- Email: [email protected]
Experimental determination of the intrinsic fluctuations from binding energy losses in SiU hadron calorimeters
Nuclear Instruments and Methods in Physics Research A 361(1995) 149-156
NUCLEAR INSTRUMENTS a METNODS IN PHYSICS RESEARCH SectionA
ELSEWER
Experimental determination of the intrinsic fluctuations from binding energy losses in Si/U hadron calorimeters SICAPO Collaboration C. Furetta al1, C. Leroy b,2,* , S. Pensotti a*3,A. Penzo ‘, P.G. Rancoita a aINFN-Milan, I-20133 Milan, Italy b Uniuersitt? de Montrkal, Montrkal (Q&bee) H3C 3J7, Canadn ’ INFN-Trieste, I-34127 Trieste, Italy Received 22 December 1994 Abstract Fluctuations due to binding energy losses were determined experimentally for a sampling hadron calorimeter with an active medium consisting of layers of silicon mosaics. The absorbers were uranium layers @i/U). The calorimeter was exposed to hadrons (protons) at incoming energies of 8, 10, and 12 GeV. The contribution tobind) of the binding energy losses fluctuations to the energy resolution of this compensating hadron calorimeter was found to be obind = 47.8%.
1. Introduction
where
The energy resolution of sampling hadron calorimeters is dominated by sampling and intrinsic fluctuations and by their relative response to electromagnetic showers
= Co/&
+ 4(e/n)
= C/&,
(1)
* Corresponding author. Fax 741 22 767 8350, e-mail leroy@eemvm. cem. ch. ’ And University of Rome, Rome, Italy. * Killam Fellow. 3 And University of Milan, Milan, Italy.
E is the incoming
hadron
energy,
in GeV, and
C = Co + +(e/rr)@; C, = dw contains the contributions from the intrinsic fluctuations mostly due to nuclear binding energy losses (or,,,), and from the sampling fluctuations (a,). The function +(e/rr) is vanishing for e/n = 1, i.e., for compensating calorimeters. Compensation (e/n = 1) is achieved through the equalization of the calorimeter response to electromagnetic and hadronic showers. This equalization in the case of a hadron calorimeter, with silicon readout and uranium as passive medium, can be achieved by suppressing the electromagnetic response of the calorimeter. Experimental evidence was found for a local hardening effect [S] obtained by inserting low-Z absorbers (thin in radiation length units, like GlO layers) next to the silicon detectors in Si/high-Z sampling calorimeters. This effect is responsible for the suppression of the electromagnetic response of the calorimeter due to the absorption (in the low-Z material) of soft electrons. It has been experimentally demonstrated that the local hardening effect was leading to the achievement of the compensation condition (e/n = 1 and, consequently +(e/n) = 0) in silicon calorimeters using U as absorber, by inserting GlO layers in front and at the rear of the silicon detector mosaics [6]. It is known [7] that, for a non-compensating calorimeter, 4(e/rr) has only moderate variations in the 5-15 GeV energy range, which covers the set of data used in the present article. Therefore, by combining direct measurements of the energy resolution with computed and/or
0168-9002/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-9002(95)00114-X
150
C. Furetta et al. /Nucl.
Instr. and Meth. in Phys. Rex A 361 (1995) 149-156
measured values of +(e/rr) (once the e/n calorimeter ratio is experimentally known [2,6,8]), it is possible to determine C,, and finally the fluctuations due to the nuclear binding energy losses, once the sampling fluctuations are evaluated [7]. The present article deals with data obtained from the operation of a calorimeter using silicon as active medium and a passive medium made of layers of uranium @i/U).
2. Sampling hadron calorimeters and binding energy losses The e/n
signal ratio, appearing
in Eq. (l), is defined
as:
e’T=(e/mip)f,,
(ebb) + (h/mip)(l -L)
.
Here, mip is the energy deposited in the sensitive part of the calorimeter by a minimum ionizing particle. The ratio e/mip, in eq. (2), measures the energy deposited in the sensitive part of the calorimeter by electron and photon showers relative to a mip; (h/mip)(l - f,,) is the hadronic energy deposited in the detector readouts by the purely hadronic component of the shower relative to a mip (see Refs. [2,7] and references therein). f,, varies with energy and is the average fraction of the converted electromagnetic energy resulting from the photon decays of rr” and 9 particles produced during the hadron cascade. The logarithmic increase of f,, with the energy, E (- 0.12 In E, E in GeV [3]), results in a e/n signal ratio which is also energy dependent. For a showering hadron, the n/mip ratio is given by n/mip
= (e/mip)f,,
+ (h/mip)(l
-f,,).
(3)
The total visible energy (electromagnetic and hadronic), deposited by hadrons in the calorimeter, can be expressed as:
(4) The energy shared (E,) by a minimum ionizing particle in the silicon detectors is given by E, = EF(Si)
= EG(Si)X,,
,
(5)
energy, and the fraction of energy lost in the depleted layers of the silicon detectors, respectively. Then, Eq. (4) can be rewritten as:
E,i,=zF(Si)[ (&) +L($ - a)].
C6)
Eq. (5) shows that it is only in the situation where e/mip = h/mip (i.e. e/n = 1, the compensation condition) that the calorimeter response is proportional to the incoming energy E, independently of f,, which varies with E. In a sampling calorimeter, the measured energy resolution, ((r(E)/E),,,, is given by: (o(E)/E)exp
= oJevis(n),
(7)
where o+ is the standard deviation value of the Gaussian like distribution of the hadronic visible energy, e,Jn), measured in the calorimeter when no correction for energy losses are included. These losses are longitudinal, lateral, and dead area energy losses. The latter have to be considered particularly for calorimeters with high granularity, which is presently the case for silicon readout mosaics. The effects of energy losses on the energy resolution have been measured experimentally for hadronic and electromagnetic showers. In particular, for hadronic showers, the linear dependence of the hadronic resolution on energy losses has been observed up to energy losses of about 15% [l]. The effect of the fraction of energy lost on the measured energy resolution, discussed in Refs. [1,2,9], can be represented (for energy losses up to 15%) according to Ref. [2]: (o(E)/E),,p
=
(o(WE)(l + CAPP)
= (C/&)(1
+ CAP),
(8)
where P is the percentage of lateral (l), longitudinal (L), and dead area (D) energy losses. A, is a coefficient depending on the type of energy loss [9]. It has been shown that fluctuations produced by the lateral energy losses are less effective, by a factor 2-3, than the longitudinal energy losses [1,9], i.e., A, < A,. Furthermore, it has been also shown [9] that the longitudinal energy losses are as effective as the dead area energy losses, i.e., A, = A,, because both of them are related to event-to-event fluctuations. The experimental data [l] have allowed to determine that, for hadronic showers, the values of A, and A, = A, are 0.027 and 0.077, respectively.
