Phys. 649: Nuclear Techniques Physics Departent Yarouk University Chapter 4: General Properties of Radiation Detectors Suppleents Dr. Nidal M. Ershaidat
Overview Phys. 649: Nuclear Techniques Physics Departent Yarouk University Chapter 4: General Properties of Radiation Detectors Introduction Siplified Detector Model Interaction of Fast Electrons Pulse Height Spectra Counting Curves and Plateaus Energy Resolution Detection Efficiency Dead Tie Dr. Nidal M. Ershaidat Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors Introduction Coon Properties Detectors have any coon properties. For all detectors we shall need to know the efficiency energy resolution But also: odes of operation and ethods of recording data. Signal treatent is finally coon to all types of detectors. But this is another course Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 4
I. Siplified Detector Model Scheatic Radiation hits the detector. Stopping tie varies between a few ns to a few ps (See schee). Ties are practically so short that we can consider the deposition alost instantaneous! Radiation Detector Charge collector First we consider that only one single particle (or one photon or quantu of radiation) is incident on the detector. The result of the interaction between the radiation and the aterial (of the detector) is a charge Q. An electric field is applied in order to "collect" the resulting electrons (currents) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 6 Collection Tie The collection tie fro t=0 (creation of the charge) varies fro a few s for ionization chabers to ns for seiconductor diode detectors. This collection tie is a function of )the obility of charge carriers within the detector and )the average distance that the charge ust travel before arriving at the collection electrodes! The figure below shows the flow of a current for a tie equal to the charge collection tie (t C ). Real Situations For any real situation, a flux of radiation is incident on on the detector. If the rate of interaction is high then current is flowing in the detector fro ore than one interaction at a given tie. For siplicity we consider that this rate is low enough such as the current resulting fro each individual interaction is distinguishable fro the others. The Magnitude figure and below duration shows of the each flow current of a current pulse depend in this case. on the type of interaction. t c i 0 ( t) dt = Q Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 7 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 8
II. Modes of Detector Operation Pulse ode Current ode MSV (Mean Square Voltage) ode General Features Current ode operation is used with any detectors when event rates are high. Detectors that are applied to radiation dosietry are also norally operated in current ode. MSV ode is appropriate for enhancing the relative response of detector to large aplitude events. This ode is especially used in reactor instruentation. Pulse ode is used when one wants to preserve the aplitude and tiing of individual events. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 0 Pulse Mode Here the easureent instruentation is designed in order to record each individual quantu of radiation that interacts in the detector. The total charge, Q, related to the energy deposited in the detector, is recorded. Measureents of individual radiation quanta (radiation spectroscopy) ust be done using detectors operated in pulse ode. The object is to easure the energy distribution of the incident radiation. Radiation spectroscopy, nae reserved to such applications, constitutes the ajor part of this course. We stress again the fact that this ode is practical and efficient in the case of low rate of interactions. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors Current Mode The sketch below shows the setup of a detector in current ode. A current easuring device (a picoaeter) is connected across the output terinals of a radiation detector. If the easuring device has a fixed response tie T then the recorded signal fro a sequence of events will be a tie-dependent current given by: I t T t T ( t) = i( t ) dt () Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 3
Averaging! The response tie T being long copared to the average tie between individual current pulses fro the detector, the effect is to average out any of the fluctuations in the intervals between individual radiation interactions and to record an average current that depends on the product of the interaction rate and the charge per interaction. Average Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 3 Average Current The average current is given by: E I 0 = r Q = r e () W r = event rate Q = Eq/W = charge produced for each event E = Average energy deposited per event W= average energy required to produce a unit charge pair (positive ion + e - ) e = fundaental charge =.6 0-9 C For a steady-state irradiation of the detector, the average current can also be rewritten as the su of a constant current I 0 plus a tie-dependent fluctuating coponent σ i (t) as in the sketch. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 4 σ i (t) Figure σ i (t) is the rando tie-dependent variable that occurs as a consequence of the rando nature of the radiation events interacting within the detector Rando Coponent σ i (t) A statistical easure of this rando coponent is the variance or the ean square value defined by: t t σ I ( t) = [ I( t ) I ] dt = σi ( t) dt T 0 T t T t T The standard deviation is thus: ( t) = σ ( t) (3) σ (4) I I Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 5 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 6 4
