 Hello, everyone. So, we have been discussing different techniques, particularly nuclear analytical techniques, last few lectures, like Newton-Rectivian analysis and beam analysis, wherein we utilize the nuclear phenomena to determine, to in analytical chemistry, to determine the concentrations or even to depth profile that elements in a matrix. As you recall, we called nuclear chemistry as a subject, where we use chemical tectudes like radiochemical separations, to understand the nuclear properties of elements, nuclear phenomena. And radiochemistry as we use radio, radiations emitted by the elements to study their chemical properties. Today, I am going to discuss a topic of research, you know, the frontier researcher, wherein we use the nuclear phenomena in understanding problems in physics and chemistry in other areas. So, the nuclear chemistry has thrown some probes, which we will discuss in today's lecture. Those probes we can utilize in understanding processes and phenomena in sciences. So, these are we call them as nuclear probes. Let us see, what are these nuclear probes? And especially, you know, in chemistry, of course, now we do not have a well-defined boundaries. There is a lot of research in the multidisciplinary research. We have chemical physics and physical chemistry, and that the boundary of physics and chemistry. So, when I say nuclear probes, it can be applied to physical chemistry, chemical physics and so on. So, that there are three techniques which are coming in the category of nuclear probes. One of them is the positron annihilation spectroscopy. I will discuss the more in detail. The perturbed angularly correlation spectroscopy, TAC. And the third is MOSBAR spectroscopy. Some of you may be knowing about MOSBAR spectroscopy. MOSBAR spectroscopy relies upon the required less absorption. A low energy gamma is limited by a nucleus in its excited state. And the same gamma is absorbed by another nucleus in the sample. So, the source is limiting that low energy gamma, the sample is absorbing. And to take care of the coil, at the Doppler bottoming, the sample is kept in this client state and also at low temperature. And the source is moved towards the sample at different velocities to take care of the Doppler. So, all these things are coming in the category of MOSBAR spectroscopy. And it is quite popular. But that has got a limitation on the number of nuclei that you can use. Like for example, iron 57, you can study the iron chemistry or tin chemistry, afneum chemistry. Certain nuclei are amenable to MOSBAR spectroscopy. So, I will not discuss this particular topic. I will discuss the positron annihilation spectroscopy and perturbed angular correlations spectroscopy. Okay. So, first let me discuss what is this positron annihilation spectroscopy. And I will give you an example of a source radioactive source which emits positrons. You can use a positron source, positron emitter. Of course, it should have sufficiently long half-life so that you do not need to change the sample repeatedly. And what is the, how this positron can be made use of in understanding chemical processes or physical processes. This let me try to explain using this slide. So, when this positron is emitted by the radioactive source, then this positron like if you recollect the interaction of fast electrons, electrons and positrons with matter, it is the energy of the positron will be a few hundred kV. Now, this positron will slowly interact with the electrons in the medium and it will slow down by its elastic scattering, elastic scattering. And the slow down so when it becomes thermalized, the positron which is thermalized undergoing your tortuous path, then this thermalized positron can undergo different types of interactions. So, one of them is annihilation with an electron. The positron is thermalized, it has no momentum. And when it is annihilating with an electron, you get two photons of 511 kV each. The rest mass of electron positron pair is 1.02 MeV and so that leads to the gamma red photons 1.02 MeV split into two photons 11 kV each. And because the initial momentum is 0, the two photons are emitted at 180 degree, then we call them as annihilation gamma res. Now, what happens that this if the electron with which the positron is annihilating is not stationary, it has some certain momentum. Then the positron annihilating with an electron which is in motion and hence has some momentum that 511 kV gamma line will get broadened. That means, it will not be exactly 511, it will be 511 plus minus delta because of the momentum of the electron. And so, there comes the technique called positron annihilation positive Doppler broadened annihilation radiation. So, this 511 kV gamma is broadened because of the Doppler broadening of because of electron momentum. And we can make use of that broadening to determine the electron momentum. Secondly, these two 511 kV gammas are 180 degree angle because of again the same process that is the conservation of linear momentum. And