Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection

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630 Principles of Radiation Interaction in Matter and Detection

Fig. 9.6 Reduction in percentage of the electromagnetic visible-energy, measured with Si/U and

Si/W calorimeters, expressed as ∆ ²/²[%] = 100[²

vis

(no G10) − ²

vis

(G10)]/²

vis

(no G10) versus the

G10 plate thickness inserted at the rear of the silicon readout detectors (from [Leroy and Rancoita

(2000)], see also [SICAPO Collab. (1989b)]).

The local hardening eﬀect requires thin (in units of radiation length) low-Z

absorbers. If their thickness is increased so much that they start to become part of

the shower generation process, the e/mip ratio will increase again as indicated by

EGS4 simulations [Wigmans (1988)] and the experimental data of Fig. 9.6. In fact,

the data show an approximate logarithmic increase of ∆²/² with the G10 thickness,

while [Eq. (9.4)] the value of 1/E

is linearly increasing with the G10 thickness.

A further reduction of the e/mip ratio is achievable by inserting low-Z plates

both behind and in front of readout detectors. The eﬀect was also observed,

when diﬀerent low-Z absorbers (like polyethylene and aluminum) [SICAPO Col-

lab. (1992b)] are employed.

The extent to which the reduction in the e/mip ratio can be achieved dep ends

on the readout layer thickness in g/cm

. As the readout layers thickness increases,

the maximum reduction achievable decreases, for instance we have e/mip(0.5 mm

Fe) ≈ 0.92 e/mip(noFe) using scintillator readout plates 2.6 mm thick in a uranium

(uranium plates wrapped in stainless steel) sampling calorimeter [Wigmans (1988)].

Although the lo cal hardening eﬀect largely reduces the e/mip ratio in calorime-

ters employing high-Z media, it was also observed when medium-Z passive samplers

(like Fe) were used [SICAPO Collab. (1993b)]. However, as predicted, the eﬀect is

smaller. In an iron calorimeter (with 30 mm-thick passive samplers), the visible

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Principles of Particle Energy Determination 631

energy is reduced by ≈ 8%, while E

is reduced by ≈ 1.2% when plexiglas layers

(1.6 mm in front of and 0.8 mm behind the silicon readout detectors) are introduced.

9.3 Principles of Calorimetry with Complex Absorbers

For complex absorbers we mean a set of media with large diﬀerences in their critical

energies and with thicknesses, which are non-negligible for the process of shower

generation. These absorbers can be used as passive samplers in sampling calorimetry.

We have seen how, in the generation and propagation process of a shower in com-

plex absorbers, low-energy photons lead to the generation of low-energy electrons

by Compton and photoelectric eﬀects, which have a diﬀerent Z dependence. This

Z-dependence explains the diﬀerential attenuation of radiation in absorbers. Most

of these generated low-energy electrons are generally absorbed before they reach

the readout medium. Thus, a signiﬁcant change in the soft-energy deposition can

be expected if materials with large diﬀerences among their critical-energy values,

i.e., with large diﬀerence in Z

absorber

values, are set in sequence in the complex

absorber sampler.

Fig. 9.7 e/mip as a function of the Pb fraction, f , in the passive sampler in various calorimeter

conﬁgurations measured using 4 GeV electrons: Pb+Fe+Pb [sandwich conﬁguration (◦)], Fe+Pb

[F-conﬁguration (×)] and Pb+Fe [R-conﬁguration (•)] (reprinted from Phys. Lett. B 222, Borchi,

E. et al., Electromagnetic shower energy ﬁltering eﬀect. A way to achieve the compensation con-

dition (e/π=1) in hadronic calorimetry, 525–532, Copyright (1989), with permission from Else-

vier, e.g, for the list of the authors see [SICAPO Collab. (1989c)]; see also [Leroy and Rancoita

(2000)]). In these conﬁgurations, the thickness of the Fe absorber in each passive sampler was

corresponding to 1.99 X

. The lines are to guide the eye.

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632 Principles of Radiation Interaction in Matter and Detection

Fig. 9.8 ²

vis

τ in MeV τ as a function of the sampling frequency τ in various calorimeter conﬁgurations measured using 4 GeV electrons: Pb+Fe+Pb

[sandwich conﬁguration (2)], Fe+Pb [F-conﬁguration (4)] and Pb+Fe [R-conﬁguration (◦)] (reprinted from Phys. Lett. B 222, Borchi, E. et al.,

Electromagnetic shower energy ﬁltering eﬀect. A way to achieve the compensation condition (e/π =1) in hadronic calorimetry, 525–532, Copyright

(1989), with permission from Elsevier, e.g, for the list of the authors see [SICAPO Collab. (1989c)]; see also [Leroy and Rancoita (2000)]). In the

above conﬁgurations, the thickness of the Fe absorber in each passive sampler was corresponding to 1.99 X

. The conﬁguration with Pb (×) and Fe

(•) absorbers alone are also shown. The lines are to guide the eye.

