- Email: [email protected]
Pulse shape discrimination
NUCLEAR INSTRUMENTS
AND M E T H O D S 14 (1961) 24--32; N O R T H - H O L L A N D P U B L I S H I N G
CO.
PULSE SHAPE DISCRIMINATION L. VARGA Central Research Institute/or Physics, Budapest?
Received 27 May 1961 Pulse shape discrimination methods used up to the present are discussed, considering in particular to what extent the possibilities offered by the shape of the scintillation decay are being exploited. A new method is then described which utilizes in a statistically optimum way and by simplest means the informa-
tion obtainable from the various pulse shapes. The application of this method to the discrimination between proton and deuteron scintillation response of CsI(T1) crystals is described. Finally, some special cases in which the separation can be improved still further are considered.
1. Introduction
i n o r g a n i c s c i n t i l l a t o r s : for t h e l a t t e r it is t h e particle of h i g h e r m e a n i o n i z a t i o n d e n s i t y w h i c h i n d u c e s s c i n t i l l a t i o n s w i t h a lower i o n i z a t i o n density2,6). A f u r t h e r difference b e t w e e n o r g a n i c a n d i n o r g a n i c p h o s p h o r s is t h a t for t h e l a t t e r t h e m e a n life of t h e f a s t c o m p o n e n t v a r i e s w i t h t b e i o n i z a t i o n d e n s i t y of t h e e x c i t i n g p a r t i c l e t h o u g h t h i s h a s so f a r b e e n verified s a t i s f a c t o r i l y for CsI (T1) o n l y . S u m m a r i z i n g we m a y s t a t e t h e following : if a p a r t i c l e of a v e r a g e i o n i z a t i o n d e n s i t y pi is a b s o r b e d b y a s c i n t i l l a t o r , in t h e r e s u l t i n g s c i n t i l l a t i o n t h e n u m b e r of p h o t o n s e m i t t e d in t h e t i m e i n t e r v a l A t will be N l ( t ) A t = [a(pi) e-t/~(~j) + b(pi) e-tla] At . (1)
I t is k n o w n t h a t a n u m b e r of s c i n t i l l a t o r s r e s p o n d to t h e a b s o r p t i o n of p a r t i c l e s w h i c h differ in m a s s or in c h a r g e b y t h e e m i s s i o n of l i g h t p u l s e s of v a r i o u s d u r a t i o n s . T h i s s c i n t i l l a t i o n c a n u s u a l l y be des c r i b e d as t h e s u m of t w o e x p o n e n t i a l s in w h i c h t h e t i m e c o n s t a n t s differ b y o n e o r d e r of m a g n i t u d e . A l t h o u g h m o r e c o m p o n e n t s m a y be i n v o l v e d , t h e i r c o n t r i b u t i o n to t h e t o t a l n u m b e r of p h o t o n s is less t h a n a few p e r c e n t l ) . T h e i n t e n s i t y r a t i o of t h e t w o e s s e n t i a l c o m p o n e n t s d e p e n d s on t h e m a s s a n d c h a r g e of t h e p a r t i c l e a b s o r b e d b y t h e p h o s p h o r in q u e s t i o n . In t h i s r e s p e c t o r g a n i c a n d i n o r g a n i c d e t e c t o r s b e h a v e differently. It h a s b e e n s h o w n b y tile e x p e r i m e n t s of Owen2, 3) t h a t in o r g a n i c p h o s p h o r s t h e slow c o m p o n e n t of t h e s c i n t i l l a t i o n e x c i t e d b y p r o t o n s is twice as i n t e n s e as t h a t d u e to electrons. T h e d e c a y c o n s t a n t s of t h e f a s t a n d slow c o m p o n e n t s of o r g a n i c p h o s p h o r s are i n d e p e n d e n t of t h e m a s s or c h a r g e of t h e e x c i t i n g particle2,3, 4) w i t h i n t h e e x p e r i m e n t a l error. T h i s o p i n i o n is n o t s h a r e d b y WrightS), his r e s u l t s , h o w e v e r , m u s t h a v e b e e n affected b y h i s n e g l e c t i n g t h e p r e s e n c e of t h e slow c o m p o n e n t . T h e case is u s u a l l y r e v e r s e d for ]) F. 13. Harrison, Nucleonics 12 (1954) 24. 2) R. B. Owen, Nucleonics 17 (1959) 92. a) R. I~. Owen, Proceedings of International Symposium on Nuclear Flectronics, Paris, 1958. Published by International Atomic Energy Agency, Vienna. *) H. Kallman and G. J. Brucker, Phys. Rev. 108 (1957) 1122. '5) G. T. \Vright, Prec. Phys. See. la;69 (1956) 358. ~) R. S. Store3, W. Jack and A. "Ward, Prec. Phys. Soc. B72 (I 959) 523,
If t h e p h o s p h o r is o r g a n i c , a a n d / 3 a r e c o n s t a n t s i n d e p e n d e n t of pi', a n d b y n o r m a l i z i n g to Ni(t = 0) = N~(t -- 0) . . . . . .
Y~(t -- 0)
...
we h a v e b(pl) < b(p2) < . . . < b ( ~ ) < . . .
when P-l b(p-2) > . . . > b(p?) ~> . . . if I n p u l s e s h a p e d i s c r i m i n a t i o n we a r e u s u a l l y c o n f r o n t e d w i t h t h e p r o b l e m of i d e n t i f y i n g t h e * Some of the work reported here was carried out during the author's I.A.E.A.-sponsored stay at the CISE Laboratory, Milano, Italy.
24
PULSE
SHAPE
particle responsible for the scintillation from the time distribution of the No photons arriving at the photocathode per scintillation. By plotting the scintillation decay curves for two particles, normalized to 1 foo N(t) dt -Vo o
1,
producing the same total number of photons (fig. 1), it is easy to realise which data are available for the solution of the problem. As seen from the figure, for a scintillation producing in total No photons, the
II~l(tJ4t
~.~
t
F i g . 1. T y p i c a l d e c a y c u r v e s n o r m a l i z e d t o t h e s a m e a r e a i n t e r s e c t i n g e a c h u t h e r a t a t i m e r l , 2 . ~ t ' ~6~ a r e t h e m e a n i o n i z a t i o n densities, a and d denote the Common area, the areas b and c contain the information.
contribution up to a certain time Zl, 2 of the particle with ionization density PI is Nob more while after this time it is Noc less than that of the particle with ionization density ~ . It is this value No(b + c) in the number of photons which distinguishes the particle characterized by pl from the particle with p2 if they produce in total the same number of photons per scintillation. The ratios shown in fig. 1 hold for organic phosphors with the restriction that pl > p2. Essentially, the picture is acceptable for inorganic crystals too, except that pl < p2. The diagram is somewhat modified also by the dependence of the fast time constant on pl. 2. On t h e V a r i o u s D i s c r i m i n a t i o n Methods
Let us now consider to what extent the information obtainable from the pulse shape, as described
DISCRIMINATION
25
above, is made use of by the various methods of particle discrimination. Not too m a n y authors have tackled this problem, and every one of them has used a different approach. The highly interesting space charge method of Owen2, 3) consists in the use of a plate dynode potential in the multiplier which suppresses in organic phosphors the slow component of the scintillation response to y-particles by means of the space charge due to the high intensity current pulse of the fast component. For protons, on the other hand, the relatively weaker fast component cannot assert itself against the more intensive slow component. The procedure is very simple. It is, however, rather difficult to show by calculation to what extent the information is being exploited, nevertheless it is obvious that only a small part of the multiplier current corresponding to the number Noc of photons can be affected by the space charge of the current due to Nob (fig. 1). In addition, as tile author realized, the repeated space charge effects due to statistical fluctuation in the slow component are rather disturbing, particularly for low energy particles. In the same paper 2) Owen describes an alternative circuit by which the voltage pulse proportional to the total number of photons is compared to the pulse height of the plate current. This, however, makes the situation even worse than before, since the current pulse height being determined by a relatively small number of photons emitted in the vicinity of the peak, is subject to even higher statistical fluctuations. A circuit which, in respect to working principle and efficiency, is quite similar to Owen's latter design, was developed by Brooks 7) using a different approach. This author assumed the mean lives Tp resp. T 7 of the fast components in the scintillation responses of anthracene to protons and ~ particles to be different from each other. He had some reason to do this considering the esperiment of WrightS). Yet, even if the values obtained by Kallmann and Brucker, showing T 7 to be equal within the experimental error to T~, did not convince Brooks, Owen's experiment verified unambiguously that for organic phosphors T~ = Tp. Notwithstanding this apT) F. D. B r o o k s , N u c l . I n s t r . a n d M e t h . 4 (1959) 151.