with
(dE/dx)si G(Si) = (dE/dx),,Ls,
3. Experimental set-up and data
+ c (dE/dx)J,
where, Xsi, Lsi, L,, (dE/dx),, E, and F(Si) are the depletion depth, the thickness of the Si detector, the thickness of the absorber i, the average energy loss per unit of length (of a mip) in the absorber i, the incoming particle
The Si/U hadron calorimeter was consisting of 30 uranium absorber plates, each about 1.5 cm thick, interspaced with silicon readout mosaics. The mosaic supporting structure, made of two GlO plates (1.0 and 0.2 mm thick) located in front and at the rear side of the detectors,
C. Furetta et al./Nucl.
151
Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
was equivalent to about 0.23% of interaction length, A 4. Data were taken for several calorimeter configurations where additional GlO plates, 1.0, 3.0, and 5.0 mm thick, were inserted both in front and at the rear of the silicon detectors. Data were also taken with no additional G10 plates. The overall calorimeter depth was about 4.6h on average (namely, about 4.4, 4.5, 4.7, 5.0 A depending on the thickness of the additional GlO plates inserted in the calorimeter structure). The readout of this calorimeter consisted of 30 mosaic planes (with an active area of _ 524 cm2) each made of 18 trapezoidal silicon detectors [6]. The detectors were 400 p,m thick and operated at a depleted layer width of 270 km. The use of serial couplings of five silicon detectors along the beam direction, although reducing the number of electronic channels and the overall detector capacitance, allowed the use of fast electronics (about 200 ns base-time signals) with a wide dynamical range (five decades) and permitted the readout of the calorimeter into six longitudinal sections. The electronic readout is described in details in Ref. [IO]. The calorimeter was operated at the t, beam at the CERN Proton Synchrotron (PSI, at incoming energies of 8, 10, and 12 GeV. Two gas Cherenkov counters were used to separate electrons and hadrons. A beam scanner, consisting of a scintillation counter of 0.5 X 0.5 cm2 area, ensured that only those hadrons impinging on the middle of the calorimeter triggered. The absolute energy calibration was performed following two independent approaches (as described elsewhere [6]): i) by measuring the energy deposited by 233U (Y sources (4.8 MeV on average) located on top of the silicon detectors; ii) by minimum ionizing particles (p) which give a well known energy-loss distribution in the silicon readout detectors. The two methods agreed well with each other and the error on the absolute energy scale was about 2%. For each group of 5 detector sets, the standard deviation of the Gaussian noise distribution was 177 keV, corresponding to a signal of = 0.4 mip. This was measured before and after each data taking run, allowing for the correction of the experimental visible energy distributions for these electronic noise effects. As mentioned above, the calorimeter was divided into 6 sections along the beam direction, each section being readout independently. This allowed an estimate of the longitudinal loss of the visible energy by extrapolating the exponential fall of the longitudinal shower development beyond the shower maximum. The longitudinal hadronic
’ A is given by A /N, u [cm] = 35 A’13/ p [cm], where A, N,,, p, and c are the mass number, the Avogadro number, the density of material, and the proton inelastic cross section for the material, respectively. The U absorber interaction length is 10.5 cm.
20
15
S g
IO
W
5
0
0
2
4
6
8
IO
12
E (GeVl Fig. 1. The visible energy lvis in the Si/U calorimeters as a function of the incoming energy. From top to bottom: no GlO plates, 1.0, 3.0, and 5.0 mm thick G10 plates, added both in front and at the rear of the silicon detector mosaics. The lines are: q&o GlO) = (1.25 +0.25)E +(1.70 k2.48) [MeV], c,&.O mm GlO) = (1.17*0.24)E +(1..54+2.35) [MeV], c&3.0 mm GlO) = (1.11+0.23)E +(1.74*2.24) [MeV], •,,~~(5.0 mm GlO) = (1.09 f 0.22)E + (1.71+ 2.17) [MeV], respectively. E is in GeV.
visible energy losses 5 were estimated to be (2.0 f 1.3)%, (3.3 rt 1.7)%, and (3.8 f 1.71% at 8, lo1 and 12 GeV, respectively. These data are in agreement with previous measurements [6,11]. The measured visible energy had to account for the energy losses in the dead zones between detectors in the mosaics. The dead area energy losses amounted to (3.7 f l.O)% (see Ref. [6]). A dedicated run was carried out to measure the visible energy lateral losses. The lateral losses were measured using two mosaics planes [12], each made of 35 trapezoidal silicon detectors (400 pm thick and depleted at 200 pm). The two mosaics planes were serially coupled in order to present an active thickness of 400 km. The measurements were made with the two mosaics installed in the calorimeter at depths varying from 0.5 to 5 A. The detectors were assembled in a mosaic to form 7 horizontal strips. Each strip, made of five silicon detectors, was about 4 cm large. The overall active area was about 1019 cm’. The estimated value of the overall lateral loss of the hadronic visible energy for the present calorimeter is (5.1 f 2.21% at incoming proton energies of 8, 10, and 12 GeV, for the present calorimeter.
’ The errors take also into account the effect of the calorimeter depth variation when the GlO plates are added.
152
C. Furetta et al. / Nuct. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
The measured visible hadron energy (E+) for the Si/U calorimeter is shown in Fig. 1 as a function of the incoming proton energy for several thicknesses of GlO plates added both in front and at the rear of the silicon detector mosaics. The values reported in Fig. 1 were corrected for the longitudinal, lateral and dead area energy losses effects described above. lVis shows a linear behaviour with the incoming proton energy, within the experimental errors.
The measured energy resolutions ((u(E)/E),,,), when no correction for dead area, lateral and longitudinal energy losses are taken into account, are shown in Figs. 2a-2d for no GlO plates, 1.0, 3.0, and 5.0 mm thick GlO plates added both in front and at the rear of the silicon mosaics, respectively. In each case, (c+(E)/E),,, behaves as a linear function of l/G, within the experimental errors. These results allows the determination of the values of C
90
(b) &
60::
W
: -
c
30-
0 0.0
0.2
0.4
0.0
/
I
I 0.2
I
I 0.4
M/m
I/&iGz 90
90 (d)
60
30
00.0
0.2
0.4
l/&Ezz as a function of l/ 6, is shown for no additional GlO plates inserted in front Fig. 2. (a) The measured energy resolution ((a(E)/E&,), as a function of l/G, is shown for 1.0 mm and at the rear of the silicon mosaics. (b) The measured energy resolution ((u(E)/E),,,) thick additional GlO plates inserted in front and at the rear of the silicon mosaics. (c) The measured energy resolution (((r(E)/E),,,) as a function of l/@, is shown for 3.0 mm thick additional GlO plates inserted in front and at the rear of the silicon mosaics. (d) The measured energy resolution ((a(E)/E),,J as a function of l/G, is shown for 5.0 mm thick additional GlO plates inserted in front and at the rear of the silicon mosaics.
153
C. Furetta et al. / Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156 Table 1 The value of C and its weighted average (C(w.v.)), as a function of the hadron energy, for the Si/U calorimeter E [GeV]
no GlO
1 mm GlO
3 mm G10
5 mm GlO
12 10 8 C(w.v.)
94.3k11.7 93.6f11.6 9O.lk11.8 92.7+ 6.8
77.6* 9.5 88.2kll.O 87.4+10.7 83.8+ 6.0
91.8+11.2 90.1+11.1 87.6+10.8 89.8+ 6.4
91.6k10.4 88.5+10.3 89.0+10.5 89.7* 6.0
electromagnetic response, can be achieved by the local hardening effect obtained by inserting low-Z absorbers (like GlO, Al, polyethylene) next to the silicon detectors [6,12,14]. The degree of hardening depends on the thickness of the low-Z absorbers and on their location in front and/or at the rear of the detectors [12,14]. These low-Z absorbers must have a small ratio: H=L
low-Z/Lhigh-Z~
(Lhigh_z) is the thickness in units of radiation low_z length, Xa, of the low-Z (high-Z) absorber. The local hardening effect has been achieved and studied for HI 2.5% [15], and for low-Z materials such as GlO, Al and polyethylene. Following the local hardening effect, at a given thickness and location of the low-Z material next to the silicon readout plane, the electromagnetic visible energy is reduced independently of the high-Z absorber sampler thickness, according to:
where L (C/ fi = a(E)/,!?) for the corrected energy resolution, once the effects of the visible energy losses on the measured energy resolution are taken into account (Eq. (8)). Table 1 shows the values of C evaluated for the various insertions of GlO plates in front and at the rear of the silicon detectors and as a function of the incoming hadron energy. The weighted average values of C (C(w.v.)) are (92.7 + 6.8)%, (83.8 + 6.0)%, (89.8 k 6.4)% and (89.7 f 6.0)% for 0.0, 1.0, 3.0, and 5.0 mm thick additional Cl0 plates inserted in the Si/U calorimeter structure, respectively.