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Principles of Particle Energy Determination 633

Fig. 9.9 Mean energy deposited by electrons in the Si/(Fe,Pb) calorimeter as a function of the

incoming energy (reprinted from Nucl. Instr. and Meth. in Phys. Res. A 332, Borchi, E.

et al., Systematic investigation of the electromagnetic ﬁltering eﬀect as a tool for achieving the

compensation condition in silicon hadron calorimetry, 85–90, Copyright (1993), with permission

from Elsevier, e.g, for the list of the authors see [SICAPO Collab. (1993b)]; see also [Leroy and

Rancoita (2000)]). The sampling thickness is 23 mm. The top points correspond to the case where

there is no Pb in the absorber. The other points correspond to conﬁgurations where the thickness of

Pb in the PbFe–Si–PbFe absorber conﬁguration is (from top to bottom) 3.0, 8.0, and 13.0 mm. The

lines are to guide the eye.

In general, when complex absorbers are employed the energy deposition rate will

change because the shower composed of charged particles and photons generated in a

medium has to deposit its energy according to the stopping power and the attenuation

length of another material. It can be concluded, as seen on page 214, that the

process of shower energy deposition is aﬀected by the sequence of absorbers. As a

consequence, the e/mip ratio also varies depending on the sequence of the absorbers,

when a complex absorber is employed. However, an additional slight variation may

be expected as a function of the type and thickness of the readout detector. This

phenomenon was experimentally observed and referred to as the electromagnetic

shower energy ﬁltering eﬀect [SICAPO Collab. (1989c)].

It has to be emphasized that low-energy phenomena, i.e., the energy loss of

electrons and positrons close to the critical energy and soft-photon interactions

by Compton or photoelectric eﬀects, are the main processes of shower energy de-

position. While interactions by soft electrons and positrons were considered in an

approximate way, the full complexity of low-energy photon interactions was not

taken into account at all in the framework of “Approximation B”. Consequently, as

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634 Principles of Radiation Interaction in Matter and Detection

Fig. 9.10 Mean energy deposited by electrons in the Si/(Fe,Pb) calorimeter as a function of the

incoming energy (reprinted from Nucl. Instr. and Meth. in Phys. Res. A 332, Borchi, E.

et al., Systematic investigation of the electromagnetic ﬁltering eﬀect as a tool for achieving the

compensation condition in silicon hadron calorimetry, 85–90, Copyright (1993), with permission

from Elsevier, e.g, for the list of the authors see [SICAPO Collab. (1993b)]; see also [Leroy and

Rancoita (2000)]). The sampling thickness is 23 mm. The top points correspond to the case where

there is no Pb in the absorber. The other points correspond to conﬁgurations where the thickness of

Pb in the FePb–Si–FePb absorber conﬁguration is (from top to bottom) 3.0, 8.0, and 13.0 mm. The

lines are to guide the eye.

remarked on page 623, the transition eﬀect introduced by Pinkau does not play any

eﬀective role in explaining the behavior of the visible energy and the e/mip ratio

for a sampling calorimeter with complex absorbers.

9.3.1 The Filtering Eﬀect and how to tune the e/mip Ratio

The reduction of the e/mip ratio as the result of the reduction of the electromag-

netic visible-energy in a sampling calorimeter was experimentally observed using

both Fe and Pb plates as passive samplers and silicon detectors as active read-

out media [SICAPO Collab. (1989c)]. The e/mip ratios of three passive sampler

conﬁgurations

∗

along the shower axis were investigated: Fe+Pb (F-conﬁguration),

Pb+Fe (R-conﬁguration) and Pb+Fe+Pb (sandwich conﬁguration). They are shown

∗

In these conﬁgurations, the thickness of the Fe absorber in each passive sampler was correspon-

ding to 1.99 X

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Principles of Particle Energy Determination 635

in Fig. 9.7 as function of the Pb absorber fraction (f) in the passive sampler, with

f =

P b

+ L

F e

, (9.14)

where L

F e

and L

P b

are the thicknesses of Fe and Pb absorbers, respectively. Data

were also taken with Fe and Pb plates alone (as passive samplers): in Fig. 9.8

the corresponding values of the visible energies (²

vis

) multiplied by the sampling

frequency (τ), measured using 4 GeV electrons, are shown as function of τ . For

f & 5%, the e/mip ratios resulted to be

e/mip (Pb+Fe+Pb) > e/mip (Fe+Pb) > e/mip (Pb+Fe).

