 Dear students, so we just discussed the interaction of different types of radiations with matter, that can be charged particles, alpha protons, live charged particles or hostile electrons, beta particles, the gamma rays and neutrons. These are the types of the radiations that one will be encountering while working in a radioactive area. So, this interaction of different radiations with matter helps in developing detectors when you want to choose a detector for a particular radiation. So, that knowledge will help in understanding the principle of different radiation detectors. Before we go to the actual detectors, different types of sensors that we will be discussing in today's this lecture, I want to discuss the basic principles of radiation detectors. So, how do we get a signal from a detector? Detector will sense the gamma ray or the alpha or beta or electron. So, how do we get the sense signal from detector that is what we try to understand? So, all of you know that rather this Henry Buckerl discovered radioactivity using simply a photographic plate. So, in essence a photographic plate also is a detector. One of the oldest detectors is a photographic plate, but that will give you a qualitative picture. So, when we want to do for quantification of radiation levels, we use different more advanced detector systems. And so, the basic principle of detection of radiation is collection of iron plates. If you recall your discussion on the interaction of heavy charge particles, the heavy charge particles cause ionization. It can also cause excitation, but the ionization will give you ion pairs. And if you collect the ion pairs, you can detect the signal. The electron also give you ion pairs. Similarly, the gamma ray by secondary means it will give us electrons by potential effect or even components getting a pair production. The neutrons also give rise to heavy charge particles by way of nuclear reactions. So, the net result of all types of interactions of this energy radiation is the production of ion pairs. So, if a radiation is going, it will give, suppose let us say alpha plus a is that and let us say atom, then alpha plus a plus this is ionized and then you have an electron. So, if you can collect this electron and positive ion at the respective electrodes, you can collect that, get the signal. So, this is a schematic of a detector. If you collect the electrons at the anode and the positive ions at the cathode by applying a potential at the anode. And so, you essentially you are charging the capacitor, the electrons will be charging the capacitor and the capacitor is fully charged, it can discharge through a load resistance R and the discharge of the system you can measure by in terms of a voltage or a current. So, you can use a detector in current mode, if you put a current emitter here or you can put a voltmeter, you can use a pulse. So, we will discuss both the mechanisms and see also their merits and demands. So, when you do, when you measure the current in this circuit, then what you essentially whatever charge was created by interaction of radiation with matter is the total charge. What is the total charge? So, if you suppose you have so many alpha particles coming. So, you will have a large number of what we will say 1 MeV gamma ray. So, it will be giving 1 MeV, how many ion pairs will produce W? So, this is W is the energy required to produce 1 ion pair. So, electron volt 1 MeV. So, you will be number of ion pairs. So, these ion pairs are collected and that is to essentially you are collecting the charge, that is what this charges. Now, when this charge is discharging through an emitter, then capacitor is discharging through an emitter, you see the current flowing in the circuit and what you see here in the time domain, you see the current is it will be rising, become flat and come down. So, one event will be like this and then there will be several other events. So, multiple events will lead to a flow of current in the circuit. Because of that, you know, since this there will be a constant current flowing in the circuit, this mechanism of current mode is not used in the counting of the activity, but it gives you the gross activity level. Like you have a subway meter in the laboratory, just you want to know what the level of radiation you can use for gross activity counting current. It is giving you a current level, how many microamp, how many nanohamp, how many milliamp, that tells you that this is the level of radiation. But if you want to count the activity, how many counts per second, quantitatively you want to know, then you require pulse. So, you will need to shape the pulse. So, what do you do? Whatever charge is produced Q, you get a potential voltage at the voltmeter Q by C. So, the maximum that voltage will go is depends upon the Q upon C, the capacitance of the circuit. Actually, this capacitance is not only this capacitor, but the detector system also will have its own capacitance. The net capacitance of the detector system is involved in determining the voltage. So, the voltage will rise, go to maximum and again fall down. So, this is the V max. And the rise and fall will depend upon the C and R. This is called C-R circuit. In fact, the detector systems have a series of C-R-R-C circuits. So, that you play with the circuitry to get a proper signal. Essentially, we want to get a voltage signal. If you see in the oscilloscope, the voltage signal will be like this. It will rise and fall