26
L. VARGA
proach, the method of Brooks proved to be successful owing to the fact that the slow component (0.370/,sec) is already approximately integrated by the R d C ~ 1/,sec circuit of the dynode, while the R a C ~ 2 × 10-s sec plate circuit delivers a pulse proportional to the multiplier current. By comparing the two voltages, a pulse " h " was obtained which was proportional to the difference in current amplitude between proton and ~, induced scintillations containing the same number of photons (fig. 1). If the subtracting circuit is set in such a way that the positive pulse coming from the dynode extinguishes the negative current pulse delivered by an electron coming from the plate, we obtain the positive "h' ~for the proton pulse of lower amplitude. We should like to remark that although Brook's measurement does not verify his assumption that T p ~ Tr, this does not diminish the applicability of his method. A method was developed by Robertson and WardS) for discrimination in CsI(T1) crystals. Their work was based on the results of Storey et al. 6) who have shown the time constants of the fast components in the scintillation responses to ~ particles T~ and to electrons Tfl to be very different. The difference in the intensities of the slow components was not exploited by their method, although this would have improved the discrimination efficiency. Forte 9) too has assumed the existence of t h e relations illustrated in fig. 1. His procedure, however, needs some modifications. The use of a diode prior to the complete evaluation of the information constitutes rather a drawback. Owing to nonlinearity it responds differently to small and large pulses and, in addition, it starts at a rather undetermined level with the rectification of the pulses which in any case have rather low amplitudes. Furthermore, a considerable loss in amplitude is caused by the integrating circuit. The arrangement as described permits on!y a very low counting rate. It is to be regretted that the author has given-only a qualitative analysis of the discrimination efficiency of the method, since this does not show how
far the otherwise accurate underlying principle has been approached by the circuit arrangement. A common disadvantage of all above methods, perhaps with the exception of that used by Robertson and Ward, is their applying rather slow circuits which cannot work with as high counting rates as it would be inherently possible with scintil: lators. Therefore, it was thought useful to develop a new method which, in addition to fully exploiting all'information available for the identification of particles, makes it possible to work with the optimum counting rate. 3. T h e o r e t i c a l C o n s i d e r a t i o n s
Let us start by considering fig. 1. If the.scintillator is struck by one of the particles of type 1, 2 .... i... (with ionisation densities pl < p2 < ... < 5, < .-.) then a pulse similar in shape to the curves seen in fig. 1 will be obtained when normalizing again to the total number of photons produced by the scintillation. In the figure only the scintillation deca3~s of the responses to particles with ionization densities Pl and 52, respectively, are shown. Now we have to deal with the separation of the particles i from the particles denoted by i - - 1 and i + 1, respectively. First, we shall consider the problem of distinguishing between the scintillation response to particles i from that to particles i - - 1. The decay curves of the two particles intersect at the time r,-1,1 for scintillations producing an identical number of photons. The number of photoelectrons produced by the two scintillations at the photocathode is given by N o ' A , and N o ' A , - I before and by No" B, and N0"Bl-1 after the time z,-1., respectively. The difference in the number of photoelectrons before and after ri-l., is given for both particles by S~ = No(Af - - B , )
and S*-I
~ N0(A~-I - - B * - I ) ,
D~-l,t
=
NoEAt - - A t - 1 + Bill - - B t ] .
This leads by using the notations of fig. 1 to D;-1,, = No(b + c)
s) j. C. Robertson and A. Ward, Proc. Phys. Soc. B78 (1959) 523. ~) M. Forte, Nuovo Cimento: Suppl. Ser. 10, No. 2 (1958) 378.
(2)
the difference between these t w o quantities being
and S~ = N o ( a - - d + b) and
respectively,
S~-I = N o ( a - - d P c )
(3)
27
PULSE SHAPE DISCRIMINATION
T h a t is to say, that the values obtained for S~ and S~-I differ from each other by the q u a n t i t y D~-l,t which is precisely all the information available for discrimination. It is rather unfortunate that S~ and S~-I contain additively also the number of electrons No(a --d), so that due to the statistical fluctuation in the latter, the effect of the relatively small differences Nob and Noc m a y be blurred. Therefore, instead of using eqs. (2), it seems more convenient to substract the number of electrons arriving after the time v,-1.t multiplied by an arbitrary factor ' / f r o m the number of electrons arriving prior to this time. Then we have D~-I,~ ~ No[(A~ - - A ~ - I ) + ~ (B~-I--B~)] = No(b + tic) • (4)
This factor ' / h a s to be so chosen t h a t the relative error in the value D,-1.t = St - - S ~ - I is kept at a minimum. In calculating '/, we shall exploit the fact that the photoelectrons produced by the photons of the scintillation obey a Poisson distribution, thus AD(-1.~ = % / N 0 " % / ~ [ + A*-I + , f ' ( B , - - B ~ - 1 ) .
(5)
Furthermore, it follows from dAD~_I. ,/D,-1,,
Some calculations can be made as to the threshold energy for discrimination. If we accept Brooks 7) definition of the resolution for pulse shape discrimination, the lower limit is given by No as calculated form the expression AD~-I.
-
-
IsI
--
1.
(9)
F r o m this we obtain A, +A,_1(2 B, )~ N o = 2B, +Bt_l A,--A,_-~ + 1 .
(10)
When starting from Owen's2, 3) experimental data of unknown accuracy relating to antracen, the graphically determined values of A and B give No = 90 which corresponds to electron and proton energies of 90 keV and 350 keV, respectively. 4. Application of the Method Let us consider now the circuit in fig. 2. There is sufficiently high resistance in the anode of the multiplier to give together with the stray capacity a time constant permitting the integration of the ///////
0
d,7 that t]°Pt
A i + A,-1 B , - 1 - - B f B, + B,-I A, --At-1 "
i '4,
As a result of normalization Bt-1 - - Bt ~ c = b ---- A, - - At-l, hence nopt
A, + A,-1 Be + B~-I
(6)
This means that the relative error in the value of the difference between S, and S,-1 will be minimized by weighting the number of photoelectrons arriving after the time tt-l., with the ratio of the average number of photoelectrons produced by the scintillations of the two kinds of particles before and after this time. By doing so St =
No A tB~_l--A ~-xB~ No A ,-1B( - - A ~B~-I a n d S~-1 = (7) Be + B~-I B~ + B~-i
t h a t is S,-1 = - - S~.
(8)
Thus if we use the weighting factor ,/opt now obtained, the discriminating pulses S will be of opposite sign for the two kinds (denoted b y i and i - - 1) of particles.
m
~R.2o
Fig. 2. Diagram showing the discrimination arrangement. CF cathode follower.
charge induced by the scintillation and assumed to be amplified without distortion by the multiplier. Using a cathode follower, the multiplier is coupled to a shorted cable reflecting the pulses with a delay time T. T is equal to the duration of the scintillation, thus at point B after a time delay 2T reckoned from the start of the pulse we are again at zero level. It is obvious that the dead time is 2T. Up to now the pulse has been only shaped, the actual pulse shape discrimination is to follow. Essentially, this is done by means of a cable closed by a resistance R reflecting the pulses at the time Ti-l,i the cable being connected to the output B of the shaping cable through a cathode follower, as seen above. W h a t happens at point C ? The reflection occurring
28
L. VARGA
at the end of the cable of characteristic impedance Z0 and being closed by R, is R Z0 P: + R~ 0 " -
-
(11)
In fig. 3 we analyse the pulse of a particle with ionization density ~, as taken from the point C in fig. 2. The pulse shape from t = 0 up to the time z,-1., follows that of the integral of the charge collected by this time at the anode. At this point, however, a break occurs caused by the return of the r . t;._~a .