R,h(LwZ) =
E,is(Lhigh-Z) - ‘vis( L10W-Z7 Lhigh-Z)
=I-
%is( f,is(
Llow-Z) Evis(
4. Determination
of the intrinsic fluctuations
in U
Sampling fluctuations (or) and intrinsic fluctuations (obind) are contributing to the overall energy resolution of hadronic sampling calorimeters, the latter being mostly due to the binding energy losses because of nuclear break-up. The contribution from the sampling fluctuations (or) can be computed from the parametrization [13]: ur = Il.S%JhE,
(9)
where AE is the average energy, in MeV, deposited by a minimum ionizing particle in one passive sampler [13]. The sampling fluctuation contributions depends on the thickness of GlO inserted in each sampling. a,, as calculated from Eq. (9) is reported in Table 2, for the various thicknesses of the GlO plates inserted and varies from or = 64.5% (no additional GlO plates inserted) up to a, = 67.6% (5.0 mm thick GlO plates inserted in front and at the rear of the silicon mosaics).
The values of the e/n ratio for the various Si/U calorimeter GlO configurations (i.e., the calorimeter configuration with no additional GlO plates, and the three configurations where two additional GlO plates 1.0, 3.0, and 5.0 mm thick were located in front and at the rear side of the detector mosaics) are about those measured in Ref. [6] for the same Si/U calorimeter GlO configurations and incoming proton energies, but with different U sampler thicknesses. This is because the tuning of the e/mip ratio, i.e. the variation of the e/mip value of a Si/U calorimeter
Lhigh-Z)
(11)
L high-Z
where E,&?I,~~~~_~)is the visible energy for a calorimeter having a passive sampler of thickness Lhigh_Z and where E,~~(L,~~_~, Lhigh_Z) is the visible energy for the same calorimeter but with low-Z absorbers (of thickness L,,.,) added next to the silicon readout planes. R,h(L,ow_Z), to a first approximation, depends on the location and thickness of the low-Z absorber, but not on the Lhigh_Z thickness of the high-Z sampler [6,12,14,15]. For an electromagnetic shower in a sampling calorimeter, lvis = (e/mip)E, (E, is given by Eq. (5)) and when only high-Z absorbers are used for samplers, the e/mip value is almost independent of the sampler thickness (see Ref. [3] for U sampler thicknesses larger than 2X, and Ref. [16] for e/mip values measured for Pb sampler thicknesses of 1.96 and 3.39 X0). For electrons incident on a Si/U electromagnetic calorimeter, with GlO plates inserted next to the active medium and the local hardening effect in operation, the ratio of e/mip(U, GlO) to e/mip(U) is given by: e/mip(U,
4.1. e/ n ratio values of the Si/ U calorimeter
L high-2 1
GlO)
E,is(UT G10) -_Es(U) GlO) e&U)
= E,(U,
e/mip(U)
’
(12)
Table 2 The value of at&eff) (weighted mean over the incoming energies), a, and e/ 7~,as a function of the thickness of the additional inserted GlO plates no
a,,&eff)[%] “r [%I e/r
GlO
67.1+4.9 64.5 1.27
1 mm GlO 3 mm GlO 5 mm GlO 50.5k3.7 65.1 1.03
6O.Ok4.3 66.4 0.90
59.4+4.0 67.6 0.86
C. Furetta et al. /Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
154
where e/mip@J, GlO) (e/m@(U)) is the e/mip ratio for a Si/U calorimeter with a sampler of length L, and additional (no additional) GlO plates present; the notations E&J, GlO), E&J>, E&U, GlO), E,(U), ~/m&&J, GlO), n/m@(U), have the same meaning for the total visible energy (E&, the energy shared (E,), and the ratio a/mip. From Eq. (ll), e/mip(U,
GlO) = E,(ttluG);o)
(I-
R,,(GIO)).
(13)
e/mip(U)
304 -I
For two Si/U calorimeters with an identical GlO structure, but with different sampler thicknesses (L, and &I), because e/mip&J) m e/mip&J’), we have (from Eq. (13)): e/mip(U,
GlO)
e/mip(U’,
GlO)
=-
E,(U)
&(U’,
GlO)
Q(U’)
-WJ,
GlO)
(14)
n/mip(U,
GlO)
GlO) = E&U’,
c,is(U, GlO) GlO)
4(U’,
GlO)
E,(U,
GlO) ’
e/rr(U,
GlO)
e/n(U’,
GlO)
= =
2
3
4
5
6
GIO (mm) Fig. 4. v represents the calculated values of ub,,,(eff) (0) and of qbind (0) (using the values of C from Table 1) which are shown as a function of the thickness of GlO (in mm) inserted in front and
(I5)
where e&J, GlO) and e&J’, GlO) are the visible hadron energies measured at the same incoming hadron energy for the sampler thicknesses L, and L,,, respectively. From Eqs. (14) and (15), the e/n signal ratios relative to these Si/U calorimeters, are related according to: R(e/n)
I
at the rear of the silicon mosaics. The curve is to guide the eye. The line corresponds to the gbind weigthed value: gbind = 47.8%.
and from Eq. (3), we have for incident hadrons:
rr/mip(U’,
0
l,is(U’)
G10)
E,(U)
E,is(U,
G10)
E,(U’)
(16) Fig. 3 shows the ratio R(e/m) for a U sampler 2.5 cm (data from Ref. [6]) and 1.5 cm thick (this experiment). The ratio Z&(2.5 cm U)/E,(1.5 cm U) was calculated using Eq. (5). The ratios ~$1.5 cm U, GlO)/e,,(2.5 cm U,
GlO) were evaluated from an average (on the incoming hadron energies of 8, 10, 12 GeV) of the measured visible energies in this experiment (Fig. 1) and those measured in the previous experiment (Ref. [6]). In Fig. 3, the four GlO structures are: no additional G10 plates (only, the 1.2 mm thick GlO supporting structure of the silicon mosaics), and the three structures where two additional GlO plates 1.0, 3.0 and 5.0 mm thick were located in front and at the rear of the silicon mosaics. It can be seen, in Fig. 3, that the R(e/n) values are well consistent with 1. This indicates that the calorimeter structure properties which determine the value of the e/a ratio are mainly due to the GlO structure, because of the local hardening effect. Thus, for the present Si/U calorimeter, the e/n ratios are those measured in Ref. [6] and reported in Table 2. Determination tions in U
4.2.
of the binding energy losses j?uctua-
Eq. (1) can be rewritten as:
0.01
3 GIO
Fig. 3. The ratio R(e/m)
5
(mm)
is shown for a U sampler 2.5 em (data 1.5 cm thick (this experiment). The line
from Ref. [6]) and represents R(e/v) = 1.
where obind(eff) includes the effect of non-compensation on the calorimeter energy resolution. For a compensating calorimeter, the e/n ratio, i.e. the ratio of the electron to hadron visible energy measured at the same particle energy and in the same calorimeter configuration, is equal to 1, and o,,&eff) = obind. From Eqs. (1) and (171, one has: a,,,(eff)
= /w.