down. And it should fall down before another event comes. So, that if they can be separated and so you can count. So, we will discuss about the dead time and all. So, different individual pulses are counted in the detectors in the pulse mode. And that pulse mode then you use for event by event counting. Each decay you can count separately in the pulse. So, the detectors actually are operated in current mode and pulse mode. Some detectors are used in current mode also like survey meters where you are interested in only gross activity level. But whenever you want to measure the even each engine event separately then you use a pulse mode. So, this is a block diagram of a reducing detection system. You have a detector. It can be a material. It can be gas, solid, liquid. And you have to apply some potential. Sometimes the charged particles have to be collected at anodes and cathodes. So, you apply the high voltage at the anode. And then once the signal is coming the Q, the charge that is collected, you have to get a signal. So, the preamplifier does the job of getting a voltage signal or a current signal from the detector system. And the preamplifier actually just giving a initial signal which have a low output impedance. Normally, detector output impedance is very high. It will get attenuated. So, you use the preamplifier to decrease the impedance of the output signal. And subsequently you can carry to long distance. And then there is an amplifier which will amplify the signal to a measurable range of 0 to 10 volts or whatever it is. And these pulses are then fed to a counting system, multi-general analyzer. You have 4000 channels or you can timer scalar. You can count in the scalar mode or you can count in it. You can generate a spectrum in the multi-general analyzer called MCA. So, this is a schematic of a particular detector system. You have a detector material. We will discuss the details of detectors separately. You need a high voltage, you need a preamplifier, amplifier and the multi-general analyzer or scalar. Now, whenever we want to set up a detector system, we should make sure that detector is functioning in a stable manner. It is the settings of the detector are proper and so that is why we need to generate these counting curves and plateau. So, counting curve and plateau means what you are whenever you are counting detector is giving you proper results. So, there is a quantity called gain. Gain means your amplification factor. So, in the amplification what is the extent of amplification you have to do so that you are counting the signal and not the noise. So, I try to illustrate this using this figure here. What I have done here the gain, the gain is like 1, 2, 3 different types of gain the pulse height. So, here is a pulse height distribution Phd. So, you have a time at the voltage versus the counts dn by dv number of pulses of a particular height. Now, what happens initially suppose you have got a low gain in the amplifier, then and you put a threshold in your timer scalar or multitalented you have a threshold let us say 1 volt. Any pulses above 1 volt will be counted it is below 1 volt it will not be counted. So, this is the threshold for let us say 1 volt. So, anything beyond this only will be counted. Now, at lower gain you can see the noise and the pulse both are below the threshold. So, you will not get anything no counts. So, this is the gain versus counts. Then you slightly increase the gain g equal to 2 and now you can see there is a the pulse is stretched to the higher pulse height, but still you see some part of the pulse is still below the threshold. So, you will get this rising part somewhere here, but not a complete all pulses are not above the threshold. Then you further increase the gain to the third one and here noise is below the threshold, but the actual all the pulses are above that you should above the threshold. So, this is what is the plate and if you further increase the gain, then you will find even the noise will go beyond the threshold and there will be a rise in the. So, this is the plateau region where you have to setup do the settings or you can operate at this particular gain. In many detectors like dagger molar counter, Oedemar and thalium, you can change the gain of the detectors in system by voltage itself. So, many a times in gm counter now instead of gain you change the high voltage and setup find out the high voltage at which the that is the stomach stable. So, this plateau and counting curves are actually used in the gm counter very routinely to set up the high voltage which you have to apply so that the detector system is functioning properly. So, counting curves and plateaus are very important for setting up a detector which will give reliable results and it will be stable system. Another important property of detector is the energy resolution. I have discussed the general property of detectors so that you know we do not have to repeat it every time. So, what is the resolution energy resolution? So, a source may be emitting different traditions like different gamma rays or different energies whether the detector can resolve those that will depend upon the energy resolution. So, the ability of a detector to resolve nearby peaks we call as the resolution energy resolution. Just to illustrate here suppose there are two peaks one and two these two peaks are nearby. So, if our resolution is good they will appear at separate peaks, but if the resolution is bad it