σ, Rate and Tie The statistics being of Poisson type, the standard deviation is: σ = n (5) n For a nuber of events occurring at rate r in an effective easureent tie T, the standard deviation is siply: σ = n r T (6) In a hypothetical (and reasonable) approxiation where we can consider that each recorded pulse contributes the sae charge, the fractional 5 standard deviation in the easured signal due to rando fluctuations in pulse arrival tie is given by: σ I ( t) σ n = = (7) I n r T 0 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 7 B. Mean Square Voltage Mode Suppose that we send the current signal through a circuit eleent that blocks the average current I 0 and only passes the fluctuating coponent σ i (t). The figure below scheatizes the processing steps: Ion Chaber Squaring Circuit Averaging Output The results correspond to the quantity defined in Eq. 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 8 MSV: Signal Aplitude Q Cobining Eq. and Eq. 7 we predict the agnitude of the signal derived in this way to be: r Q σ I ( t) = (8) T This ean square signal is directly proportional to the event rate r and ore significantly proportional to the square of the charge Q produced in each event This is the MSV node, also called Capbelling ode (Capbell was the first to devise this ode!) MSV: Application The MSV ode is ost useful when aking easureents in ixed radiation environent when the charge produced by one type of radiation is uch different fro the second type. A standard application is in the detection of neutron in reactors where one can distinguish easily the fast electrons fro the salleraplitude gaa-rays events. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 9 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 0 5
C. Pulse Mode This ode is used when one wants to preserve inforation on the aplitude and tiing of individual events. This is the ode which will be dealt with in this chapter. The nature of the signal pulse fro a single event depends on the input characteristics of the circuit to which the detector is connected (usually a preaplifier). Typical Circuit in Pulse Mode The following figure is a schee of a circuit used in pulse ode. R represents the input resistance of the circuit and C represents the equivalent capacitance of both the detector and the easuring circuit (including cables) The potential difference (V(t)) across the load resistance is the fundaental signal voltage on which the pulse ode is based! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors Capacitive Tie Constant The capacitive tie constant of the previous circuit is τ = RC Two extree cases are used in pulse ode. Case : Sall RC (τ << t C ) Here the current flowing through the resistance is essentially equal to the instantaneous value of the current flowing in the detector. This configuration is used when high event rates or tiing inforation are ore iportant than accurate energy inforation. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 3 σ >> t C Case : large RC (τ >> t C ) This configuration is used for accurate energy easureents. Very little current flows in R during the charge collection tie and the detector current is oentarily integrated on the capacitance. The voltage here has a long tail that is created as the capacitor discharges. If the tie between pulses is sufficiently large, the capacitance will discharge through the resistance, returning the voltage across R to zero This configuration is the ost coonly used. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 4 6
τ >> t C The agnitude of the axiu voltage is equal to Q (the total charge) divided by C. Instead of integrating the signal (as we should do in the case "sall RC ), we siply easure V ax of the pulse. See Next Chapters III. Pulse Height Spectra IV. Counting Curves and Plateaus Figure 3 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 5 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 6 Detectors in Radiation Spectroscopy. Response to onoenergetic source of radiation Fig. 4 shows the so-called response-function which represents the differential pulse height distribution. V. Energy Resolution Figure 4 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 8 7
Detectors in Radiation Spectroscopy In both cases, good resolution and poor resolution, the sae energy is deposited in the detector. This eans that that the area under both curves is the sae. Although they are both centered on the sae value, the difference coes fro the fact that the detector with poor resolution has recorded a large aount of fluctuation fro pulse to pulse. On the other extree side, if these fluctuations are ade saller, the resolution becoes better and in an ideal case we should, reach a clear spike or even an alost delta function. (There is still the broadening resulting fro the nature of the easured energy Uncertainty principle) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 9 Detectors in Radiation Spectroscopy Fig. 5 illustrates the foral definition of energy resolution. Figure 5 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 30 R = FWHM/H 0 The energy resolution (R) is defined by: FWHM R = H 0 unitless where FWHM is the full width at half axiu and H 0 is the "centroid" of the gaussian signal. R expresses the ability of the detector to distinguish between two radiations whose energies are near each other. Roughly speaking the detector should be able to resolve two energies that are separated by ore than one value of the detector FWHM. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 3 Sources of Signal Noise There are a nuber of potential sources of fluctuation in the response of a given detector: ) Drift of the operating characteristics of the detector during the easureent. ) Rando noise within the detector and the whole instruentation syste (preaplifiers, aplifiers and the easureent electronics). 3) The statistical fluctuation (noise) which will be present whatever the reainder of the syste is. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 33 8