so, the angular correlation between these two gamma rays that means, if you measure the coincidence counts as a function of theta W theta versus theta, then we should get a line at 180 degree. But because of the electron momentum, there is a angular correlation. So, more than plus minus 180, there are some counts. So, this angular correlation deviation from 180 degree is again because of the momentum of the electron. So, you can study the electron, what type of electrons are involved when the positron is annihilated. So, these are the two techniques Doppler broadened annihilation radiation, EVAR and angular correlation between annihilation. So, we will not talk about this angular correlation. So, it can also be used to obtain the electron momentum. And third technique is like when the sodium 22 decayed by bit electron positron to this excited state of neon 22, this is giving. So, the lifetime of this intermediate level is the external level is very very short. So, in less than a picosecond and so, this 1270 kV gamma 1275 kV gamma is emitted almost instantaneously upon the decay of sodium 22. So, we can say that this 1275 kV gamma ray tells you the time when the positron was born. And subsequently, the positron is thumb lighting, interacting with the electron and annihilating with the electron to give you a 511 kV gamma ray. So, that tells you the depth of the positron. Positron is finished now. And the time difference between these two is called the lifetime of positron. So, depending upon the environment, chemical environment in which the positron is dying or positron is annihilating with an electron, this lifetime can change. And so, this lifetime essentially tells you about the electron density in the medium where the positron is annihilated. So, this is another experimental technique. If you can determine the lifetime of positron, how do we determine the lifetime? That time between 1275 kV and 511 kV gamma rays. So, I will explain the instrumentation for this lifetime. So, these are the three experimental techniques, Doppler broadening of unilaterally addition, angular correlation between gamma rays and light ionization, which are used in positronium, positron chemistry, positron analysis spectroscopy. And one of the other than this electron momentum and electron density measurements, another very interesting field is positronium chemistry. See the chemistry of positronium. Positronium is an atom similar to hydrogen atom. In hydrogen atom, you have a proton and an electron. Reduce mass of hydrogen atom is one mass of electron. Reduce mass of positronium is 1 by 2 Me, M1 M2 by M1 percent. And so, accordingly, the binding energy or the annihilation potential of the positronium is 6.4 6.8 electron volt, which is half of the hydrogen atom potential 13.6 electron volt. Radius of hydrogen atom is 0.54, the radius of positronium is 1.08. So, double of the, so you will see the beautiful chemistry of positronium atom. So, when the positronium atom is formed, the positronium means a positron and an electron. So, depending upon the spins, if they are anti-parallel, so you form a singlet state, anti-parallel spins of positron and electrons called singlet state or para-positronium. And this is the ground state of positronium. And there is a orthopositronium triplet state where both these spins are parallel. So, this para-positronium has got a much shorter half-life of 1, 5, 25 picosecond, which you can determine from this light times photroscopic data. And this is disintegrating, this decays by 2 photons, that means 2, 5, 11 KeV, gamma rays. So, that is the normal positronium decay. Whereas, the orthopositronium is a triplet state of a positron and electron and in vacuum has got a lifetime of 140 nanoseconds, a very high lifetime. And since this has got a spin of 1, though if it has to decay on its own, it decays into 3 photons, 1.02 MeV upon 3, about roughly up to 370 KeV each photon. But what happens now? Till 140 nanoseconds, it is very difficult, highly improbable that positronium will remain as an orthopositronium. Before that, it undergoes different types of reactions like pick-off, oxidation, spin conversion and so on. And so, you see an orthopositronium signature in a higher component instead of 125, you may have 150, 200, 250 picosecond light. So, another area is chemistry of positronium atom itself. These are the three techniques by which you can do study with positron annihilation spectroscopy. So, let us discuss in more detail these experimental techniques of Doppler-Brotene and light-light spectroscopy. So, as I mentioned the finite momentum of the electron-positron pair when the pair is annihilating leads to the Doppler-Brotene. And so, instead of 511 KeV, if you call the typical gamma spectrum of the determinant using a germanium detector, HPG, high-putting germanium detector has got very high resolution. And so, you will see that 511 KeV, if you have a source emitting 511 KeV, not positron. The positron emitting source also gives 511 