Furthermore, a strong evidence of anomalous energy deposition during the shower

propagation was obtained by the measurements of e/mip ratios for Fe alone, Pb

alone and a R-conﬁguration, in which the Pb absorber was a fraction

f ≈ 36%

of the total Pb+Fe length (= L

P b

+ L

F e

); the e/mip ratios found were 0.78±0.02,

0.69±0.04, and 0.60±0.02, respectively. These measurements indicate that, using

Pb and Fe absorbers together (Fe+Pb), the e/mip value is lower than the cor-

responding values obtained, when Fe and Pb absorbers are used alone [SICAPO

Collab. (1989c)]. Furthermore for the R-conﬁguration, the measured e/mip ratio

was found to decrease linearly with the increase of the Pb fraction f (Fig. 9.7).

The visible-energy variation was also experimentally observed, when scintillators

were used as the readout medium. The SDC calorimeter group has carried out

measurements using the so-called Hanging-File Calorimeter, in which scintillator

plates were read out by wavelength shifting ﬁbers [Beretvas et al. (1993)]. Two of

the tested conﬁgurations [Byon-Wagner (1992); Beretvas et al. (1993); Job et al.

(1994)] had the passive sampler made of 25.4 mm Fe and 3.2 mm Pb absorbers:

along the shower axis, one had the aluminium cladded scintillator sandwiched by

lead upstream and iron downstream (as for the F-conﬁguration), the other one by

iron upstream and lead downstream (as for the R-conﬁguration). An analysis of

experimental data (see [Byon-Wagner (1992); Job et al. (1994)] and Sect. 9.9.2)

shows that the e/mip ratio is larger in the former conﬁguration than in the latter

one, again because of the ﬁltering eﬀect (experimentally observed for the ﬁrst time

by SICAPO Collaboration in [SICAPO Collab. (1989c)]).

A systematic study of the ﬁltering eﬀect was performed ([SICAPO Collab.

(1993b)] and references therein) using silicon detectors as readout medium. Data

were taken for Fe+Pb (F-conﬁguration) and Pb+Fe (R-conﬁguration) with an over-

all ﬁxed length of 23 mm for the passive sampler, as a function of the Pb thickness

(no Pb, and 3, 8, 13 mm of Pb). For a given Pb thickness and conﬁguration, the

thickness of lead was kept constant, as well as the respective positions of the ab-

sorbers plates inside each passive sampler. Data were also taken with Fe as the

only absorber for comparison. The mean energies deposited in the calorimeter for

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636 Principles of Radiation Interaction in Matter and Detection

incoming electron energies between 6 and 12 GeV are shown in Figs. 9.9 (for R-

conﬁguration) and 9.10 (for F-conﬁguration). In all cases, ²

vis

is found to be a

linear function of the incident energy. The value of E

does not depend on the ab-

sorber sequence order, i.e., on the conﬁguration, as can be seen from Eq. (9.4) for

ﬁxed Fe and Pb thicknesses. Then, Eq. (9.6) shows that the ratio of the measured

vis

for the two conﬁgurations gives the ratio of their e/mip values:

vis

(F)

vis

(R)

e/mip(F)

e/mip(R)

. (9.15)

The ratio (averaged over the incoming energies) of the visible electromagnetic ener-

gies, i.e., the ratio of the e/mip values measured in the F- to the R-conﬁgurations, is

observed to increase with the thickness of Pb: 1.08 ±0.02 (3 mm of Pb), 1.20 ±0.02

(8 mm of Pb), and 1.23±0.03 (13 mm of Pb). Data were also taken with 30 mm deep

samplers, as a function of the Pb thickness (no Pb, and 5, 10, 15 mm of Pb). The ra-

tio of the electromagnetic visible-energy measured in the F- to the R-conﬁgurations,

for the 30 mm thick passive samplers and averaged over the incoming energies, varies

from 1.17 ± 0.02 (5 mm of Pb) up to 1.26 ± 0.02 (15 mm of Pb). Thus, the general

behavior of the e/mip ratios as a function of the Pb thickness, observed in the

data obtained with 23 mm thick samplers, is conﬁrmed. These determined ratios of

e/mip values are shown in Fig. 9.11 as a function of the Pb thickness: the beha-

vior indicates a value increasing almost linearly with the Pb thickness. All above

reported results can be understood in terms of the ﬁltering eﬀect.