can appear like this also. So, it could be like this or it could be broad. So, bad resolution and good resolution this is what we want to mean. So, you have to see that the resolution is low. So, when you say better resolution the R value the R value how it is defined? R is the resolution in percentage. So, if I show this normally you know when you will see the pulses pulse height spectra they will appear like a Gaussian or a single peak and the full width at half maximum of a Gaussian. So, FWHM full when the counts have become half the width at that time is called full width at half maximum upon the mean value of the pulse height FWHM upon H naught into 100. So, they have the same unit this and this have the same unit it is in terms of percentage. So, this is how we define the resolution. So, lower the value of R better is the resolution. So, FWHM has to be low as low as possible. So, now how let us go a little more details of the how do we you know define this resolution and how we can improve this resolution. So, when the variation is falling on a detector system you we cannot define a priori how many amplitudes will be created though we say E by gamma E by W is the number and pairs every time a single energy photon interacts or the alpha particle interacts it will not give the same value of N though energy is constant W value is average energy. So, N is not constant. So, this is a statistical process you will say random fluctuation in the number of ion pairs. So, you have a large number of atoms in the material and so, you have what you follow is the Poisson distribution probability of interaction of the radiation the particular atom is very small. So, we follow Poisson distribution whenever the probability is very small and the ensemble size is very large. For a Poisson distribution the second moment the variance is equal to the mean. So, take the mean as the number of ion pairs that are produced N then the variance is equal to mean and variance means the variance is square of the standard deviation. So, sigma will be root of mean. So, sigma will be root of mean that means the fluctuation in the. So, it will not be sigma it will be actually 2.35 sigma for a Gaussian. The fluctuations in the pulse height are related to square root of the number of ion pairs. So, if you want to have a better resolution go for a high number of ion pairs or low WF. So, that consequences we will see subsequently. So, for a Gaussian the WHM is given by 2.35 into the sigma you can derive from the full width of maximum how it relate to the standard deviation of a Gaussian. So, the R now resolution will be 2.35 sigma WHM upon H naught. H naught is the number of actually proportional number of ion pairs. So, N and sigma is root N. So, you can convert this in terms of root N upon N 2.35 root N upon N where N is the number of ion pairs formed. And so, you can now see that resolution it depends upon is equal to 2.35 upon root of N where N is the number of ion pairs formed. So, higher the number of ion pairs better the energy resolution. This is how the resolution when we detect this the different detectors you will find that the resolutions are different because of the number of ion pairs that are produced. Another important property of detectors is the detection efficiency. How efficiently the detector can count yours of maximum counts you can you can count. So, the radioactive sources you know they will be emitting the radiation in all possible directions in 4 pi. We can which though even if you put a collimator then we are loosing the radiations imitating other directions. So, isotropic emission of radiation is the property of radioactive sources they are emitting in all directions. But your detector has got a finite dimension. So, if suppose you have a cylindrical detector having a radius r and at a distance d from the source. So, there is a something called the geometrical factor what fraction of the radiation is falling on the detector that is called the geometric efficiency. Out of that fraction whatever is falling on detector what fraction is the content that is called the intrinsic efficiency and the product of the two we will call as the absolute efficiency. So, we will go in the reverse direction. Geometric efficiency is the solid angle subtended by the detector at the point is omega upon 4 pi and this omega upon 4 pi can be written in terms of the area of the detector surface into surface area of the sphere 4 pi t square. Because this detector can be considered as the part of this area of a sphere. So, like you know you can have a sphere on this surface you have a small portion is covered by the detector. So, pi r square this is the fraction covered by the detector. So, that is called the geometric efficiency it becomes r square upon 4 d square. So, you can play with the geometric efficiency have a large area detector bring it close to the source and so on. Then out of this whatever fraction it is in the detector what fraction is counted that is called the intrinsic efficiency. Intensive efficiency number of counts upon number of quanta incident on detector because every radiation that is following on detector may not be counted. So, there may be other processes or radiation may escape. So, that is called the intrinsic efficiency. And the product of the intrinsic efficiency and geometric efficiency is called the absolute efficiency. So, absolute efficiency equal to intrinsic efficiency into geometric efficiency and