155
C. Furetta et al. / Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
-
35
a-”
25 60-
b
50-
15
403020 0.3
5 “s’m”‘~‘m” 0.5 0.7
0.9
I.1
1.3
1.5
1.7
e/r
value: rhind = 47.8%.
The calculated weighted average (on the incoming energies) values of mbind(eff) (using, at each energy, the values of C from Table 1) are shown in Fig. 4 as a function of the thickness of GlO inserted in front and at the rear of the silicon mosaics. The values of ubind(eff) are also shown in Fig. 5 as a function of the e/r ratio. It can be observed that gbind(eff) = (50.5 + 0.3)% for a thickness of 1.0 mm for the additional G10 plates inserted in front and at the rear of the readout silicon active planes, namely for a ratio e/a = 1.03. The intrinsic fluctuations contributions in the Si/U calorimeter, cbind, can be determined once the function 4(e/T) (see Eq. (1)) is evaluated. As emphasized before, the function $(e/v) accounts for the effect of non-compensation on the calorimeter energy resolution. From Eq. (l), one has: ubind =
{(c - +(e/71)&)’- u:.
(18)
The values of 4(e/n) have been estimated by interpolating the results of Monte Carlo simulations on the energy resolution dependence on incoming energy reported in Ref. [7], for e/n ratios of 0.76, 0.85, 1.14, 1.26 and 1.47, at 10 GeV. From these simulations, one can estimate 4(e/n) and e/n which are almost energy independent in the 5-15 GeV energy range. The function &e/T) is shown in Fig.
7\D
e
.
5-
F
3
9
I
1
0.6
Fig. 5. (r represents the calculated values of cbi,,&eff) (0) and of crbind (0) which are shown as a function of the e/r ratio. The curve is to guide the eye. The line corresponds to the gbind weigthed
~
--
_---.-----I
I
I
0.8
I
1.0
I
I
1.2
a
_I
I.4
e/*
Fig. 7. The additive tern function of e/r
@(e/m)&. (E = 8, 10, 12 GeV).
in [%I, is shown
as a
6 as a function of e/n, for the 5-15 GeV energy range. In Fig. 6, &e/a) is estimated to be about 0.9% (in the 5-15 GeV energy region) for e/r about 1.11. This value is in agreement, within the experimental errors, with the results reported in Ref. [16], where @(e/n) = (1.0 f O.l)% for e/n = 1.107 f 0.006 at 9.7 GeV. In Fig. 7, 4(e/a)& is shown for the incoming energies of 8, 10 and 12 GeV. Using the values of 4(e/r)& (corresponding to the e/a ratios given in Table 2), those of C reported in Table 1, and the values of ur as given by Eq. (9), it becomes possible to estimate cbind (Eq. (18)). The weighted average values of cbind (from a weighted average of the ubind values obtained for the different GlO calorimeter structures) is (47.8 + 1.9)%. This result is in agreement with the value gbind = (4246)% predicted in Refs. [3,7] for the case of negligible or low neutron absorption. In order to decrease the contribution due to the intrinsic fluctuations, particularly for high-A materials, it is necessary to employ hydrogeneous materials, in which part of the neutron energy can be detected by the scintillation process induced by the recoiling proton after a proton-neutron scattering. Calorimeters which have a scintillator as active medium and a larger ratio, R, of the active (scintillator 3.0 mm thick) to passive (U thickness of 3.2 mm) medium thicknesses, have shown smaller binding energy losses fluctuations [16]: cbind = (20.4 + 2.4)%, as previously predicted in Refs. [3,7].
5. Discussion and conclusions
0)
; _
I. 0.5
-_---
\J_
--_--
I.
1
0.7
0.9
.
I
I.1
I
I
I
1.3
e/*
Fig. 6. 4(e/ 7~)is shown as a function of the e/ TI ratio.
I 1.5
Binding energy losses originate from the fluctuating large amount of the deposited energy which goes in breaking nuclei during the hadronic cascading. The resulting fluctuations contribute to the energy resolution of hadron calorimeters. The fluctuations due to binding energy losses for U were determined by combining direct measurements of the energy resolution (which give C), estimates of
156
C. Furetta et al. /Nucl.
Ins@. and Meth. in Phys. Res. A 361 (1995) 149-156
+(e/n) using previous experimental measurements of the e/n ratio, and calculation of sampling fluctuations, for silicon calorimeters with U as absorbers. The determined values of the effective binding energy loss fluctuations (at e/n = 1.27, 1.03, 0.90, 0.861, u,,,,(eff), which include both the intrinsic fluctuations and the non-compensating effect on the energy resolution, have the lower value for e/n = 1.03. The binding energy losses depend on the fraction of neutron energy detected by the active sampler. In the present work, the ratio, R, of active to passive medium thicknesses is very small and little of the neutron energy is seen by the active medium, leading to large intrinsic fluctuations from binding energy losses. Our result obind = 47.8% is found in agreement with earlier predictions made when neutron absorption is negligible [3]. It can be also compared to previous results [2] obtained for Fe and Pb: o,,ind[Fe] = (16-B)% and osind[Pb] = (49-45)%. It was also observed [2] that, for an almost compensating Si/Fe + Pb calorimeter, the contribution of the intrinsic fluctuations to the overall energy resolution originated mostly from the binding energy losses, ubind[Fe + Pb], which was about 24.5%. Furthermore, the visible energy, lVis, has shown a linear dependence on the incoming hadron energy, within the experimental errors.
References [ll U. Amaldi, Phys. Scripta 23 (1981) 409.
La C. Furetta, C. Leroy, S. Pensotti, A. Penzo and P.G. Ran-
[31 [41 [51
[d t71
if31 [91 DOI [ill [12] [13] [14] [15] [16]
Acknowledgements One of the authors (C.L.1 thanks the Killam Foundation and Canada Council for their support.
coita, Experimental determination of the intrinsic fluctuations from binding energy losses in Si/Fe and Si/Fe + Pb hadron calorimeters, accepted for publication in Nucl. Instr. and Meth. A. R. Wigmans, Nucl. Instr. and Meth. A 259 (1987) 389. C. Leroy, Y. Sirois and R. Wigmans, Nucl. Instr. and Meth. A 252 (1986) 4. F. Lemeilleur et al., SICAPO Collaboration, Phys. Lett. B 222 (1989) 518. A.L.S. Angelis et al., SICAPO Collaboration, Phys. Lett. B 242 (1990) 293. R. Wigmans, Nucl. Instr. and Meth. A 265 (1988) 273. E. Borchi et al., SICAPO Collaboration, Nucl. Instr. and Meth. A 332 (1993) 85. M. Bosetti et al., Nucl. Instr. and Meth. A 345 (1994) 244. S. Pensotti et al., Nucl. Instr. and Meth. A 270 (1988), 327. E. Borchi et al., SICAPO Collaboration, Phys. Lett. B 280 (1992) 169. E. Borchi et al., SICAPO Collaboration, IEEE Trans. Nucl. Sci. NS-38 (1991) 403. G. Drews et al., Nucl. Instr. and Meth. A 290 (19901 335. C. Furetta et al., SICAPO Collaboration, IEEE Trans. Nucl. Sci. NS-35 (1988) 446. A.L.S. Angelis et al., SICAPO Collaboration, Nucl. Instr. and Meth. A 314 (1992) 425. D. Acosta et al., Nucl. Instr. and Meth. A 308 (1991) 481.
