydrogen give rise to helium-3 and 4 q value is 4. Now, as you know that these are all charged particles. So, if you want to fuse the charged particles you need to cross the coulomb barrier and so, there are different channels which are people are trying to explore for achieving a nuclear fusion process which you can sustain. I will discuss this soon what are the problems in which sustaining a fusion reaction. So, this is a simple deuterium plus deuterium giving rise to helium-3 plus neutron 3.2 like that you will have deuterium plus tritium. So, let us see what are the problems in achieving a fusion reaction. So, as I was mentioning these reactions different fusion reactions of lighter isotopes of hydrogen the one which is having deuterium plus tritium having the lowest threshold that means the coulomb barrier. So, the coulomb barrier you know already z1 z2 e square upon r1 plus r2. So, for deuterium plus tritium the coulomb barrier in terms of kilo electron volt or so that is having about 10 kV. So, the coulomb barrier for this will be 10 kV and if you translate this 10 kV into temperature it becomes 10 power 8 degree Kelvin. So, if you want to it is like a threshold reaction threshold energy. So, if you want to induce fusion of deuterium and tritium you require to achieve a temperature of 10 power 8 Kelvin. Now, you can imagine unlike in the case of neutron induced fission you did not have this problem because thermonutron can induce fission, but for charged particles you have you require to have very high temperatures and then if you have to achieve high temperature how to what kind of container you will have to hold reactants at such a high temperature. So, the storage materials storage vessels how to achieve at this temperature material matter will be in the form of a plasma. So, you have to contain the plasma in a container. So, all these are the limitations for achieving a fusion reaction. So, now there have been attempts going on for last many many years several decades have been spent and there are mainly two types of approach people have followed one is the inertial confinement. So, what is that you are trying to confine that deuterium tritium plasma the deuterium tritium you they have to fuse together and you require a temperature of 10 power 8 degree Kelvin. So, how do you contain this plasma? So, the one approach is called inertial confinement by inertial confinement you mean that by virtue of their mass you can confine the solid fuel in a very small volume and but you have to also have a high temperature. So, you achieve high temperature by bombarding them with the high power laser beams CO2 or NDR laser beams and you take a solidified fuel. So, when the laser beams are bombard on the solidified fuel it will ablate the surface atoms outside and this ablating atoms now will give a recoil to the core and they will density will increase. So, you contain the core of the solidified fuel by ablating the surface atoms using a laser beam. So, the evaporating atoms on the surface bring together the interior atoms by the recoil of the ablating atoms and that will lead to rise in the density of the core and in the process by when the density is rising temperatures can go beyond that what 8 Kelvin, but then it may not sustain for long time. So, there is in fact a Lawson's criterion which I will discuss very shortly. So, for a very short time you can achieve very high temperature, but during that time the fusion can take place. So, in the process of inertial confinement the reacting particles like bacterium and tritium are held together by virtue of their mass and that is why it is called as the inertial confinement. So, this inertial confinement by using the laser beams to ablate the outer surface layer to increase the density of the core is experiments are going on, but it has not been that successful as the next experiment of magnetic confinement. In the magnetic confinement again you take the bacterium tritium fuel in the shape of a donut like a tire and that you have so you have it the tire in the central portion of this tire the plasma can rotate move and you how do you confine how do you know avoid the plasma touching the container walls using the electric and magnetic fields that is in fact that is called as the tokamak system where the electric field will accelerate the particles it will increase the category of the reacting particles and the magnetic field will keep the fuel away from the surface. So, you have to adjust the electric field and the magnetic field to have the plasma and when they are using they should not touch the container walls. So, the magnetic confinement strategy has been working and there have been several attempts to generate the tokamak type of reactor worldwide. One of the conditions to achieve to sustain a fusion reactor is called the Lawson Schuykeren. The Lawson Schuykeren essentially emphasizes how to achieve a plasma density of a beyond certain number for a reasonably long confinement time. So, we have to confine the plasma for a reasonable length of time. So, this criterion is rho tau rho is the plasma density and tau is the confinement time. So, if you have to have higher energy output than the energy input energy input is being given to heat the plasma to a temperature 10 power 8 degree Kelvin. If the product of plasma density and confinement time is more than 10 power 14 second per cc for the deuterium addition. For deuterium deuterium we 10 power 16 second per cc. So, for this is the one which you know which have lower threshold. So, the lowest temperatures required for this fusion reaction. So, this is the confinement. So, if you have a high plasma you will find high plasma density then slightly lower temperatures or lower confinement time also will do. So, overall attempt is to increase the confinement time and the plasma density. So, these are the two efforts are being made to have Lawson's criterion if you can have a high plasma density and high confinement time nothing like that. So, let me see what are the what is the current status in the form of for producing energy electricity from fusion reactor. Since this is a very costly affair to have to build a reactor which we still do not know when it will work. So, there has been an international effort called ITER international thermo nuclear experimental reactor which is a you know all most of the majority of the countries which I have interested in this fusion energy have come together and they have proposed a fusion reactor at Kaderash, France, south of France. So, this is the world's largest experimental prokomak fusion reactor which is being proposed. It is funded by European Union largely and India, China, Russia, Japan, South Korea and USA contributing 9 percent each. So, every country you know whoever has a stake in the fusion power they want to contribute this and this construction of this fusion reactor began in 2007, this is 2022. So, already 15 years have passed and the first plasma from this fusion reactor is expected to be produced by 2025. In fact, India has contributed a great deal in cash and kind. In fact, the cryo state for this reactor was built in our country and many universities in the country are also participating. We have in Institute of Plasma Research at Khandabar, Nandinagar they are leading agency in the country to contribute in the plasma research in the fusion reactor. So, this fusion reactor based on deuterium fusion fusion is expected to start operation by 2035 and this reactor is expected to have a power of 500 megawatt which will be sustained up to 1000 seconds. So, you can see here that even this is a very meager you know target was what do you do for after 1000 seconds. So, but this is such a challenge it is a really big challenge. So, this kind of mega projects if you can sustain if the such a high power of fusion power for 1000 second it will open up gates for the sustaining that actually materializing realizing the fusion electricity from the fusion in the times to come. So, this is the one area where there is a lot of scope for research for students in the country. There are many universities are also contributing in this fusion research and the department of economic energy is also contributing in a big way both in terms of producing the materials the different systems and that of course in the government of India is contributing by way of gas. So, what I wanted to share with you today that why the nuclear fission has been already utilized for producing electricity in our nuclear reactors. The nuclear fusion is yet to be realized for producing city, but maybe you young students will see one day that we are producing electricity from the fusion power and so the challenge it is a challenge for all the students to participate in such big mega projects those who are in the field of nuclear chemistry or nuclear physics or you may in fact many you know engineering students, mechanical engineers all types of disciplines are involved in producing this kind of a fascinating. So, I will stop here and the next I will take in the next lecture the production of radioisotopes in different types of nuclear reactions. Thank you very much.