~-t,i A
'""
i
~
Bi
si.-p~-(,.p)~,.
~25 m'~,e,l
L;
Fig. 3. Time variation of the voltage appearing in point 13 (dotted line) and that appearing in point C (full line) of fig. 2.The line marked by small dots is the (1 + p)-fold of the dotted line.
initial pulse multiplied by p(p < 0 in the figure) from the shorted cable. The resultant pulse can be now considered as the superposition of two parts: the initial one multiplied by 1 + p and the same multiplied by - - p and shaped by the shorted cable with reflection time v,-1.,. Thus at the time ~'*-l,f the pulse is given by (1 + p)A~ plus --pA~. It is seen from the figure that S, = --A,p
--
(1 +
p)B,.
(12)
As observed previously, the optimum discrimination will be obtained if the condition S, = Ai - - ~optB~
is satisfied. From this we have #=
1 1 + ~opt
< o.
(13)
By comparing (13) with (11), it follows that R
~opt 20. 2 ,+ 7]opt
(14)
The size of the discriminating pulse S, is given by the difference between the maximum occurring at
the time rf-l.i and the integrated pulse built up during the time T. This difference is given for the time T,-1,, in the mirror image of the ascending part of our pulse. Such is the case if prior to the time v,-1., the particle producing a higher number of photoelectrons has been absorbed by the crystal. Now, if the crystal is struck by the other particle, we have Si-1 which owing to (8) does not become positive by the time T + ~-1,~, but remains negative because of S,-I = - - S~. Two such pulse shapes are seen in fig. 4. From (7) it is apparent that S, and S,-1 are proportional to No and thus to the energy and therefore the points S, and S~-1 lie along straight lines in the S-energy coordinate system, having identical absolute values but slopes of opposite sign, provided in the scintillation the ratio of fast to slow photons and the average lifetimes of the two components are independent of the energy. It is seen that in this simple way discriminatingpulses are obtained only for the particle responsible for the fast component of relatively higher intefisity, that is with the use of organic phosphors for particles with lower and with inorganic phosphors for those with the higher ionization density. If the crystal is struck by more than two kinds of particles, a further cable, Similar to the previous one, has to be coupled to the cathode follower. ri-,d
'
r r+~.~, [ ~
ec Fig. 4. Pulse shapes in point C of fig. 2 for two particles ot different ionization densities.
Since the cut-off time Tf-l., as well as the reflection coefficient have been chosen so as to obtain the optimum separation of two kinds of particles, the same circuit cannot discriminate between A, and A,+I as well. In order to separate the scintillation response of the particle with ionization density ~f from that characterized by P*+I, a cable with delay time r~.~+l and circuited by R~.t+l is required. These latter values are determined by the difference in pulse shape of the two particles in question. In the first stage positive discriminating pulses S are
PULSE
SHAPE
obtained for all incident particles (denoted by i, i + 1. . . . ) which produce integral curves of higher slope than that of the particles with ionization density PH, while in the second stage the pulses S will be negative but for particles denoted by i + 1, i + 2 . . . . . The anticoincidence of the pulses + S in the two circuits occursthus precisely for the absorption of the particle i in question. 5. Experiment on CsI(TI) Crystal The measurements of Storey, Jack and Ward~) give full information on the pulse shape of the scintillation of CsI(T1) crystals. The time constant of the fast component is shown by their measurement to be decreasing exponentiallywith increasing mean ionization density. Furthermore, it is possible to calculate from their measurement the ratio of ,the total number of slow to fast photons
f:slow dt / f : fast dt
(15)
as shown in fig. 5. From these two data the pulse shape of particles with any ionization density can be determined. Thus, for instance, the pulse shapes 9
~2
Lt f.O ~g
0.6 0,7 O.e
0.0 0.4 0.3 0 4
e,O.~l~V
/
8~61"leV2~.t4eV ¢.8t.fev
io
I t
~o
I
¢~oo
~ ~
Fig. 5. R a t i o of p h o t o n s belonging to t h e s l o w and fast comp o n e n t of scintillation corresponding to different m e a n ionization densities on t h e basis of the d a t e s given int).
of 2.2 MeV protons and of 2.26 MeV deuterons of identical scintillation responses, further those of
29
DISCRIMINATION
8.6 MeV protons and of their counterparts the 8.85 MeV deuterons, can be calculated as follows: Np,~.~(t)At = (1.33 e-t/o.5~ + 0.044 e-t/7.0) At, (16a) Nd,a.26(t)At = (1.48 e-t/o.48 + 0.041 e-t/7.o) At,
Np,s.e(t)At ~ (1.074e-rio.6 + 0.051 e-t/7.°) At, Nd,s.ss(t)At = (1.225 e-t/o.56 + 0.046 e-t/7.o) At.
(16b) (16c) (16d)
The response curves of the 2.2 MeV particles intersect at zdp = 0.66 #se'c. Now, the values A and B and the factor ~opt can be calculated from (16a) aq
T"
]"
_ _ ~
a2
scE~ :
i
,-~+-s-.~
i
11
i_
I
i
l
~ 6-7---~..<9 ,5-~l,'~v
1
Fig. 6. Discriminating pulses relating to proton and deuteron in dependence on t h e e n e r g y of t h e proton, T h e reflexion coefficient was chosen so as to obtain o p t i m u m discrimination b e t w e e n proton of 2.2 MeV e n e r g y and deuterons of t h e s a m e scintillation efficiency.
and (16b), which values in turn yield the discriminating pulses S~ = Sd.~.~6 and S~-1 = Sp,~.~ irrespective of their absolute values, since the total number No of the photoelectrons is irrelevant in this problem. The discriminating pulses for 8.6 MeV protons and those for deuterons corresponding from the point of view of scintillation efficiency to these protons can be determined from (16c) and (16d), though it has to be taken into account that Tdp and Rap have been chosen for the optimum discrimination of 2.2 MeV particles. The results of our calculations are shown in fig. 6. These two sets of points may be completed by our knowledge that Sp = Sd = 0 for E = 0. It is immediately apparent that Sd(E) ¢ k E ¢ Sp(E). This problem has been investigated experimentally and the result is shown in fig. 7. The pictures were taken by irradiating a deuterized paraffin layer with 14 MeV neutrons. The aluminium plate supporting the paraffin was mounted on 1.5mm thick CsI(T1) phosphor. particles were obtained from the Al(n, ~) reactions, deuterons, from the elastic scattering and protons from both the Al(n,p) and the D(n,p) reactions. Owing to the (n,7) radiation of the surroundings 7pulses too were obtained. The scintillations were
30
L. VARGA
detected by a Dumont 6292 photomultiplier. From the point C in fig. 2 the pulses were transmitted to the vertical amplifier of a Tektronix type 515A oscilloscope, while the pulses coming from the first cathode follower and delayed for/, > rdr~ were being
Fig. 7. Photograph of oscilloscope obtained for various particles incident simultaneously using the arrangement of fig. 2.
passed to the horizontal amplifier. The electron beam of the oscilloscope was opened at T q-rap and kept open for t ~ 50 re#see. The best photographs were obtained with T -- 3 ,usec and rap 0.5/~sec. The number of ~ particles is relatifely low. The upper limit of the 7 line is quite sharp, the lower limit, however, is blurred and broadened since only a small fraction of fast electron energy is lost to the crystal and such scintillation appear at lower energies. In consequence of the lower average ionization densities, the S is more negative than for electrons having the same photon yield but being completely absorbed by the scintillator. It is also apparent that the discriminating pulses for a and y-induced scintillation showing a great difference in fast component versus lifetime curves, lie, in terms of the energy, on an approximately straight line. The deuteron and proton lines are curved. Usually, however, a reflection coefficient differing from the optimum can be found for which the two curves rise above the energy axis, so that above a given energy and as compared to a certain U > 0 discrimination level, we have I Sp I < U < 15"a I" The energy scale was calculated for the maximum deuteron energy possible upon bombardment with 14 gleV neutrons. Proton-deuteron discrimination seems to be feasible above ~ 3 MeV. Their separation from the y, p, ~ background can be achieved
with the aid of the arrangement shown in fig. 8. The second cathode follower is coupled to two cables of delay time ra and rap and closed by impedances Rap and Ra~. The input of these cables is connected to the discriminator. The necessity for this arrangement has been already discussed in connection with the d - p discrimination, yet it is not superfluous for the ~-d channel either, since, thougt the discriminator of the d p channel delivers pulse for each discriminating S above the preset level, thus for S~ too, no signals are obtained for c~ particles having lower 5" than the discrimination level set for the d - p channel. It follows from the above that by discriminating subsequently in the c~-(l channel at 0 volt, anticoincidences would be brought about by pulses which, though produced by e particles, could be identified as deuterons since their S appears between 0 and Udp. Considering that, usually, the energies of the discriminated particles have also to be measured, it is useful to wait for the scintillation to die out. Sometimes, however, a higher counting rate is required, even at the expense of analysis and separation. In this case the time T has to be reduced which necessitates some modification also for. If we have to Ra~ Y /11///
Fig. 8. Block diagram of circuit selecting one type of particles fronl among the different components of the background.