Statistical Noise This is by far the ost iportant noise to the detection signal. Statistical noise arises fro the fact that the charge Q generated within the detector is not a continuous variable but instead represents a discrete nuber of charge carriers. In an ion chaber the carriers are the ion pairs produced by the passage of the radiation, whereas in a scintillator the charge carriers are the nuber of electrons collected fro the photocathode of the photoultiplier tube. In all cases this nuber is discrete and subject to rando fluctuation fro event to event even though exactly the sae aount of energy is deposited in the detector. 34 Estiate of Statistical Noise We can consider that the foration of each charge carrier is a Poisson process, i.e. the nuber of carriers created per event is sall. If the total nuber N of charge carriers is generated on the average, the standard deviation and thus the inherent statistical fluctuation is given by N If this were the only source of fluctuation in the signal, the response function is a Gaussian, N being a sufficiently large nuber (See Fig. 5). Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 35 FWHM The Gaussian function (Average H 0 and standard deviation σ) is: ( ) ( ) A H H ( ) = 0 H H G H exp = C exp 0 σ π (0) σ σ The Full Width at Half Maxiu is by definition: C = C exp h σ h ln = h = σ ln0.5 = ln σ σ FWHM = h = ln σ =. 355σ () Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 36 Resolution (Poisson Liit) For the ajority of detectors, the average pulse height H 0 is proportional to N, i.e. H 0 = K N The standard deviation σ of the peak in the pulse height spectru is K/NK N and the FWHM is.355 K N. A liiting resolution R due only to statistical fluctuation in the nuber of charge carriers is thus given by: FWHM.355 K N.355 R = = = Poisson liit H0 K N N () Note the inverse proportionality between R and N. N should be greater than 55000 in order to achieve a resolution better than % (R =0.0) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 37 9
Fano Factor Practically, easureents of R give lower energy resolution by a factor of 3 or 4. This is essentially due to the fact that the processes that give rise to the foration of each charge carrier are not independent and in this case Poisson statistics is no ore valid! The Fano factor is introduced in order to quantify the departure of (difference between) the observed statistical fluctuation in the nuber of charge carriers fro pure Poisson statistics. It is defined by: observed variance in N F = (3) Poisson Predicted variance ( = N ) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 38 Overall FWHM For typical seiconductor diode detectors the Fano factor is less than unity, while for scintillators this factor is alost unity. In general one should add all "noises" and the overall FWHM in this case is defined by: ( FWHM ) = ( FWHM ) + ( FWHM ) + ( FWHM ) + L (4) overall statistical Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 39 noise drift VI. Detection Efficiency What is Detection Efficiency? Upon entry in the active volue, a charged particle, alpha or beta, and after traveling a sall fraction of its range, enough pairs of ion-electron are created. Their nuber is sufficient to ensure that the resulting pulse is large enough to be recorded. In this case a detector will see every alpha or beta particle that enters its active volue. The detection efficiency, under these conditions, is 00% Things are different in the case of uncharged radiation since they ust first undergo a significant interaction before being detected. The detection efficiencies in this case are often less than 00% 4 0
Absolute and Intrinsic efficiencies We define the absolute efficiency by: nuber of pulses recorded ε abs = nuber of radiation quanta eitted by source It is dependent on the detector nature and on the counting geoetry (essentially the distance between the source of radiation and the detector). The intrinsic efficiency defined by: nuber of pulses recorded ε int = 6 nuber of radiation quanta incident on detector no longer includes the solid angle subtended by the detector as an iplicit factor. 5 Intrinsic Efficiency The intrinsic efficiency depends on three factors: ) The detector aterial, ) Radiation energy, 3) Thickness of the detector in the direction of the incident radiation. The dependence on the distance sourcedetector is still there, since it affects the range of the radiation in the detector. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 4 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 43 Total Efficiency If we accept all pulses fro the detector, in this case one talks about total efficiency. εabs Ω = εint 4π (7) In practice, soe constraint is iposed on the output signal, using a discriinator or a gate, in order to eliinate very sall pulses fro electronic noise sources. A threshold is iposed and the total efficiency is theoretically approached if this threshold is as sall as possible. Fig. 6 shows a hypothetical differential pulse height distribution. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 45 Peak to Total ratio The peak efficiency assues that only those interactions that deposit the full-energy of the incident radiation are counted. Figure 6 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 46