KeV, but there are sources which emit 511 KeV gamma ray after the decay of the, so that gamma is much narrower. And so, this is the inherent resolution of the detector for 511 KeV. But because of this Doppler-Brotene, if it is a positron, if this peak is due to the annihilation gamma ray coming from positron annihilation, that this peak becomes much broader. And it is significantly broader, it is not that you do not see it. In a gamma ray spectrum, if it is due to radioactive decay, you will see a much narrow peak at 511. If it is due to Doppler-Brotene positron annihilation, you will see a much broader peak. And so, the, if you can determine that white broadening of this 511 KeV peak, you can study the momentum. So, the instrumentation for this Doppler-Brotene annihilation radiation is we have a germanium detector. I put germanium, it has to be cooled at liquid nitrogen temperature 7 to 7 K to take care of the leakage, to reduce the leakage current. Then you have the pre-amplifier and then you put it to the multichannel analyzer through ADC and so on. So, this MCA spectrum gives you the 511 KeV gamma ray. And if you measure the width of the source, instead of the width, you will see different parameters which I will explain in the next slide. And from this simple gamma ray spectrum it will be set up, but it has to be highly stabilized gamma ray spectrum because you are looking for the broadening over 511 KeV by few electron volts broadening or maybe 0.5 KeV or so. So, how do you get the momentum of the electron? So, the momentum of that photon is given by H nu by C, momentum of the photon is E by C. And so, if H nu 0 was the 511 KeV and H nu is the Doppler-Brotene, then you have H nu C minus H nu dot C and into 2 delta E. So, it is delta E into plus minus 2 delta E. So, 2 delta E by E is P and so, the broadening is PC upon 2. So, you can determine from the broadening the momentum of the electron that is the methodology for Doppler-Brotene. So, in Doppler-Brotene, what is important is the line shape parameter. So, this is a typical 511 KeV gamma ray and you can see the 511 KeV gamma ray FWHM will be here. So, if it is the FWHM of a normal gamma ray is 1 KeV, you will see 2 KeVs, you can see from 510 to 512. And so, there are certain parameterization called S parameter. The S parameter is defined as the width, the area under this graph up to certain width upon the total area. So, area of the pink shaded area upon the total peak area is called S parameter. So, essentially it tells you the momentum of the valence electron, because these are the low momentum events. Whereas, if you take the tail part of the I11 KeV spectrum, this tail part expanded here and you take this parameter, then that area upon A0 is called W parameter, the wide part and that gives you the momentum of the 4 electrons. So, you can try to get from the Doppler-Brotene valence electrons and 4 electron momentum from the Doppler-Brotene or annihilation radius. In fact, from the normal DVAR experiment data, it is difficult to get the W parameter, because the W, this width is in the tail part of it, the wider part. So, the tail, you may have the content due to other high energy gamma rays or there can be background, so background will be more. So, if you can reduce the background by some technique called coincidence Doppler-Brotene, then you can have more accurate data about the 4 electron moment. So, here this is the again the Doppler-Brotene spectrum. So, this was the normal, this is the same as this spectrum where you just have an HPG detector and record the gamma spectrum of 511 kV around that. You can see here 500 to 525 kV is the region of interest for the annihilation radiation. But what you do if you put a Sodium agate thalium or Sintlation counter in coincidence with the germanium detector. So, this gamma is this particular spectrum is gated by a coincident between 2 511 kV, 1 511 is measured in HPG and other one is just in this other Sintlation counter that will trigger this gamma spectrum. You can see there is a significant reduction in the background. And on top of that, if you have 2 HPG detector and then you get this Doppler-Brotene spectrum. In fact, this 511 kV gamma you in coincident between the 2 HPG detectors if you that is gating this gamma spectrum then you can see there is a significant reduction in the background. And this then you can study the, these are the core electron momenta because of core momentum. So, you can achieve the core electron momentum distribution in the coincidence Doppler-Brotene. So, normally a laboratory which is doing positive on condition positive analysis, they will be having a coincidence Doppler-Brotene setup. Another technique I would mention you is the positron annihilation lifetimes professor. And you measure the lifetime of a positronium or positron by a setup called as the slow coincident setup where this 1275 kV gamma-A is triggering the start and the 511 kV are triggering the stop. So, you have, you have to have a circuit by means