work extremely fast, the arrangement shown in fig. 9 m a y be convenient, although only scintillations of very short duration would then give positive discriminating pulses, if the reflecting resistance R is suitably chosen and Ra Z0. The length of the cable is determined by the requirement that the reflected wave should return at a
POLSE
SHAPE
time a b o u t the m a t h e m a t i c a l m e a n value of the decay c o n t a n t s of t h e fast c o m p o n e n t s of t h e particles to be discriminated. F o r ~ discrimination in Cs(T1) it is a b o u t ~ 0.56/~sec. //////
2
&~
.Zo
Fig. 9. Simple circuit for f a s t d i s c r i m i n a t i o n .
6. R e d u c t i o n o f the Threshold E n e r g i e s for Discrimination
I n special cases when the i n c i d e n t b e a m of particles is well collimated, the m e t h o d can be imp r o v e d b y s u i t a b l y combining t h e i n f o r m a t i o n s obt a i n e d from t h e m e a s u r e m e n t of d E / d x with the shape discrimination. I t is obvious t h a t , similar to the discriminating pulses S being meaningless without t h e m e a s u r e m e n t of the energy (total n u m b e r of photons), the particle will be d e t e r m i n e d b y d E / d x only if we know the energy of t h e particle which l o s e s - - t o a foil of given t h i c k n e s s - t h e a m o u n t of energy p a x (o = dE/dx). Now, since in the course of shape discrimination the particle energy h a s alr e a d y been determined, we h a v e only to combine the knowledge of these three e x p e r i m e n t a l values. Let us use a scintillator foil for t h e m e a s u r e m e n t of P. A particle of energy E0 loses the fraction d E = p a x of its energy. Eo - - d E be absorbed b y t h e analysing crystal. The n u m b e r of photoelectrons produced in the foil per scintillation be n. This c u r r e n t be amplified b y a factor k in a multiplier a n d possibly w i t h the help of o t h e r electronical devices. The o t h e r scintillator deliver N photoelectrons proportional in n u m b e r to the energy Eo - - d E a n d this be multiplied b y k'. In accordance with the previous d e n o t a t i o n for the arrival of the particle denoted b y i, we o b t a i n a q u a n t i t y k,ni + k ' N v W h a t is the difference in the composition of these two equal q u a n t i t i e s kni-1 + k'Ni-1 = knl + k'N~ o b t a i n e d for particles i a n d i - 1, respectively ? If pi > Pi-1 it follows t h a t ui > u,-1 a n d b y choosing a suitable inorganic measuring crystal we h a v e Si > Sl-1 as well. Let us choose a foil the scintillation decay of
DISCRIMINATION
31
which is m u c h faster t h a n t h a t of the measuring crystal. I t should be fast enough to p e r m i t the scintillation to die out completely prior to the time characteristic for the analyzer. This r e q u i r e m e n t is fully m e t b y coupling an organic scintillator foil with an inorganic m e a s u r i n g crystal. I n this case the sign of Ai - - A,:-I will be the same as t h a t of n, - - h i - 1 . This m e a n s t h a t virtually only the inf o r m a t i o n "b" in fig. I increases in accordance with ni n i l . I t h a s to be kept in m i n d t h a t owing to the change in n o r m a l i z a t i o n Z*-l,l needs some correction which will induce some change in *jopt as well. W e calculate now in the same way as above t~*
k
ni + ni 1
N~A* + N~->'~*I
k" N~B~ + NI-1B~-I + NiB**. + N~-IB~_I
. (17)
The t e r m s with asterisk correspond to those, used in the previous t r e a t m e n t , t h o u g h differing from t h e m as regards their normalization a n d in consequence of the new Ti-l.t. T h e second t e r m of the expression for ~* is incidentally the perfect analogue of ~opt. F u r t h e r , it can be readily shown t h a t S*= (kn, + k'N,A~)N,_IB,_I - - (knt 1 + k'N, 1A*-I)NIB* N~B* + Ni-IB*-I = > S~--I.
(|8)
Assuming in a rough a p p r o x i m a t i o n the q u a n tities A a n d / 3 to be i n d e p e n d e n t of energy, a n d N to be proportional to E, while u to l/E, it becomes a p p a r e n t t h a t S*(E) is the superposition of a h y p e r b o l a a n d a s t r a i g h t line. The weight factors of the superposition can be influenced b o t h b y the foil thickness d x a n d the multiplying factors k and k'. The k (amplification of the channel p) however, energy loss d E in order to d e t e r m i n e the spectra more accurately, it is obvious t h a t the o p t i m u m setting is k -- k'. I t is to be n o t e d t h a t even J E c a n n o t be arbitrarily small. In the calculation of ~?* the L a n d a u effect has not been t a k e n into account: this m e a n s t h a t .lIE m u s t be higher b v an order of m a g n i t u d e t h a n the m a x i m u m energy which can l)e transferred from the particle detected to an electron of the foil. If this condition is not satisfied, the I.andau effect has to be calculated too.
32
L. V A R G A
7. Telescope The above considerations can be applied without any alteration to the so-called telescopes. The previously used proportional counter-crystal detector combination is now being replaced at an ever increasing rate by scintillator foil-crystal analyser arrangement. It is to be noted that the above results will hold only if the detectors conform to the above requirements. By adding the integrated pulses of the two multipliers and transmitting this sum pulse to the shape discriminator, we obtain with corrections z -+ r* and r/opt ~ ~* the results of the preceding paragraph.
8. Shape Discrimination with Sandwich-detectors Similarly, the above considerations are readily applicable to the plastic phosphor-inorganic crystal sandwich arrangement. This combination has been
0
Fig. 10. \Vhen combining the measurement of dl'J/dx w i t h pulse shape di~crinlination, tile ptlls(?s for x particles call be separated from those of ~*l a v s even at low energies.
experimentally tested by the author. A plastic foil of about 1 mg/'cm 2 was mounted on a CsI(T1) crystal plate and irradiated with the a rays of a Po 210 source. The c~radiation released the electrons in the CsI crystal so that they were not affected by
the foil, the discriminating straight line S*(E), however, rose above its previous level as it is seen in fig. 10. In this case the condition k = k' is automatically satisfied, since both scintillations are counted by the same multiplier, thus the circuit shown in fig. 2 m a y be kept unaltered but for and R. Something has to be said also on the part played by the multipliers. Actually, no fast multipliers are needed for the integration, nevertheless it is desirable that the multiplier should sufficiently well respond to any variation in the emission of the light pulses since it is the rise time of the integrated pulse which is exploited for discrimination. This means that only a minimum fraction of the charge collected prior to time z should be permitted to pass into the subsequent time interval because of the distortion caused by the multiplier. This problem does not arise with "slow" scintillators, such as CsI, NaI etc. For faster organic phosphors, however, the choice of the multiplier becomes of considerable importance. If the distortion due to the multiplier becomes appreciable, the optimum conditions for discrimination had better be determined from the time distribution of the charge collected on the anode than from the parameters of the scintillation decay. This does not involve additional work, since our present knowledge of the scintillation mechanism still requires the experimental correction of the predicted data.