NUCLEAR INSTRUMENTS a METNODS IN PHYSICS RESEARCH SectionA
ELSEWER
Experimental determination of the intrinsic fluctuations from binding energy losses in Si/U hadron calorimeters SICAPO Collaboration C. Furetta al1, C. Leroy b,2,* , S. Pensotti a*3,A. Penzo ‘, P.G. Rancoita a aINFN-Milan, I-20133 Milan, Italy b Uniuersitt? de Montrkal, Montrkal (Q&bee) H3C 3J7, Canadn ’ INFN-Trieste, I-34127 Trieste, Italy Received 22 December 1994 Abstract Fluctuations due to binding energy losses were determined experimentally for a sampling hadron calorimeter with an active medium consisting of layers of silicon mosaics. The absorbers were uranium layers @i/U). The calorimeter was exposed to hadrons (protons) at incoming energies of 8, 10, and 12 GeV. The contribution tobind) of the binding energy losses fluctuations to the energy resolution of this compensating hadron calorimeter was found to be obind = 47.8%.
1. Introduction
where
The energy resolution of sampling hadron calorimeters is dominated by sampling and intrinsic fluctuations and by their relative response to electromagnetic showers
= Co/&
+ 4(e/n)
= C/&,
(1)
* Corresponding author. Fax 741 22 767 8350, e-mail leroy@eemvm. cem. ch. ’ And University of Rome, Rome, Italy. * Killam Fellow. 3 And University of Milan, Milan, Italy.
E is the incoming
hadron
energy,
in GeV, and
C = Co + +(e/rr)@; C, = dw contains the contributions from the intrinsic fluctuations mostly due to nuclear binding energy losses (or,,,), and from the sampling fluctuations (a,). The function +(e/rr) is vanishing for e/n = 1, i.e., for compensating calorimeters. Compensation (e/n = 1) is achieved through the equalization of the calorimeter response to electromagnetic and hadronic showers. This equalization in the case of a hadron calorimeter, with silicon readout and uranium as passive medium, can be achieved by suppressing the electromagnetic response of the calorimeter. Experimental evidence was found for a local hardening effect [S] obtained by inserting low-Z absorbers (thin in radiation length units, like GlO layers) next to the silicon detectors in Si/high-Z sampling calorimeters. This effect is responsible for the suppression of the electromagnetic response of the calorimeter due to the absorption (in the low-Z material) of soft electrons. It has been experimentally demonstrated that the local hardening effect was leading to the achievement of the compensation condition (e/n = 1 and, consequently +(e/n) = 0) in silicon calorimeters using U as absorber, by inserting GlO layers in front and at the rear of the silicon detector mosaics [6]. It is known [7] that, for a non-compensating calorimeter, 4(e/rr) has only moderate variations in the 5-15 GeV energy range, which covers the set of data used in the present article. Therefore, by combining direct measurements of the energy resolution with computed and/or
0168-9002/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-9002(95)00114-X
150
C. Furetta et al. /Nucl.
Instr. and Meth. in Phys. Rex A 361 (1995) 149-156
measured values of +(e/rr) (once the e/n calorimeter ratio is experimentally known [2,6,8]), it is possible to determine C,, and finally the fluctuations due to the nuclear binding energy losses, once the sampling fluctuations are evaluated [7]. The present article deals with data obtained from the operation of a calorimeter using silicon as active medium and a passive medium made of layers of uranium @i/U).
2. Sampling hadron calorimeters and binding energy losses The e/n
signal ratio, appearing
in Eq. (l), is defined
as:
e’T=(e/mip)f,,
(ebb) + (h/mip)(l -L)
.
Here, mip is the energy deposited in the sensitive part of the calorimeter by a minimum ionizing particle. The ratio e/mip, in eq. (2), measures the energy deposited in the sensitive part of the calorimeter by electron and photon showers relative to a mip; (h/mip)(l - f,,) is the hadronic energy deposited in the detector readouts by the purely hadronic component of the shower relative to a mip (see Refs. [2,7] and references therein). f,, varies with energy and is the average fraction of the converted electromagnetic energy resulting from the photon decays of rr” and 9 particles produced during the hadron cascade. The logarithmic increase of f,, with the energy, E (- 0.12 In E, E in GeV [3]), results in a e/n signal ratio which is also energy dependent. For a showering hadron, the n/mip ratio is given by n/mip
= (e/mip)f,,
+ (h/mip)(l
-f,,).
(3)
The total visible energy (electromagnetic and hadronic), deposited by hadrons in the calorimeter, can be expressed as:
(4) The energy shared (E,) by a minimum ionizing particle in the silicon detectors is given by E, = EF(Si)
= EG(Si)X,,
,
(5)
energy, and the fraction of energy lost in the depleted layers of the silicon detectors, respectively. Then, Eq. (4) can be rewritten as:
E,i,=zF(Si)[ (&) +L($ - a)].
C6)
Eq. (5) shows that it is only in the situation where e/mip = h/mip (i.e. e/n = 1, the compensation condition) that the calorimeter response is proportional to the incoming energy E, independently of f,, which varies with E. In a sampling calorimeter, the measured energy resolution, ((r(E)/E),,,, is given by: (o(E)/E)exp
= oJevis(n),
(7)
where o+ is the standard deviation value of the Gaussian like distribution of the hadronic visible energy, e,Jn), measured in the calorimeter when no correction for energy losses are included. These losses are longitudinal, lateral, and dead area energy losses. The latter have to be considered particularly for calorimeters with high granularity, which is presently the case for silicon readout mosaics. The effects of energy losses on the energy resolution have been measured experimentally for hadronic and electromagnetic showers. In particular, for hadronic showers, the linear dependence of the hadronic resolution on energy losses has been observed up to energy losses of about 15% [l]. The effect of the fraction of energy lost on the measured energy resolution, discussed in Refs. [1,2,9], can be represented (for energy losses up to 15%) according to Ref. [2]: (o(E)/E),,p
=
(o(WE)(l + CAPP)
= (C/&)(1
+ CAP),
(8)
where P is the percentage of lateral (l), longitudinal (L), and dead area (D) energy losses. A, is a coefficient depending on the type of energy loss [9]. It has been shown that fluctuations produced by the lateral energy losses are less effective, by a factor 2-3, than the longitudinal energy losses [1,9], i.e., A, < A,. Furthermore, it has been also shown [9] that the longitudinal energy losses are as effective as the dead area energy losses, i.e., A, = A,, because both of them are related to event-to-event fluctuations. The experimental data [l] have allowed to determine that, for hadronic showers, the values of A, and A, = A, are 0.027 and 0.077, respectively.