so, you can in fact, call absolute efficiency as number of counts in the detector system upon number of quanta emitted by the source. So, suppose it is emitting 100 counts per second 100 radiation per second out of those 100 how many are counted by the detector that is called the absolute efficiency. So, in practice we will be using absolute efficiency you can have a standard source and find out how many counts you are getting. But it is a product of two quantities geometric efficiency and intrinsic efficiency. Geometric efficiency depends on the geometry of the detector system intrinsic efficiency depends on the detector material or even it can depend upon the energy of the radiation. So, when we count the activity we say counts per second in the peak suppose you have a peak like this take the counts this is the energy versus count. So, this area will be the counts we have counter for a particular time divided by the time we call the counts per second. And so, but it is not necessary that all the disintegrations are being converted into counts. So, there will be suppose it is emitting certain photons. So, efficiency is taken care of the fraction it is actually counting. So, if the disintegration per second suppose you have got let us say activity is a 0 into efficiency equal to activity. So, initial activity this is the source activity and this is the counts. So, you can if you know the efficiency if you know the counts you can find out the absolute efficiency a 0 absolute activity a upon efficiency. So, if you know the counts per second you know efficiency you can find out the disintegration per second. So, this efficiency is a very important property of a detector. Now, comes the counting statistics. So, when you are counting a source you should know for how much time you should count because there is a limitation on the time also. So, for that let us discuss this in more detail. So, essentially the errors the uncertainty in the numbers dictate for almost time count. So, radioactivity we have already discussed activity equal to n lambda. How many atoms are decaying in one second atoms per second it is called number of atoms into the probability of decay in one second lambda. So, again going by the you know the probabilistic aspect of this number of atoms in a sample can be very very large but they can grant you can mean I look close to Avogadro number if we and then the lambda decay constant is a very small quantity. So, whenever you have a very small probability of decay and very large sample size the decay follows a Poisson's distribution. And so, for large number of atoms and a small decay probability we use Poisson. So, counting of the radiation in a detector system we follow Poisson's distribution for which the variance is equal to the mean that means if you have a single counts you counted the sample and you get some number n from that extent we can find out the uncertainty into them. So, suppose you get n counts in a detector system and so, you have only one value how do you find out the uncertainty use this formula. So, standard deviation sigma equal to root of n. So, that is how you get the uncertainty in the counts. So, just let us take an example that if suppose you get 100 counts in a detector system then sigma equal to 10. So, uncertainty will be error will be 10 by 100 into 110 percent. But if you count for 10,000 counts uncertainty sigma is 100 an error on that will be 1 percent 100 upon 10,000 into 100 1 percent. You can see that by counting by accumulating more counts you can decrease the uncertainty in your counts. So, that is what dictates for how much time you should count a sample if you are 1 percent uncertainty and then you could count for 10,000 you accumulate 10,000 counts. So, your time counting time is governed by what is the uncertainty that you want to achieve. So, many a times you know you have sample will have your detector system will have a background also. So, you when you are counting a sample it will also have background. So, you have to subtract the background without the sample you count you get background and so, the net count will be gross count minus the background. So, you put the sample you get a count because you remove the sample and you just count without sample called background. So, net counts equal to gross count minus background and so, correspondingly the uncertainty is sigma n square will be sigma g square plus sigma e square. So, they have their own uncertainty. So, the errors are additive though you are subtracting gross count minus background the errors are additive. So, if you have let us say background equal to background gross count is let us say 1000 and background is 900 count net count is equal to 100, but error will be 100 plus 900 square root of sigma n, sigma n will be 100 this is the error on the g plus 900 and square this is the same. So, if the background is high the error on the numbers is very high. So, you have to reduce the background to get more reliable results. These are the things one has to take care when counting and the last thing property of detectors is the dead time. Dead time is now when a detector is processing a particular event for that event it cannot process another pulse. So, during that time I will be processing one pulse it is say it is dead to receive another pulse. So, the essentially the dead time is the minimum amount of time which must separate two events so that they are recorded as two separate events. So, this