Acknowledgement I take this opportunity to express again m y thanks to the International Atomic Energy Agency for sponsoring m y study abroad. Thanks are due to the Nuclear Physics Department of the C.I.S.E., in particular, to Prof. U. Facchini for continued interest in my work as well as to Prof. E. Gatti for helpful discussions.
AND M E T H O D S 14 (1961) 24--32; N O R T H - H O L L A N D P U B L I S H I N G
CO.
PULSE SHAPE DISCRIMINATION L. VARGA Central Research Institute/or Physics, Budapest?
Received 27 May 1961 Pulse shape discrimination methods used up to the present are discussed, considering in particular to what extent the possibilities offered by the shape of the scintillation decay are being exploited. A new method is then described which utilizes in a statistically optimum way and by simplest means the informa-
tion obtainable from the various pulse shapes. The application of this method to the discrimination between proton and deuteron scintillation response of CsI(T1) crystals is described. Finally, some special cases in which the separation can be improved still further are considered.
1. Introduction
i n o r g a n i c s c i n t i l l a t o r s : for t h e l a t t e r it is t h e particle of h i g h e r m e a n i o n i z a t i o n d e n s i t y w h i c h i n d u c e s s c i n t i l l a t i o n s w i t h a lower i o n i z a t i o n density2,6). A f u r t h e r difference b e t w e e n o r g a n i c a n d i n o r g a n i c p h o s p h o r s is t h a t for t h e l a t t e r t h e m e a n life of t h e f a s t c o m p o n e n t v a r i e s w i t h t b e i o n i z a t i o n d e n s i t y of t h e e x c i t i n g p a r t i c l e t h o u g h t h i s h a s so f a r b e e n verified s a t i s f a c t o r i l y for CsI (T1) o n l y . S u m m a r i z i n g we m a y s t a t e t h e following : if a p a r t i c l e of a v e r a g e i o n i z a t i o n d e n s i t y pi is a b s o r b e d b y a s c i n t i l l a t o r , in t h e r e s u l t i n g s c i n t i l l a t i o n t h e n u m b e r of p h o t o n s e m i t t e d in t h e t i m e i n t e r v a l A t will be N l ( t ) A t = [a(pi) e-t/~(~j) + b(pi) e-tla] At . (1)
I t is k n o w n t h a t a n u m b e r of s c i n t i l l a t o r s r e s p o n d to t h e a b s o r p t i o n of p a r t i c l e s w h i c h differ in m a s s or in c h a r g e b y t h e e m i s s i o n of l i g h t p u l s e s of v a r i o u s d u r a t i o n s . T h i s s c i n t i l l a t i o n c a n u s u a l l y be des c r i b e d as t h e s u m of t w o e x p o n e n t i a l s in w h i c h t h e t i m e c o n s t a n t s differ b y o n e o r d e r of m a g n i t u d e . A l t h o u g h m o r e c o m p o n e n t s m a y be i n v o l v e d , t h e i r c o n t r i b u t i o n to t h e t o t a l n u m b e r of p h o t o n s is less t h a n a few p e r c e n t l ) . T h e i n t e n s i t y r a t i o of t h e t w o e s s e n t i a l c o m p o n e n t s d e p e n d s on t h e m a s s a n d c h a r g e of t h e p a r t i c l e a b s o r b e d b y t h e p h o s p h o r in q u e s t i o n . In t h i s r e s p e c t o r g a n i c a n d i n o r g a n i c d e t e c t o r s b e h a v e differently. It h a s b e e n s h o w n b y tile e x p e r i m e n t s of Owen2, 3) t h a t in o r g a n i c p h o s p h o r s t h e slow c o m p o n e n t of t h e s c i n t i l l a t i o n e x c i t e d b y p r o t o n s is twice as i n t e n s e as t h a t d u e to electrons. T h e d e c a y c o n s t a n t s of t h e f a s t a n d slow c o m p o n e n t s of o r g a n i c p h o s p h o r s are i n d e p e n d e n t of t h e m a s s or c h a r g e of t h e e x c i t i n g particle2,3, 4) w i t h i n t h e e x p e r i m e n t a l error. T h i s o p i n i o n is n o t s h a r e d b y WrightS), his r e s u l t s , h o w e v e r , m u s t h a v e b e e n affected b y h i s n e g l e c t i n g t h e p r e s e n c e of t h e slow c o m p o n e n t . T h e case is u s u a l l y r e v e r s e d for ]) F. 13. Harrison, Nucleonics 12 (1954) 24. 2) R. B. Owen, Nucleonics 17 (1959) 92. a) R. I~. Owen, Proceedings of International Symposium on Nuclear Flectronics, Paris, 1958. Published by International Atomic Energy Agency, Vienna. *) H. Kallman and G. J. Brucker, Phys. Rev. 108 (1957) 1122. '5) G. T. \Vright, Prec. Phys. See. la;69 (1956) 358. ~) R. S. Store3, W. Jack and A. "Ward, Prec. Phys. Soc. B72 (I 959) 523,
If t h e p h o s p h o r is o r g a n i c , a a n d / 3 a r e c o n s t a n t s i n d e p e n d e n t of pi', a n d b y n o r m a l i z i n g to Ni(t = 0) = N~(t -- 0) . . . . . .
Y~(t -- 0)
...
we h a v e b(pl) < b(p2) < . . . < b ( ~ ) < . . .
when P-l
24
PULSE
SHAPE
particle responsible for the scintillation from the time distribution of the No photons arriving at the photocathode per scintillation. By plotting the scintillation decay curves for two particles, normalized to 1 foo N(t) dt -Vo o
1,
producing the same total number of photons (fig. 1), it is easy to realise which data are available for the solution of the problem. As seen from the figure, for a scintillation producing in total No photons, the
II~l(tJ4t
~.~
t
F i g . 1. T y p i c a l d e c a y c u r v e s n o r m a l i z e d t o t h e s a m e a r e a i n t e r s e c t i n g e a c h u t h e r a t a t i m e r l , 2 . ~ t ' ~6~ a r e t h e m e a n i o n i z a t i o n densities, a and d denote the Common area, the areas b and c contain the information.
contribution up to a certain time Zl, 2 of the particle with ionization density PI is Nob more while after this time it is Noc less than that of the particle with ionization density ~ . It is this value No(b + c) in the number of photons which distinguishes the particle characterized by pl from the particle with p2 if they produce in total the same number of photons per scintillation. The ratios shown in fig. 1 hold for organic phosphors with the restriction that pl > p2. Essentially, the picture is acceptable for inorganic crystals too, except that pl < p2. The diagram is somewhat modified also by the dependence of the fast time constant on pl. 2. On t h e V a r i o u s D i s c r i m i n a t i o n Methods
Let us now consider to what extent the information obtainable from the pulse shape, as described
DISCRIMINATION
25
above, is made use of by the various methods of particle discrimination. Not too m a n y authors have tackled this problem, and every one of them has used a different approach. The highly interesting space charge method of Owen2, 3) consists in the use of a plate dynode potential in the multiplier which suppresses in organic phosphors the slow component of the scintillation response to y-particles by means of the space charge due to the high intensity current pulse of the fast component. For protons, on the other hand, the relatively weaker fast component cannot assert itself against the more intensive slow component. The procedure is very simple. It is, however, rather difficult to show by calculation to what extent the information is being exploited, nevertheless it is obvious that only a small part of the multiplier current corresponding to the number Noc of photons can be affected by the space charge of the current due to Nob (fig. 1). In addition, as tile author realized, the repeated space charge effects due to statistical fluctuation in the slow component are rather disturbing, particularly for low energy particles. In the same paper 2) Owen describes an alternative circuit by which the voltage pulse proportional to the total number of photons is compared to the pulse height of the plate current. This, however, makes the situation even worse than before, since the current pulse height being determined by a relatively small number of photons emitted in the vicinity of the peak, is subject to even higher statistical fluctuations. A circuit which, in respect to working principle and efficiency, is quite similar to Owen's latter design, was developed by Brooks 7) using a different approach. This author assumed the mean lives Tp resp. T 7 of the fast components in the scintillation responses of anthracene to protons and ~ particles to be different from each other. He had some reason to do this considering the esperiment of WrightS). Yet, even if the values obtained by Kallmann and Brucker, showing T 7 to be equal within the experimental error to T~, did not convince Brooks, Owen's experiment verified unambiguously that for organic phosphors T~ = Tp. Notwithstanding this apT) F. D. B r o o k s , N u c l . I n s t r . a n d M e t h . 4 (1959) 151.