with
(dE/dx)si G(Si) = (dE/dx),,Ls,
3. Experimental set-up and data
+ c (dE/dx)J,
where, Xsi, Lsi, L,, (dE/dx),, E, and F(Si) are the depletion depth, the thickness of the Si detector, the thickness of the absorber i, the average energy loss per unit of length (of a mip) in the absorber i, the incoming particle
The Si/U hadron calorimeter was consisting of 30 uranium absorber plates, each about 1.5 cm thick, interspaced with silicon readout mosaics. The mosaic supporting structure, made of two GlO plates (1.0 and 0.2 mm thick) located in front and at the rear side of the detectors,
C. Furetta et al./Nucl.
151
Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
was equivalent to about 0.23% of interaction length, A 4. Data were taken for several calorimeter configurations where additional GlO plates, 1.0, 3.0, and 5.0 mm thick, were inserted both in front and at the rear of the silicon detectors. Data were also taken with no additional G10 plates. The overall calorimeter depth was about 4.6h on average (namely, about 4.4, 4.5, 4.7, 5.0 A depending on the thickness of the additional GlO plates inserted in the calorimeter structure). The readout of this calorimeter consisted of 30 mosaic planes (with an active area of _ 524 cm2) each made of 18 trapezoidal silicon detectors [6]. The detectors were 400 p,m thick and operated at a depleted layer width of 270 km. The use of serial couplings of five silicon detectors along the beam direction, although reducing the number of electronic channels and the overall detector capacitance, allowed the use of fast electronics (about 200 ns base-time signals) with a wide dynamical range (five decades) and permitted the readout of the calorimeter into six longitudinal sections. The electronic readout is described in details in Ref. [IO]. The calorimeter was operated at the t, beam at the CERN Proton Synchrotron (PSI, at incoming energies of 8, 10, and 12 GeV. Two gas Cherenkov counters were used to separate electrons and hadrons. A beam scanner, consisting of a scintillation counter of 0.5 X 0.5 cm2 area, ensured that only those hadrons impinging on the middle of the calorimeter triggered. The absolute energy calibration was performed following two independent approaches (as described elsewhere [6]): i) by measuring the energy deposited by 233U (Y sources (4.8 MeV on average) located on top of the silicon detectors; ii) by minimum ionizing particles (p) which give a well known energy-loss distribution in the silicon readout detectors. The two methods agreed well with each other and the error on the absolute energy scale was about 2%. For each group of 5 detector sets, the standard deviation of the Gaussian noise distribution was 177 keV, corresponding to a signal of = 0.4 mip. This was measured before and after each data taking run, allowing for the correction of the experimental visible energy distributions for these electronic noise effects. As mentioned above, the calorimeter was divided into 6 sections along the beam direction, each section being readout independently. This allowed an estimate of the longitudinal loss of the visible energy by extrapolating the exponential fall of the longitudinal shower development beyond the shower maximum. The longitudinal hadronic
’ A is given by A /N, u [cm] = 35 A’13/ p [cm], where A, N,,, p, and c are the mass number, the Avogadro number, the density of material, and the proton inelastic cross section for the material, respectively. The U absorber interaction length is 10.5 cm.
20
15
S g
IO
W
5
0
0
2
4
6
8
IO
12
E (GeVl Fig. 1. The visible energy lvis in the Si/U calorimeters as a function of the incoming energy. From top to bottom: no GlO plates, 1.0, 3.0, and 5.0 mm thick G10 plates, added both in front and at the rear of the silicon detector mosaics. The lines are: q&o GlO) = (1.25 +0.25)E +(1.70 k2.48) [MeV], c,&.O mm GlO) = (1.17*0.24)E +(1..54+2.35) [MeV], c&3.0 mm GlO) = (1.11+0.23)E +(1.74*2.24) [MeV], •,,~~(5.0 mm GlO) = (1.09 f 0.22)E + (1.71+ 2.17) [MeV], respectively. E is in GeV.
visible energy losses 5 were estimated to be (2.0 f 1.3)%, (3.3 rt 1.7)%, and (3.8 f 1.71% at 8, lo1 and 12 GeV, respectively. These data are in agreement with previous measurements [6,11]. The measured visible energy had to account for the energy losses in the dead zones between detectors in the mosaics. The dead area energy losses amounted to (3.7 f l.O)% (see Ref. [6]). A dedicated run was carried out to measure the visible energy lateral losses. The lateral losses were measured using two mosaics planes [12], each made of 35 trapezoidal silicon detectors (400 pm thick and depleted at 200 pm). The two mosaics planes were serially coupled in order to present an active thickness of 400 km. The measurements were made with the two mosaics installed in the calorimeter at depths varying from 0.5 to 5 A. The detectors were assembled in a mosaic to form 7 horizontal strips. Each strip, made of five silicon detectors, was about 4 cm large. The overall active area was about 1019 cm’. The estimated value of the overall lateral loss of the hadronic visible energy for the present calorimeter is (5.1 f 2.21% at incoming proton energies of 8, 10, and 12 GeV, for the present calorimeter.
’ The errors take also into account the effect of the calorimeter depth variation when the GlO plates are added.
152
C. Furetta et al. / Nuct. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
The measured visible hadron energy (E+) for the Si/U calorimeter is shown in Fig. 1 as a function of the incoming proton energy for several thicknesses of GlO plates added both in front and at the rear of the silicon detector mosaics. The values reported in Fig. 1 were corrected for the longitudinal, lateral and dead area energy losses effects described above. lVis shows a linear behaviour with the incoming proton energy, within the experimental errors.
The measured energy resolutions ((u(E)/E),,,), when no correction for dead area, lateral and longitudinal energy losses are taken into account, are shown in Figs. 2a-2d for no GlO plates, 1.0, 3.0, and 5.0 mm thick GlO plates added both in front and at the rear of the silicon mosaics, respectively. In each case, (c+(E)/E),,, behaves as a linear function of l/G, within the experimental errors. These results allows the determination of the values of C
90
(b) &
60::
W
: -
c
30-
0 0.0
0.2
0.4
0.0
/
I
I 0.2
I
I 0.4
M/m
I/&iGz 90
90 (d)
60
30
00.0
0.2
0.4
l/&Ezz as a function of l/ 6, is shown for no additional GlO plates inserted in front Fig. 2. (a) The measured energy resolution ((a(E)/E&,), as a function of l/G, is shown for 1.0 mm and at the rear of the silicon mosaics. (b) The measured energy resolution ((u(E)/E),,,) thick additional GlO plates inserted in front and at the rear of the silicon mosaics. (c) The measured energy resolution (((r(E)/E),,,) as a function of l/@, is shown for 3.0 mm thick additional GlO plates inserted in front and at the rear of the silicon mosaics. (d) The measured energy resolution ((a(E)/E),,J as a function of l/G, is shown for 5.0 mm thick additional GlO plates inserted in front and at the rear of the silicon mosaics.
153
C. Furetta et al. / Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156 Table 1 The value of C and its weighted average (C(w.v.)), as a function of the hadron energy, for the Si/U calorimeter E [GeV]
no GlO
1 mm GlO
3 mm G10
5 mm GlO
12 10 8 C(w.v.)
94.3k11.7 93.6f11.6 9O.lk11.8 92.7+ 6.8
77.6* 9.5 88.2kll.O 87.4+10.7 83.8+ 6.0
91.8+11.2 90.1+11.1 87.6+10.8 89.8+ 6.4
91.6k10.4 88.5+10.3 89.0+10.5 89.7* 6.0
electromagnetic response, can be achieved by the local hardening effect obtained by inserting low-Z absorbers (like GlO, Al, polyethylene) next to the silicon detectors [6,12,14]. The degree of hardening depends on the thickness of the low-Z absorbers and on their location in front and/or at the rear of the detectors [12,14]. These low-Z absorbers must have a small ratio: H=L
low-Z/Lhigh-Z~
(Lhigh_z) is the thickness in units of radiation low_z length, Xa, of the low-Z (high-Z) absorber. The local hardening effect has been achieved and studied for HI 2.5% [15], and for low-Z materials such as GlO, Al and polyethylene. Following the local hardening effect, at a given thickness and location of the low-Z material next to the silicon readout plane, the electromagnetic visible energy is reduced independently of the high-Z absorber sampler thickness, according to:
where L (C/ fi = a(E)/,!?) for the corrected energy resolution, once the effects of the visible energy losses on the measured energy resolution are taken into account (Eq. (8)). Table 1 shows the values of C evaluated for the various insertions of GlO plates in front and at the rear of the silicon detectors and as a function of the incoming hadron energy. The weighted average values of C (C(w.v.)) are (92.7 + 6.8)%, (83.8 + 6.0)%, (89.8 k 6.4)% and (89.7 f 6.0)% for 0.0, 1.0, 3.0, and 5.0 mm thick additional Cl0 plates inserted in the Si/U calorimeter structure, respectively.