essentially the dead time is a time required to process a pulse. During that pulse if another event comes another pulse comes that may not be or may be counted that depends upon what type of system you have and this happens when the system has got high count rate then there will be some need pulses will be lost. So, the dead time losses are important. So, that tells you what will be the sample count? What is the activity? Suppose you put a one military sample then for 7, 3.7, 7 buckles you cannot count. You require very small quantity just then a macro query to count yourself. So, I will just try to explain there are two models of dead time parallelizable and non-parallelizable. That means, see this there is a trail of events this pulse these are the pulses coming in the detector system and for each pulse you require certain time to come process the pulse. So, this instead of that instead of this if you recall this we are shown time versus voltage Q by C. So, this is a voltage signal I am showing a logic signal square pulse. Now, I have shown the five other six events are coming in the detector spaced by the time in different manner. So, here this pulse is counted this pulse you know there is a before this pulse is over another pulse has come and here two pulses have come. So, one after one more one more three pulses have come depending upon whether it is parallelizable mode or non-parallelizable mode you will get different events in the detector system. In the non-parallelizable mode in the second pulse you know when this is coming the second pulse is not counted you see here whereas, this here there are three events they are counted as two events because after this the detector is available to take the other pulse. Whereas, in the parallelizable mode in the parallelizable mode you get one event here this is again one event and this whole thing is coming as one event because it is parallelized. So, this detector is seeing this whole thing as one event. So, you get three events you get four events actually there were six. So, that is the different meaning of the parallelizable and non-parallelable mode of dead time and depending upon the type of model for dead time there are the observed count rate. So, the n is the true count rate how many counts the sample is limiting event sample limiting how many observed m m is observed count rate and tau is just dead time system dead time. So, the relationship between the observed count rate and the true count rate for parallelizable r m equal to n e raised to minus n tau and for non-parallelizable is n equal to m upon 1 minus m tau. So, you can use it means the detector system will follow either parallelizable or non-parallelizable one has to do an experiment to see what kind of model the detector follows. So, just to know see how this one can determine the dead time of a detector system. So, for this purpose people follow a two source method. Two source method let us say one is S1 and S2. So, you count a source one source separately you count second times the S2 and then you count S1 S2 together. So, when you count S1 S2 together there will be losses in the counts because the count rate has increased and so, this can be made use of in finding out dead time and this D1 D2 are the dummy. Dummy means you when you are not putting any sample you put a dummy source there is no activity in that that is what dummy source. So, you put you have now four sources S1 S2 D1 D2 D1 D2 are the dummy D value these are these sources the dimensions are of a semicircle and so, you can put so, N1 is a true count rate for N1 sample one source one N2 true count rate for source two and when you put them together and count you get the N1 2 true count rate combined source and there is a two background count rate. But actually what you get is not N you get M. So, you can try to analyze N1 2 minus 12 B NB the background you subtract the background N1 minus NB plus N2 minus NB the true counts. So, you can arrange N1 2 plus NB is N1 plus N2. This is not the this is not the count what you are counting what you are the true activity counts of the sample. Now, you apply the nonparallelizable model N1 2 M1 2 upon 1 minus M1 tau. So, all you get replaced by the M value. So, this is an equation where you are observing the counts M1 is when the you have put this one M2 is when you put the S2 and M1 2 is when you put both of them together and D1 D2 when you put backgrounds it called NB. So, this from this you can solve this equation to find out the tau and the tau comes in terms of x y z where x equal to this term y equal to this term x z equal to this term they all depend upon the M1 M2 MB and M1. So, you can actually just calculate the dead time by the in the in the nonparallelizable model for the detector system. Particularly, there is an experiment for in the GM counter and if you are if you happen to use a GM counter one can use this setup true source method to find out the dead time of a data counter. This is a very you know general experiment for the radiochemistry people that determine the dead time of a GM counter and that comes to about few hundreds of microseconds. So, today what I try to show you the different properties of the detector systems and these properties will be used and we will use the different detectors then we will use the terms quite often in our discussion. So, I will stop here and next time we will we will discuss the different types of detectors. Thank you very much.