26
L. VARGA
proach, the method of Brooks proved to be successful owing to the fact that the slow component (0.370/,sec) is already approximately integrated by the R d C ~ 1/,sec circuit of the dynode, while the R a C ~ 2 × 10-s sec plate circuit delivers a pulse proportional to the multiplier current. By comparing the two voltages, a pulse " h " was obtained which was proportional to the difference in current amplitude between proton and ~, induced scintillations containing the same number of photons (fig. 1). If the subtracting circuit is set in such a way that the positive pulse coming from the dynode extinguishes the negative current pulse delivered by an electron coming from the plate, we obtain the positive "h' ~for the proton pulse of lower amplitude. We should like to remark that although Brook's measurement does not verify his assumption that T p ~ Tr, this does not diminish the applicability of his method. A method was developed by Robertson and WardS) for discrimination in CsI(T1) crystals. Their work was based on the results of Storey et al. 6) who have shown the time constants of the fast components in the scintillation responses to ~ particles T~ and to electrons Tfl to be very different. The difference in the intensities of the slow components was not exploited by their method, although this would have improved the discrimination efficiency. Forte 9) too has assumed the existence of t h e relations illustrated in fig. 1. His procedure, however, needs some modifications. The use of a diode prior to the complete evaluation of the information constitutes rather a drawback. Owing to nonlinearity it responds differently to small and large pulses and, in addition, it starts at a rather undetermined level with the rectification of the pulses which in any case have rather low amplitudes. Furthermore, a considerable loss in amplitude is caused by the integrating circuit. The arrangement as described permits on!y a very low counting rate. It is to be regretted that the author has given-only a qualitative analysis of the discrimination efficiency of the method, since this does not show how
far the otherwise accurate underlying principle has been approached by the circuit arrangement. A common disadvantage of all above methods, perhaps with the exception of that used by Robertson and Ward, is their applying rather slow circuits which cannot work with as high counting rates as it would be inherently possible with scintil: lators. Therefore, it was thought useful to develop a new method which, in addition to fully exploiting all'information available for the identification of particles, makes it possible to work with the optimum counting rate. 3. T h e o r e t i c a l C o n s i d e r a t i o n s
Let us start by considering fig. 1. If the.scintillator is struck by one of the particles of type 1, 2 .... i... (with ionisation densities pl < p2 < ... < 5, < .-.) then a pulse similar in shape to the curves seen in fig. 1 will be obtained when normalizing again to the total number of photons produced by the scintillation. In the figure only the scintillation deca3~s of the responses to particles with ionization densities Pl and 52, respectively, are shown. Now we have to deal with the separation of the particles i from the particles denoted by i - - 1 and i + 1, respectively. First, we shall consider the problem of distinguishing between the scintillation response to particles i from that to particles i - - 1. The decay curves of the two particles intersect at the time r,-1,1 for scintillations producing an identical number of photons. The number of photoelectrons produced by the two scintillations at the photocathode is given by N o ' A , and N o ' A , - I before and by No" B, and N0"Bl-1 after the time z,-1., respectively. The difference in the number of photoelectrons before and after ri-l., is given for both particles by S~ = No(Af - - B , )
and S*-I
~ N0(A~-I - - B * - I ) ,
D~-l,t
=
NoEAt - - A t - 1 + Bill - - B t ] .
This leads by using the notations of fig. 1 to D;-1,, = No(b + c)
s) j. C. Robertson and A. Ward, Proc. Phys. Soc. B78 (1959) 523. ~) M. Forte, Nuovo Cimento: Suppl. Ser. 10, No. 2 (1958) 378.
(2)
the difference between these t w o quantities being
and S~ = N o ( a - - d + b) and
respectively,
S~-I = N o ( a - - d P c )
(3)
27
PULSE SHAPE DISCRIMINATION
T h a t is to say, that the values obtained for S~ and S~-I differ from each other by the q u a n t i t y D~-l,t which is precisely all the information available for discrimination. It is rather unfortunate that S~ and S~-I contain additively also the number of electrons No(a --d), so that due to the statistical fluctuation in the latter, the effect of the relatively small differences Nob and Noc m a y be blurred. Therefore, instead of using eqs. (2), it seems more convenient to substract the number of electrons arriving after the time v,-1.t multiplied by an arbitrary factor ' / f r o m the number of electrons arriving prior to this time. Then we have D~-I,~ ~ No[(A~ - - A ~ - I ) + ~ (B~-I--B~)] = No(b + tic) • (4)
This factor ' / h a s to be so chosen t h a t the relative error in the value D,-1.t = St - - S ~ - I is kept at a minimum. In calculating '/, we shall exploit the fact that the photoelectrons produced by the photons of the scintillation obey a Poisson distribution, thus AD(-1.~ = % / N 0 " % / ~ [ + A*-I + , f ' ( B , - - B ~ - 1 ) .
(5)
Furthermore, it follows from dAD~_I. ,/D,-1,,
Some calculations can be made as to the threshold energy for discrimination. If we accept Brooks 7) definition of the resolution for pulse shape discrimination, the lower limit is given by No as calculated form the expression AD~-I.
-
-
IsI
--
1.
(9)
F r o m this we obtain A, +A,_1(2 B, )~ N o = 2B, +Bt_l A,--A,_-~ + 1 .
(10)
When starting from Owen's2, 3) experimental data of unknown accuracy relating to antracen, the graphically determined values of A and B give No = 90 which corresponds to electron and proton energies of 90 keV and 350 keV, respectively. 4. Application of the Method Let us consider now the circuit in fig. 2. There is sufficiently high resistance in the anode of the multiplier to give together with the stray capacity a time constant permitting the integration of the ///////
0
d,7 that t]°Pt
A i + A,-1 B , - 1 - - B f B, + B,-I A, --At-1 "
i '4,
As a result of normalization Bt-1 - - Bt ~ c = b ---- A, - - At-l, hence nopt
A, + A,-1 Be + B~-I
(6)
This means that the relative error in the value of the difference between S, and S,-1 will be minimized by weighting the number of photoelectrons arriving after the time tt-l., with the ratio of the average number of photoelectrons produced by the scintillations of the two kinds of particles before and after this time. By doing so St =
No A tB~_l--A ~-xB~ No A ,-1B( - - A ~B~-I a n d S~-1 = (7) Be + B~-I B~ + B~-i
t h a t is S,-1 = - - S~.
(8)
Thus if we use the weighting factor ,/opt now obtained, the discriminating pulses S will be of opposite sign for the two kinds (denoted b y i and i - - 1) of particles.
m
~R.2o
Fig. 2. Diagram showing the discrimination arrangement. CF cathode follower.
charge induced by the scintillation and assumed to be amplified without distortion by the multiplier. Using a cathode follower, the multiplier is coupled to a shorted cable reflecting the pulses with a delay time T. T is equal to the duration of the scintillation, thus at point B after a time delay 2T reckoned from the start of the pulse we are again at zero level. It is obvious that the dead time is 2T. Up to now the pulse has been only shaped, the actual pulse shape discrimination is to follow. Essentially, this is done by means of a cable closed by a resistance R reflecting the pulses at the time Ti-l,i the cable being connected to the output B of the shaping cable through a cathode follower, as seen above. W h a t happens at point C ? The reflection occurring
28
L. VARGA
at the end of the cable of characteristic impedance Z0 and being closed by R, is R Z0 P: + R~ 0 " -
-
(11)
In fig. 3 we analyse the pulse of a particle with ionization density ~, as taken from the point C in fig. 2. The pulse shape from t = 0 up to the time z,-1., follows that of the integral of the charge collected by this time at the anode. At this point, however, a break occurs caused by the return of the r . t;._~a .
~-t,i A
'""
i
~
Bi
si.-p~-(,.p)~,.