R,h(LwZ) =
E,is(Lhigh-Z) - ‘vis( L10W-Z7 Lhigh-Z)
=I-
%is( f,is(
Llow-Z) Evis(
4. Determination
of the intrinsic fluctuations
in U
Sampling fluctuations (or) and intrinsic fluctuations (obind) are contributing to the overall energy resolution of hadronic sampling calorimeters, the latter being mostly due to the binding energy losses because of nuclear break-up. The contribution from the sampling fluctuations (or) can be computed from the parametrization [13]: ur = Il.S%JhE,
(9)
where AE is the average energy, in MeV, deposited by a minimum ionizing particle in one passive sampler [13]. The sampling fluctuation contributions depends on the thickness of GlO inserted in each sampling. a,, as calculated from Eq. (9) is reported in Table 2, for the various thicknesses of the GlO plates inserted and varies from or = 64.5% (no additional GlO plates inserted) up to a, = 67.6% (5.0 mm thick GlO plates inserted in front and at the rear of the silicon mosaics).
The values of the e/n ratio for the various Si/U calorimeter GlO configurations (i.e., the calorimeter configuration with no additional GlO plates, and the three configurations where two additional GlO plates 1.0, 3.0, and 5.0 mm thick were located in front and at the rear side of the detector mosaics) are about those measured in Ref. [6] for the same Si/U calorimeter GlO configurations and incoming proton energies, but with different U sampler thicknesses. This is because the tuning of the e/mip ratio, i.e. the variation of the e/mip value of a Si/U calorimeter
Lhigh-Z)
(11)
L high-Z
where E,&?I,~~~~_~)is the visible energy for a calorimeter having a passive sampler of thickness Lhigh_Z and where E,~~(L,~~_~, Lhigh_Z) is the visible energy for the same calorimeter but with low-Z absorbers (of thickness L,,.,) added next to the silicon readout planes. R,h(L,ow_Z), to a first approximation, depends on the location and thickness of the low-Z absorber, but not on the Lhigh_Z thickness of the high-Z sampler [6,12,14,15]. For an electromagnetic shower in a sampling calorimeter, lvis = (e/mip)E, (E, is given by Eq. (5)) and when only high-Z absorbers are used for samplers, the e/mip value is almost independent of the sampler thickness (see Ref. [3] for U sampler thicknesses larger than 2X, and Ref. [16] for e/mip values measured for Pb sampler thicknesses of 1.96 and 3.39 X0). For electrons incident on a Si/U electromagnetic calorimeter, with GlO plates inserted next to the active medium and the local hardening effect in operation, the ratio of e/mip(U, GlO) to e/mip(U) is given by: e/mip(U,
4.1. e/ n ratio values of the Si/ U calorimeter
L high-2 1
GlO)
E,is(UT G10) -_Es(U) GlO) e&U)
= E,(U,
e/mip(U)
’
(12)
Table 2 The value of at&eff) (weighted mean over the incoming energies), a, and e/ 7~,as a function of the thickness of the additional inserted GlO plates no
a,,&eff)[%] “r [%I e/r
GlO
67.1+4.9 64.5 1.27
1 mm GlO 3 mm GlO 5 mm GlO 50.5k3.7 65.1 1.03
6O.Ok4.3 66.4 0.90
59.4+4.0 67.6 0.86
C. Furetta et al. /Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
154
where e/mip@J, GlO) (e/m@(U)) is the e/mip ratio for a Si/U calorimeter with a sampler of length L, and additional (no additional) GlO plates present; the notations E&J, GlO), E&J>, E&U, GlO), E,(U), ~/m&&J, GlO), n/m@(U), have the same meaning for the total visible energy (E&, the energy shared (E,), and the ratio a/mip. From Eq. (ll), e/mip(U,
GlO) = E,(ttluG);o)
(I-
R,,(GIO)).
(13)
e/mip(U)
304 -I
For two Si/U calorimeters with an identical GlO structure, but with different sampler thicknesses (L, and &I), because e/mip&J) m e/mip&J’), we have (from Eq. (13)): e/mip(U,
GlO)
e/mip(U’,
GlO)
=-
E,(U)
&(U’,
GlO)
Q(U’)
-WJ,
GlO)
(14)
n/mip(U,
GlO)
GlO) = E&U’,
c,is(U, GlO) GlO)
4(U’,
GlO)
E,(U,
GlO) ’
e/rr(U,
GlO)
e/n(U’,
GlO)
= =
2
3
4
5
6
GIO (mm) Fig. 4. v represents the calculated values of ub,,,(eff) (0) and of qbind (0) (using the values of C from Table 1) which are shown as a function of the thickness of GlO (in mm) inserted in front and
(I5)
where e&J, GlO) and e&J’, GlO) are the visible hadron energies measured at the same incoming hadron energy for the sampler thicknesses L, and L,,, respectively. From Eqs. (14) and (15), the e/n signal ratios relative to these Si/U calorimeters, are related according to: R(e/n)
I
at the rear of the silicon mosaics. The curve is to guide the eye. The line corresponds to the gbind weigthed value: gbind = 47.8%.
and from Eq. (3), we have for incident hadrons:
rr/mip(U’,
0
l,is(U’)
G10)
E,(U)
E,is(U,
G10)
E,(U’)
(16) Fig. 3 shows the ratio R(e/m) for a U sampler 2.5 cm (data from Ref. [6]) and 1.5 cm thick (this experiment). The ratio Z&(2.5 cm U)/E,(1.5 cm U) was calculated using Eq. (5). The ratios ~$1.5 cm U, GlO)/e,,(2.5 cm U,
GlO) were evaluated from an average (on the incoming hadron energies of 8, 10, 12 GeV) of the measured visible energies in this experiment (Fig. 1) and those measured in the previous experiment (Ref. [6]). In Fig. 3, the four GlO structures are: no additional G10 plates (only, the 1.2 mm thick GlO supporting structure of the silicon mosaics), and the three structures where two additional GlO plates 1.0, 3.0 and 5.0 mm thick were located in front and at the rear of the silicon mosaics. It can be seen, in Fig. 3, that the R(e/n) values are well consistent with 1. This indicates that the calorimeter structure properties which determine the value of the e/a ratio are mainly due to the GlO structure, because of the local hardening effect. Thus, for the present Si/U calorimeter, the e/n ratios are those measured in Ref. [6] and reported in Table 2. Determination tions in U
4.2.
of the binding energy losses j?uctua-
Eq. (1) can be rewritten as:
0.01
3 GIO
Fig. 3. The ratio R(e/m)
5
(mm)
is shown for a U sampler 2.5 em (data 1.5 cm thick (this experiment). The line
from Ref. [6]) and represents R(e/v) = 1.
where obind(eff) includes the effect of non-compensation on the calorimeter energy resolution. For a compensating calorimeter, the e/n ratio, i.e. the ratio of the electron to hadron visible energy measured at the same particle energy and in the same calorimeter configuration, is equal to 1, and o,,&eff) = obind. From Eqs. (1) and (171, one has: a,,,(eff)
= /w.