Peak to Total ratio The nuber of events having deposited all their energy (full energy events) is siply obtained by integrating the area under the peak! Events which deposited only a part of their energy are spread to the left of the peak. A peak to total ratio relates the peak and the total efficiencies: ε peak r = ε Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter tot 4: General Properties of Radiation Detectors 47 Peak to ratio The peak to ratio efficiency is soeties tabulated separately. But it is often better to use the peak efficiency because the nuber of full energy events is not sensitive to perturbing effects such as scattering fro surrounding objects or spurious noise. Therefore, the peak efficiencies are copiled and tabulated and applied to a wide variety of laboratory conditions. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 48 VII. Dead Tie What is the "Dead Tie"? There will always be a iniu aount of tie that ust separate two events in order that they be recorded as two separate pulses. This liiting tie called the dead tie of the counting syste ay be due to one of the following reasons (or both): Processes in the detector itself and/or Associated Electronics used for pulse processing and recording. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 50
A. Models for Dead Tie Behavior There are two coon odels: Paralyzable response Nonparalyzable response http://www.youtube.co/watch?v=yeh0ux-88fs Definitions A detector is said to be paralyzable if it is affected by the radiation even if the signal is not processed. This could happen if the detector or its electronics are slow. Here pulses that arrive while the first pulse is being processed further delay the recovery of the counting syste. The detector is nonparalyzable if it has a fixed dead tie. Here the pulses arriving while the first pulse is being processed are siply ignored. These odels represent idealized behavior, one or the other of which often adequately resebles the response of a real counting syste. Fig. 7 illustrates the fundaental assuptions of these odels. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 5 Exaple Extree Cases Figure 7 Six randoly spaced events in tie in the detector A paralyzable detector would record 3 events. A nonparalyzable one would records 4 events. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 53 Real Case A fixed tie τ is assued to follow each true event that occurs during the "live period" of the detector. The true events that occur during the dead period are lost and assued to have no effect whatsoever on the behavior of the detector. In the exaple shown, the nonparalyzable detector would record four of the six events. In the case of the paralyzable detector, assuing the sae τ, true events although not recorded by the detector extend the dead tie by another period τ following the lost event! Here only three events out of the true six ones are recorded. This is an idealized case and the two odels predict the sae first-order losses and differ only when true events rates are high. A practical case would be soething between these two extrees! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 54 3
Dead Tie Nonparalyzable Model Let's consider a steady-state source of radiation. Let n = true interaction rate = recorded count rate τ = syste dead tie We need to know the dead tie in order to ake appropriate corrections to easured data in order to have the true interaction rate (n)! In the nonparalyzable case (fixed τ) the fraction of all tie that the detector is dead is given siply by the product τ. The total loss rate is here nτ The rate previous of losses relation also is equals used n to calculate thus we n, have: knowing τ and easuring. We n have = n τ n = Nonparalyzable odel (8) τ Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 55 Dead Tie Paralyzable Model In the paralyzable case, as we said earlier, dead periods are not always of fixed length. The rate is identical to the rate of occurrences of tie intervals between true events which exceed τ. The distribution of intervals between rando events occurring at an average rate n is given by: nt ( T ) dt = ne dt P (9) where P (T)dT is the probability of observing an interval whose length lies within dt about T. The probability of intervals larger than τ can be obtained by integrating this distribution between τ and, i.e. nt nτ P( > τ) = P ( τ) = ne dt = e (0) τ Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 56 Dead Tie Paralyzable Model The rate of occurrences of such intervals (tie intervals between true events which exceed τ) is thus: nτ = ne Paralyzable odel () Here we cannot solve explicitly for n. The solution is nuerical (iteration) P nt ( T ) dt = n e dt () Fig. 8 shows the observed rate vs. the true rate n for both odels. For low rates, the two odes give virtually the sae result. For high rates it is another story! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 57 The High Rate Case High rates Low rates Figure 8 We seek values of which approach the line =n Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 58 4