of which you determine the time difference between 2 gamma-A's 275 and 511 kV. So, what you do, you have a single channel analyzer where you get the gamma-A per 75, another single channel analyzer you get 511 kV gamma. And you in fact take, you take a start signal and you take a stop signal from time to amplitude converter the time to amplitude converter converts the signal into time, time to some voltage signal. So, the time gap between these 2 detectors for an event is converted into a voltage signal by this unit called amplitude converter type. And this type then spectrum, the type output is a type is an output, analog output which will get you the spectrum the x axis is the time and y axis is the count. So, this kind of a coincident setup it is called the fast slow coincident setup. So, when we say fast means time signal, slow means energy. So, you have one circuit for energy to get the gamma-A, 1275 and 511 and you have one circuit for timing, you have fast signals coming from the PMT of the 2 detectors wherein you put them into that at start and stop signal and you get the type output. Now, this output looks like this, you can see here this is called the time spectrum counts versus time. What you get is a fast rise and slow exponential decay. That exponential decay shows multiple exponential decays. The counts is a superposition of maybe 2 or 3 exponentials. So, every component has got intensity i1, i2, i3 and your tau, lifetime tau 1, tau 2 type. So, you can fit this data into multi exponential curve and get the constants ii. So, what you get the output is ii tau i. So, i1, i2, i3, tau 1, tau 2 type, tau 1 and its intensity is i1. So, what do these lifetimes represent? They are called lifetime components. This tau 1 is actually that 125 picosecond that is the lifetime of the para positronium that is the shortest component. So, when the para positronium annihilates you get 125 picosecond. So, that first shortest component will be para positronium annihilation and it does not really give you any chemical information because time is too short. The second one is the tau 2 after more than tau 1 you have tau 2 and it tells you the free positron or positron molecular species annihilation. So, it is actually a sort of a pickup that positronium can interact with the molecular species and undergo changes. So, that will increase the positron. When your positron is binding with the molecular species lifetime will increase and that gives you about the chemical species that is formed. And third is tau 3 that is the orthopojetronium annihilation. Orthopojetron lifetime is 140 nanoseconds but this tau 3 is not 140 it will be a few nanoseconds. So, you have 125, another one maybe 150 to 200 something like that and tau 3 is the longest lip component that can vary depending upon the type of material that you have. So, what information you get from positron annihilation lifetime copy? The orthopojetronium lifetime 140 nanoseconds decreased by pick off annihilation that means when you have a orthopojetronium where both electron positrons are parallel it can pick off this electron can be picked up by a chemical species and it will annihilate with another electron. So, this essentially tells you the electron density or the suppose you have a zone in which there are not many electrons the positronium will survive for more time. So, the orthopojetronium lifetime depends upon electron density if electron density is high lifetime is short if lifetime is high electron density is low. So, like a defect defect this much there are no electrons in the defect size. So, positronium will go and sit there it will prefer to stay in its site when there are not many electrons like in metals you do not see tau 3 you only see tau 1 So, it tells you about the electron density or even pore size in polymers when there are pores. So, polymers will have areas where pore it can be pore can be open or closed and the positron has a tendency to go and sit in the pores so that it can survive longer and so the lifetime essentially tells you the pore size defects wherever the electron density is less that means it is a defects defective site. So, it will give you the defect concentrations and the phase change in terms of polymers you know if there is a change in the polymer pore size because it is going through a phase change then it can tell you about the pore size change in pore size or essentially phase change like certain plastics plastic materials can undergo changes. So, then it can tell you about different phases that like glass transition in plastics can be monitored and of course the positronium chemistry also can be said that positron can undergo oxidation if the electron is taken up by the metal ion and you have a positron similarly it can undergo spin conversion with another chemical species. So, positronium chemistry itself is a subject there are books on only positronium chemistry. So, you can refer to if you are interested in doing research in positronium chemistry or positron