155
C. Furetta et al. / Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 149-156
-
35
a-”
25 60-
b
50-
15
403020 0.3
5 “s’m”‘~‘m” 0.5 0.7
0.9
I.1
1.3
1.5
1.7
e/r
value: rhind = 47.8%.
The calculated weighted average (on the incoming energies) values of mbind(eff) (using, at each energy, the values of C from Table 1) are shown in Fig. 4 as a function of the thickness of GlO inserted in front and at the rear of the silicon mosaics. The values of ubind(eff) are also shown in Fig. 5 as a function of the e/r ratio. It can be observed that gbind(eff) = (50.5 + 0.3)% for a thickness of 1.0 mm for the additional G10 plates inserted in front and at the rear of the readout silicon active planes, namely for a ratio e/a = 1.03. The intrinsic fluctuations contributions in the Si/U calorimeter, cbind, can be determined once the function 4(e/T) (see Eq. (1)) is evaluated. As emphasized before, the function $(e/v) accounts for the effect of non-compensation on the calorimeter energy resolution. From Eq. (l), one has: ubind =
{(c - +(e/71)&)’- u:.
(18)
The values of 4(e/n) have been estimated by interpolating the results of Monte Carlo simulations on the energy resolution dependence on incoming energy reported in Ref. [7], for e/n ratios of 0.76, 0.85, 1.14, 1.26 and 1.47, at 10 GeV. From these simulations, one can estimate 4(e/n) and e/n which are almost energy independent in the 5-15 GeV energy range. The function &e/T) is shown in Fig.
7\D
e
.
5-
F
3
9
I
1
0.6
Fig. 5. (r represents the calculated values of cbi,,&eff) (0) and of crbind (0) which are shown as a function of the e/r ratio. The curve is to guide the eye. The line corresponds to the gbind weigthed
~
--
_---.-----I
I
I
0.8
I
1.0
I
I
1.2
a
_I
I.4
e/*
Fig. 7. The additive tern function of e/r
@(e/m)&. (E = 8, 10, 12 GeV).
in [%I, is shown
as a
6 as a function of e/n, for the 5-15 GeV energy range. In Fig. 6, &e/a) is estimated to be about 0.9% (in the 5-15 GeV energy region) for e/r about 1.11. This value is in agreement, within the experimental errors, with the results reported in Ref. [16], where @(e/n) = (1.0 f O.l)% for e/n = 1.107 f 0.006 at 9.7 GeV. In Fig. 7, 4(e/a)& is shown for the incoming energies of 8, 10 and 12 GeV. Using the values of 4(e/r)& (corresponding to the e/a ratios given in Table 2), those of C reported in Table 1, and the values of ur as given by Eq. (9), it becomes possible to estimate cbind (Eq. (18)). The weighted average values of cbind (from a weighted average of the ubind values obtained for the different GlO calorimeter structures) is (47.8 + 1.9)%. This result is in agreement with the value gbind = (4246)% predicted in Refs. [3,7] for the case of negligible or low neutron absorption. In order to decrease the contribution due to the intrinsic fluctuations, particularly for high-A materials, it is necessary to employ hydrogeneous materials, in which part of the neutron energy can be detected by the scintillation process induced by the recoiling proton after a proton-neutron scattering. Calorimeters which have a scintillator as active medium and a larger ratio, R, of the active (scintillator 3.0 mm thick) to passive (U thickness of 3.2 mm) medium thicknesses, have shown smaller binding energy losses fluctuations [16]: cbind = (20.4 + 2.4)%, as previously predicted in Refs. [3,7].
5. Discussion and conclusions
0)
; _
I. 0.5
-_---
\J_
--_--
I.
1
0.7
0.9
.
I
I.1
I
I
I
1.3
e/*
Fig. 6. 4(e/ 7~)is shown as a function of the e/ TI ratio.
I 1.5
Binding energy losses originate from the fluctuating large amount of the deposited energy which goes in breaking nuclei during the hadronic cascading. The resulting fluctuations contribute to the energy resolution of hadron calorimeters. The fluctuations due to binding energy losses for U were determined by combining direct measurements of the energy resolution (which give C), estimates of
156
C. Furetta et al. /Nucl.
Ins@. and Meth. in Phys. Res. A 361 (1995) 149-156
+(e/n) using previous experimental measurements of the e/n ratio, and calculation of sampling fluctuations, for silicon calorimeters with U as absorbers. The determined values of the effective binding energy loss fluctuations (at e/n = 1.27, 1.03, 0.90, 0.861, u,,,,(eff), which include both the intrinsic fluctuations and the non-compensating effect on the energy resolution, have the lower value for e/n = 1.03. The binding energy losses depend on the fraction of neutron energy detected by the active sampler. In the present work, the ratio, R, of active to passive medium thicknesses is very small and little of the neutron energy is seen by the active medium, leading to large intrinsic fluctuations from binding energy losses. Our result obind = 47.8% is found in agreement with earlier predictions made when neutron absorption is negligible [3]. It can be also compared to previous results [2] obtained for Fe and Pb: o,,ind[Fe] = (16-B)% and osind[Pb] = (49-45)%. It was also observed [2] that, for an almost compensating Si/Fe + Pb calorimeter, the contribution of the intrinsic fluctuations to the overall energy resolution originated mostly from the binding energy losses, ubind[Fe + Pb], which was about 24.5%. Furthermore, the visible energy, lVis, has shown a linear dependence on the incoming hadron energy, within the experimental errors.
References [ll U. Amaldi, Phys. Scripta 23 (1981) 409.
La C. Furetta, C. Leroy, S. Pensotti, A. Penzo and P.G. Ran-
[31 [41 [51
[d t71
if31 [91 DOI [ill [12] [13] [14] [15] [16]
Acknowledgements One of the authors (C.L.1 thanks the Killam Foundation and Canada Council for their support.
coita, Experimental determination of the intrinsic fluctuations from binding energy losses in Si/Fe and Si/Fe + Pb hadron calorimeters, accepted for publication in Nucl. Instr. and Meth. A. R. Wigmans, Nucl. Instr. and Meth. A 259 (1987) 389. C. Leroy, Y. Sirois and R. Wigmans, Nucl. Instr. and Meth. A 252 (1986) 4. F. Lemeilleur et al., SICAPO Collaboration, Phys. Lett. B 222 (1989) 518. A.L.S. Angelis et al., SICAPO Collaboration, Phys. Lett. B 242 (1990) 293. R. Wigmans, Nucl. Instr. and Meth. A 265 (1988) 273. E. Borchi et al., SICAPO Collaboration, Nucl. Instr. and Meth. A 332 (1993) 85. M. Bosetti et al., Nucl. Instr. and Meth. A 345 (1994) 244. S. Pensotti et al., Nucl. Instr. and Meth. A 270 (1988), 327. E. Borchi et al., SICAPO Collaboration, Phys. Lett. B 280 (1992) 169. E. Borchi et al., SICAPO Collaboration, IEEE Trans. Nucl. Sci. NS-38 (1991) 403. G. Drews et al., Nucl. Instr. and Meth. A 290 (19901 335. C. Furetta et al., SICAPO Collaboration, IEEE Trans. Nucl. Sci. NS-35 (1988) 446. A.L.S. Angelis et al., SICAPO Collaboration, Nucl. Instr. and Meth. A 314 (1992) 425. D. Acosta et al., Nucl. Instr. and Meth. A 308 (1991) 481.