B. Methods of Dead Tie Measureent Technique! More often the dead tie will not be known or ay vary with operating conditions and ust therefore be easured directly. The technique is to assue that one of the two odes is applicable and easure two different true rates which differ by a known ratio. In the two-source ethod, the rate fro the two sources separately is easured (values n and n ) and a third easureent with the two sources cobined is achieved (n ). Due to the fact that energy losses are not linear, the third easureent, n, is saller the su n +n. The discrepancy is used to copute the dead tie. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 60 The Two-Source Method Let n, n and n be the true counting rates (saple plus background) with sources, and and cobined respectively. Let the corresponding easured rates be, and. Also let n b and b be the true and easured background rates with both sources reoved. Then we have: n nb = ( n nb ) + ( n nb ) n + nb = n + n (3) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 6 Nonparalyzable Model Assuing the nonparalyzable odel, we have: b + = + (4) τ b τ τ τ Solving this equation explicitly for τ we get: ( ) X Z τ = where Y X = b ( + b ) b ( b ) ( + ) Y + = Y Z = X Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 6 b (5) 5
No Background approxiation In the case where b 0, we have: X =, Y = + Z = ( ) and τ = ( ) [ ( )( )] = ( + ) (6) Approxiations Siplifications of Eq. 5 are based on any approxiations. One should be aware that these approxiations could introduce significant errors. See Geiger-Muller Experient for details on how to proceed. The Short-lived isotope case: See Knoll for the decaying source ethod for the calculations in the case of a short-lived isotope (pages 3-4) Study Fig. 4.9 carefully. Nonparalyzable ode: λ e t = n τ + Paralyzable ode: 0 n 0 λ t + λ t + ln = n0 τ e ln n 0 (7-a) (7-)b Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 63 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 64 C. Statistics of Dead Tie Loses D. Dead Tie Loses fro Pulsed Sources Self Reading (pages 4-5) 6
Pulsed Sources Until now we have assued steady state sources. In soe situations non steady state sources of radiation are encountered. For exaple: - Electron linear accelerator used to generate high-energy X-rays can be operated to produce a few icrosecond width with a repetition frequency of several kilohertz. The analysis for dead tie loses effects is different here fro the one we detailed in the previous sections. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 67 Analysis The sketch below shows a source of pulsed source We assue that the radiation intensity is constant throughout the duration T of each pulse and that the pulses occur at a constant frequency /f. Note that the tie between two consecutive pulses is /f. Depending on the relative value of the detector dead tie τ, several conditions ay apply: Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 68 τ vs. T If τ is uch saller than T, the fact that the source is pulsed has little or negligible effect and this case becoes alost siilar to the case of steady state sources If τ is less than T but not by a large factor, only a sall nuber of counts ay be registered by the detector during a single pulse. This is a coplicated situation which we will not treat here in this course. If τ is larger than T but less than the "off" tie between pulses (T /f), the following analysis is applied Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 69 Counts In the following we do not need to ipose that the radiation be constant over the pulse length T but we require that each radiation pulse be of the sae intensity. Using the sae sybols in the steady state analysis, the probability of an observed count per second pulse is given by /f. The average nuber of true events per (source) pulse is by definition equal to n/f. Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 70 7
τ > T The statistics here is of Poissonian type and the probability that at least one true event occurs per source pulse is given by: P ( > 0) = P( 0) n f = e x = e (8) Since the detector is live at the start of each pulse, a count will be recorded if at least one true event occurs during the pulse. Only one such count can be recorded, so the above expression is also the probability of recording a count per source pulse, i.e. n f = e n f Or = f ( e ) (9) f Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 7 τ > T We plot here this behavior. We see that that the axiu observable counting rate is just the pulse repetition frequency No dependence on the length of the dead tie or the detailed dead tie behavior of the syste (paralyzable or not) Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 7 Correction Forula As usual we are interested in predicting the true rate (n) Solving Eq. 9 for n we get: n = f ln f This condition is valid only under the conditions T < τ < (/f T). In this case, the dead tie loses are sall under the condition << f. At this liit we have: n f 0 f (30) (3) Effective Dead Tie Using the siilarity with eq. 8, the previous relation can be viewed as predicting an effective dead tie value of ½ f in this lowloss liit Last reark: Since the value is now one half the source pulsing period, it can be any ties larger than the actual physical dead tie of the detection syste! Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 73 Dr. Nidal M. Ershaidat - Nuclear Techniques - Chapter 4: General Properties of Radiation Detectors 74 8
Next Lecture Chapter 5 Gas-Filled Detectors Dr. Nidal M. Ershaidat 9