analysis microscopy one can go to the literature and read the books. So, what are the areas in which the one can do research using positrons the major areas of research include solid state condensed metal physics you can study positron analysis microscopy in metals alloys semiconductors to determine their electronic structure like if you are determining what is the you know what are the like the bands due to the in metals and semiconductors you have the different bands overlapping which electrons are participating in these bands you can study the momentum of electrons by Doppler broadening of annihilation radiations. If you are going to study defects you can go to light and soapy and that essentially the defects will will can dictate the properties of materials. So, you can analyze the properties of materials through factorization of the defects. So, in fact, new defects play a big role in governing the properties of different types of material they can be optical property, electrical properties and so on. So, it is a vast area when you want to because defects by using light time microscopy and you have the positronium chemistry the positronium atom formation mechanism how the positronium will be formed in different like for example water and benzene you would find that the positronium formation is different in water and benzene and their reaction processes like what is the chemical reactivity of positronium atom towards different species and the dynamics of the positronium atom formation. And this is associated with the applications in molecular solids and liquids. So, is another area where you can study the structures of polymers, catalysts, surfactants, liquid crystals and so on wherever you will find that the molecular arrangement in the sample is going to change. So, that will affect the either the pore size or electron density. So, that will affect the positron light time. Now, there have been several advancement in the techniques of positronium inhalation. So, there are now positron beams from the sodium 22 whatever positron is coming out you can analyze and then accelerate to a required energy. So, you can have mono energetic positron beam of energy iu electron volt to 50 keV and this positron this positrons of a mono energetic energy can be used in depth profiling of defects correction of thin films. So, whenever there is a energy dependent process you can do the study using mono energetic positron beams. Not only it is not that you have only sodium 22 as a source of positron. You can have copper 64 in a reactor or you can have positrons from electron oscillator. You can stop the electrons in a high jet material produced beam Stalin and that beam Stalin upon pair production will give you positrons or you can have positrons generated in situ. Suppose you have a high energy gamma ray produced in a nuclear reaction and you stop that gamma ray in your material of interest then you can do in situ that gamma ray will produce positron inhalation pair production and the unrelated high level keV spectrum you can use the you can find out the electron momentum in the machine. So, a lot of high technology materials have been also studied using the in situ the positron inhalation spectroscopy using in situ gamma ray. So, just to give you an example of positron instance spectroscopy by Doppler broadening as I mentioned you essentially get the momentum of electrons and if you do coincidence Doppler broadening you can do momentum of core electrons. So, you can see the fraction of positrons annihilating with core electrons by coincidence Doppler broadening can be obtained for different metals aluminium silicon and germanium. You can study in all types of metals how the positron is annihilating with core electrons and valence electron. So, the role of core electron valence electron in positron inhalation can be studied and this in turn you can actually characterize an element by the core electron momentum. So, suppose you have a sample from the core electron momentum you can find out which so index you can index the metals gem of the particular element you can index. And another example is the lifetime from the lifetime spectroscopy you can find out the pore size distribution this is the radius of the pore. So, certain materials like you know like poly methyl methylate is a polymeric material which will undergo changes in the pore size distribution with temperature and you can see the pore size distribution is changing with the temperature. So, how the polymeric material is undergoing changes the internal transitions in the polymeric material can be investigated by pore size distribution study using lifetime spectroscopy. So, these are just to give you examples of what you can do, but you can take a topic and see how positron inhalation can be utilized in the study of a particular topic. So, there is a vast area of research in using positron inhalation spectroscopy. So, I will stop here and take up the next part in the next lecture. Thank you very much.