~25 m'~,e,l
L;
Fig. 3. Time variation of the voltage appearing in point 13 (dotted line) and that appearing in point C (full line) of fig. 2.The line marked by small dots is the (1 + p)-fold of the dotted line.
initial pulse multiplied by p(p < 0 in the figure) from the shorted cable. The resultant pulse can be now considered as the superposition of two parts: the initial one multiplied by 1 + p and the same multiplied by - - p and shaped by the shorted cable with reflection time v,-1.,. Thus at the time ~'*-l,f the pulse is given by (1 + p)A~ plus --pA~. It is seen from the figure that S, = --A,p
--
(1 +
p)B,.
(12)
As observed previously, the optimum discrimination will be obtained if the condition S, = Ai - - ~optB~
is satisfied. From this we have #=
1 1 + ~opt
< o.
(13)
By comparing (13) with (11), it follows that R
~opt 20. 2 ,+ 7]opt
(14)
The size of the discriminating pulse S, is given by the difference between the maximum occurring at
the time rf-l.i and the integrated pulse built up during the time T. This difference is given for the time T,-1,, in the mirror image of the ascending part of our pulse. Such is the case if prior to the time v,-1., the particle producing a higher number of photoelectrons has been absorbed by the crystal. Now, if the crystal is struck by the other particle, we have Si-1 which owing to (8) does not become positive by the time T + ~-1,~, but remains negative because of S,-I = - - S~. Two such pulse shapes are seen in fig. 4. From (7) it is apparent that S, and S,-1 are proportional to No and thus to the energy and therefore the points S, and S~-1 lie along straight lines in the S-energy coordinate system, having identical absolute values but slopes of opposite sign, provided in the scintillation the ratio of fast to slow photons and the average lifetimes of the two components are independent of the energy. It is seen that in this simple way discriminatingpulses are obtained only for the particle responsible for the fast component of relatively higher intefisity, that is with the use of organic phosphors for particles with lower and with inorganic phosphors for those with the higher ionization density. If the crystal is struck by more than two kinds of particles, a further cable, Similar to the previous one, has to be coupled to the cathode follower. ri-,d
'
r r+~.~, [ ~
ec Fig. 4. Pulse shapes in point C of fig. 2 for two particles ot different ionization densities.
Since the cut-off time Tf-l., as well as the reflection coefficient have been chosen so as to obtain the optimum separation of two kinds of particles, the same circuit cannot discriminate between A, and A,+I as well. In order to separate the scintillation response of the particle with ionization density ~f from that characterized by P*+I, a cable with delay time r~.~+l and circuited by R~.t+l is required. These latter values are determined by the difference in pulse shape of the two particles in question. In the first stage positive discriminating pulses S are
PULSE
SHAPE
obtained for all incident particles (denoted by i, i + 1. . . . ) which produce integral curves of higher slope than that of the particles with ionization density PH, while in the second stage the pulses S will be negative but for particles denoted by i + 1, i + 2 . . . . . The anticoincidence of the pulses + S in the two circuits occursthus precisely for the absorption of the particle i in question. 5. Experiment on CsI(TI) Crystal The measurements of Storey, Jack and Ward~) give full information on the pulse shape of the scintillation of CsI(T1) crystals. The time constant of the fast component is shown by their measurement to be decreasing exponentiallywith increasing mean ionization density. Furthermore, it is possible to calculate from their measurement the ratio of ,the total number of slow to fast photons
f:slow dt / f : fast dt
(15)
as shown in fig. 5. From these two data the pulse shape of particles with any ionization density can be determined. Thus, for instance, the pulse shapes 9
~2
Lt f.O ~g
0.6 0,7 O.e
0.0 0.4 0.3 0 4
e,O.~l~V
/
8~61"leV2~.t4eV ¢.8t.fev
io
I t
~o
I
¢~oo
~ ~
Fig. 5. R a t i o of p h o t o n s belonging to t h e s l o w and fast comp o n e n t of scintillation corresponding to different m e a n ionization densities on t h e basis of the d a t e s given int).
of 2.2 MeV protons and of 2.26 MeV deuterons of identical scintillation responses, further those of
29
DISCRIMINATION
8.6 MeV protons and of their counterparts the 8.85 MeV deuterons, can be calculated as follows: Np,~.~(t)At = (1.33 e-t/o.5~ + 0.044 e-t/7.0) At, (16a) Nd,a.26(t)At = (1.48 e-t/o.48 + 0.041 e-t/7.o) At,
Np,s.e(t)At ~ (1.074e-rio.6 + 0.051 e-t/7.°) At, Nd,s.ss(t)At = (1.225 e-t/o.56 + 0.046 e-t/7.o) At.
(16b) (16c) (16d)
The response curves of the 2.2 MeV particles intersect at zdp = 0.66 #se'c. Now, the values A and B and the factor ~opt can be calculated from (16a) aq
T"
]"
_ _ ~
a2
scE~ :
i
,-~+-s-.~
i
11
i_
I
i
l
~ 6-7---~..<9 ,5-~l,'~v
1
Fig. 6. Discriminating pulses relating to proton and deuteron in dependence on t h e e n e r g y of t h e proton, T h e reflexion coefficient was chosen so as to obtain o p t i m u m discrimination b e t w e e n proton of 2.2 MeV e n e r g y and deuterons of t h e s a m e scintillation efficiency.
and (16b), which values in turn yield the discriminating pulses S~ = Sd.~.~6 and S~-1 = Sp,~.~ irrespective of their absolute values, since the total number No of the photoelectrons is irrelevant in this problem. The discriminating pulses for 8.6 MeV protons and those for deuterons corresponding from the point of view of scintillation efficiency to these protons can be determined from (16c) and (16d), though it has to be taken into account that Tdp and Rap have been chosen for the optimum discrimination of 2.2 MeV particles. The results of our calculations are shown in fig. 6. These two sets of points may be completed by our knowledge that Sp = Sd = 0 for E = 0. It is immediately apparent that Sd(E) ¢ k E ¢ Sp(E). This problem has been investigated experimentally and the result is shown in fig. 7. The pictures were taken by irradiating a deuterized paraffin layer with 14 MeV neutrons. The aluminium plate supporting the paraffin was mounted on 1.5mm thick CsI(T1) phosphor. particles were obtained from the Al(n, ~) reactions, deuterons, from the elastic scattering and protons from both the Al(n,p) and the D(n,p) reactions. Owing to the (n,7) radiation of the surroundings 7pulses too were obtained. The scintillations were
30
L. VARGA
detected by a Dumont 6292 photomultiplier. From the point C in fig. 2 the pulses were transmitted to the vertical amplifier of a Tektronix type 515A oscilloscope, while the pulses coming from the first cathode follower and delayed for/, > rdr~ were being
Fig. 7. Photograph of oscilloscope obtained for various particles incident simultaneously using the arrangement of fig. 2.
passed to the horizontal amplifier. The electron beam of the oscilloscope was opened at T q-rap and kept open for t ~ 50 re#see. The best photographs were obtained with T -- 3 ,usec and rap 0.5/~sec. The number of ~ particles is relatifely low. The upper limit of the 7 line is quite sharp, the lower limit, however, is blurred and broadened since only a small fraction of fast electron energy is lost to the crystal and such scintillation appear at lower energies. In consequence of the lower average ionization densities, the S is more negative than for electrons having the same photon yield but being completely absorbed by the scintillator. It is also apparent that the discriminating pulses for a and y-induced scintillation showing a great difference in fast component versus lifetime curves, lie, in terms of the energy, on an approximately straight line. The deuteron and proton lines are curved. Usually, however, a reflection coefficient differing from the optimum can be found for which the two curves rise above the energy axis, so that above a given energy and as compared to a certain U > 0 discrimination level, we have I Sp I < U < 15"a I" The energy scale was calculated for the maximum deuteron energy possible upon bombardment with 14 gleV neutrons. Proton-deuteron discrimination seems to be feasible above ~ 3 MeV. Their separation from the y, p, ~ background can be achieved
with the aid of the arrangement shown in fig. 8. The second cathode follower is coupled to two cables of delay time ra and rap and closed by impedances Rap and Ra~. The input of these cables is connected to the discriminator. The necessity for this arrangement has been already discussed in connection with the d - p discrimination, yet it is not superfluous for the ~-d channel either, since, thougt the discriminator of the d p channel delivers pulse for each discriminating S above the preset level, thus for S~ too, no signals are obtained for c~ particles having lower 5" than the discrimination level set for the d - p channel. It follows from the above that by discriminating subsequently in the c~-(l channel at 0 volt, anticoincidences would be brought about by pulses which, though produced by e particles, could be identified as deuterons since their S appears between 0 and Udp. Considering that, usually, the energies of the discriminated particles have also to be measured, it is useful to wait for the scintillation to die out. Sometimes, however, a higher counting rate is required, even at the expense of analysis and separation. In this case the time T has to be reduced which necessitates some modification also for. If we have to Ra~ Y /11///
Fig. 8. Block diagram of circuit selecting one type of particles fronl among the different components of the background.
work extremely fast, the arrangement shown in fig. 9 m a y be convenient, although only scintillations of very short duration would then give positive discriminating pulses, if the reflecting resistance R is suitably chosen and Ra Z0. The length of the cable is determined by the requirement that the reflected wave should return at a
POLSE
SHAPE
time a b o u t the m a t h e m a t i c a l m e a n value of the decay c o n t a n t s of t h e fast c o m p o n e n t s of t h e particles to be discriminated. F o r ~ discrimination in Cs(T1) it is a b o u t ~ 0.56/~sec. //////
2
&~
.Zo
Fig. 9. Simple circuit for f a s t d i s c r i m i n a t i o n .
6. R e d u c t i o n o f the Threshold E n e r g i e s for Discrimination
I n special cases when the i n c i d e n t b e a m of particles is well collimated, the m e t h o d can be imp r o v e d b y s u i t a b l y combining t h e i n f o r m a t i o n s obt a i n e d from t h e m e a s u r e m e n t of d E / d x with the shape discrimination. I t is obvious t h a t , similar to the discriminating pulses S being meaningless without t h e m e a s u r e m e n t of the energy (total n u m b e r of photons), the particle will be d e t e r m i n e d b y d E / d x only if we know the energy of t h e particle which l o s e s - - t o a foil of given t h i c k n e s s - t h e a m o u n t of energy p a x (o = dE/dx). Now, since in the course of shape discrimination the particle energy h a s alr e a d y been determined, we h a v e only to combine the knowledge of these three e x p e r i m e n t a l values. Let us use a scintillator foil for t h e m e a s u r e m e n t of P. A particle of energy E0 loses the fraction d E = p a x of its energy. Eo - - d E be absorbed b y t h e analysing crystal. The n u m b e r of photoelectrons produced in the foil per scintillation be n. This c u r r e n t be amplified b y a factor k in a multiplier a n d possibly w i t h the help of o t h e r electronical devices. The o t h e r scintillator deliver N photoelectrons proportional in n u m b e r to the energy Eo - - d E a n d this be multiplied b y k'. In accordance with the previous d e n o t a t i o n for the arrival of the particle denoted b y i, we o b t a i n a q u a n t i t y k,ni + k ' N v W h a t is the difference in the composition of these two equal q u a n t i t i e s kni-1 + k'Ni-1 = knl + k'N~ o b t a i n e d for particles i a n d i - 1, respectively ? If pi > Pi-1 it follows t h a t ui > u,-1 a n d b y choosing a suitable inorganic measuring crystal we h a v e Si > Sl-1 as well. Let us choose a foil the scintillation decay of
DISCRIMINATION
31
which is m u c h faster t h a n t h a t of the measuring crystal. I t should be fast enough to p e r m i t the scintillation to die out completely prior to the time characteristic for the analyzer. This r e q u i r e m e n t is fully m e t b y coupling an organic scintillator foil with an inorganic m e a s u r i n g crystal. I n this case the sign of Ai - - A,:-I will be the same as t h a t of n, - - h i - 1 . This m e a n s t h a t virtually only the inf o r m a t i o n "b" in fig. I increases in accordance with ni n i l . I t h a s to be kept in m i n d t h a t owing to the change in n o r m a l i z a t i o n Z*-l,l needs some correction which will induce some change in *jopt as well. W e calculate now in the same way as above t~*
k
ni + ni 1
N~A* + N~->'~*I
k" N~B~ + NI-1B~-I + NiB**. + N~-IB~_I
. (17)
The t e r m s with asterisk correspond to those, used in the previous t r e a t m e n t , t h o u g h differing from t h e m as regards their normalization a n d in consequence of the new Ti-l.t. T h e second t e r m of the expression for ~* is incidentally the perfect analogue of ~opt. F u r t h e r , it can be readily shown t h a t S*= (kn, + k'N,A~)N,_IB,_I - - (knt 1 + k'N, 1A*-I)NIB* N~B* + Ni-IB*-I = > S~--I.
(|8)
Assuming in a rough a p p r o x i m a t i o n the q u a n tities A a n d / 3 to be i n d e p e n d e n t of energy, a n d N to be proportional to E, while u to l/E, it becomes a p p a r e n t t h a t S*(E) is the superposition of a h y p e r b o l a a n d a s t r a i g h t line. The weight factors of the superposition can be influenced b o t h b y the foil thickness d x a n d the multiplying factors k and k'. The k (amplification of the channel p) however, energy loss d E in order to d e t e r m i n e the spectra more accurately, it is obvious t h a t the o p t i m u m setting is k -- k'. I t is to be n o t e d t h a t even J E c a n n o t be arbitrarily small. In the calculation of ~?* the L a n d a u effect has not been t a k e n into account: this m e a n s t h a t .lIE m u s t be higher b v an order of m a g n i t u d e t h a n the m a x i m u m energy which can l)e transferred from the particle detected to an electron of the foil. If this condition is not satisfied, the I.andau effect has to be calculated too.
32
L. V A R G A
7. Telescope The above considerations can be applied without any alteration to the so-called telescopes. The previously used proportional counter-crystal detector combination is now being replaced at an ever increasing rate by scintillator foil-crystal analyser arrangement. It is to be noted that the above results will hold only if the detectors conform to the above requirements. By adding the integrated pulses of the two multipliers and transmitting this sum pulse to the shape discriminator, we obtain with corrections z -+ r* and r/opt ~ ~* the results of the preceding paragraph.
8. Shape Discrimination with Sandwich-detectors Similarly, the above considerations are readily applicable to the plastic phosphor-inorganic crystal sandwich arrangement. This combination has been
0
Fig. 10. \Vhen combining the measurement of dl'J/dx w i t h pulse shape di~crinlination, tile ptlls(?s for x particles call be separated from those of ~*l a v s even at low energies.
experimentally tested by the author. A plastic foil of about 1 mg/'cm 2 was mounted on a CsI(T1) crystal plate and irradiated with the a rays of a Po 210 source. The c~radiation released the electrons in the CsI crystal so that they were not affected by
the foil, the discriminating straight line S*(E), however, rose above its previous level as it is seen in fig. 10. In this case the condition k = k' is automatically satisfied, since both scintillations are counted by the same multiplier, thus the circuit shown in fig. 2 m a y be kept unaltered but for and R. Something has to be said also on the part played by the multipliers. Actually, no fast multipliers are needed for the integration, nevertheless it is desirable that the multiplier should sufficiently well respond to any variation in the emission of the light pulses since it is the rise time of the integrated pulse which is exploited for discrimination. This means that only a minimum fraction of the charge collected prior to time z should be permitted to pass into the subsequent time interval because of the distortion caused by the multiplier. This problem does not arise with "slow" scintillators, such as CsI, NaI etc. For faster organic phosphors, however, the choice of the multiplier becomes of considerable importance. If the distortion due to the multiplier becomes appreciable, the optimum conditions for discrimination had better be determined from the time distribution of the charge collected on the anode than from the parameters of the scintillation decay. This does not involve additional work, since our present knowledge of the scintillation mechanism still requires the experimental correction of the predicted data.
Acknowledgement I take this opportunity to express again m y thanks to the International Atomic Energy Agency for sponsoring m y study abroad. Thanks are due to the Nuclear Physics Department of the C.I.S.E., in particular, to Prof. U. Facchini for continued interest in my work as well as to Prof. E. Gatti for helpful discussions.