The combination of low-Z (Fe) and high-Z (Pb) materials in passive samplers

of a silicon calorimeter leads to an electromagnetic cascade energy transformation

eﬀect, generated by changing the medium generating the shower when the critical

energies diﬀer greatly (²

= 7.4 MeV and 21.0 MeV for Pb and Fe, respectively). The

value of ²

is the value of the electron energy below which the energy loss by ioni-

zation begins to dominate the energy loss by bremsstrahlung. Consequently, the in-

crease of the critical energy of the absorber favors the energy loss by ionization with

respect to the energy loss by radiation. The energy spectra of incident electrons (and

positrons) are softer in a high-Z absorber (Pb) than in a low-Z (Fe) absorber. The

stopping power by collision is larger and dominates the stopping power by radiation

up to higher electron energies, namely up to about 21 MeV, in Fe absorber com-

pared with lead. Then, for R-conﬁgurations, in which the electromagnetic cascade

develops at ﬁrst in lead and subsequently in iron, the forward-going electrons are

absorbed faster. These experimental data were reproduced by EGS4 Monte-Carlo

simulations [Hirayama (1992)], which were also predicting that the ﬁltering eﬀect

can be applied to sampling calorimeters using scintillators as the active media.

The eﬀect depends on the Pb fraction, f, since the number of low energy elec-

trons generated in lead increases by increasing f, and is also related to the Fe sam-

pling thickness, because this thickness determines the maximum absorbable electron

energy.

The reduction of the electromagnetic visible-energy for the R-conﬁguration with

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Principles of Particle Energy Determination 637

respect to the F-conﬁguration is the result of a larger energy deposition in the Fe

absorber, before the shower traverses the active readout detectors. This reduction

increases with the thickness of Pb in the absorber. As a consequence, the e/mip

ratio of the R-conﬁguration decreases compared with the one of the F-conﬁguration,

as shown in Fig. 9.11. The largest observed reduction [SICAPO Collab. (1993b)]

takes place for the case where 15 mm Fe and 15 mm Pb absorbers are used as passive

samplers:

e/mip(F-conﬁguration)

e/mip(R-conﬁguration)

≈ 1.26,

namely,

e/mip(15mmPb + 15mmFe) ≈ 0.79 e/mip(15mmFe + 15mmPb). (9.16)

In summary, the ﬁltering eﬀect is produced by the combination of low- and high-

Z materials in the absorber, which leads to a transformation of the development of

the electromagnetic cascade energy. Here, two absorbers are used to transform the

distribution of the cascade energy before it reaches the readout, which has to be

properly located in the calorimeter conﬁguration (high-Z)-(low-Z)-readout in order

to obtain the required electromagnetic visible-energy reduction and consequently a

decreased e/mip value.

In the case of the ﬁltering eﬀect, the e/mip ratio is controlled by the modiﬁed in-

trinsic absorption of soft particles, mainly in the passive samplers during the shower

generation and propagation. This is a feature unique to the ﬁltering eﬀect. In fact,

it should be stressed that, in the case of the local hardening eﬀect, the properties

of soft electrons were also exploited, but the additional low-Z absorbers had to

be thin in units of radiation length in order not to modify the shower generation

and propagation characteristics. Indeed, the ﬁltering eﬀect uses the combination of

low-Z and high-Z absorber materials, as cascade generators, in order to produce a

considerable transformation of the initial incoming cascade.

9.3.2 e/mip Reduction by Combining Local Hardening and

Filtering Eﬀects

The e/mip ratio can be further reduced by combining the local hardening and

ﬁltering eﬀects [SICAPO Collab. (1989c, 1992b)], when medium- (or low-) and

high-Z materials are jointly used as shower generators: the high-Z material will

generate soft-charged particles also going backwards with respect to the shower

axis (see Sect. 9.2.3). These electrons can be absorbed by introducing thin, in units

of radiation length (in order not to take part in the shower-generation process), low-

Z additional absorbers b etween the high-Z material and the readout detector. In

this way, part of the soft shower charged component can be absorbed before entering

the readout detector, thus providing a further reduction of the visible energy.

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638 Principles of Radiation Interaction in Matter and Detection

Fig. 9.11 Ratio of e/mip values of F- to R-conﬁguration for passive samplers made of Fe and Pb

absobers, as a function of Pb absorber thickness (from [Leroy and Rancoita (2000)]). The line is

to guide the eye.

Results obtained with 30 mm thick passive samplers ([SICAPO Collab. (1993b)]

and Sect. 9.3.1) can be compared with results obtained, when plexiglas layers

(1.6 mm in front and 0.8 mm behind every active plane of silicon detectors) are

inserted in R- and F-conﬁgurations. The ratio between e/mip values, of the electro-

magnetic visible-energy measured in F- to R-conﬁgurations modiﬁed by the insertion

of plexiglas plates, increases from 1.17 ±0.02 up to 1.29 ±0.02 and is similar to the

ratio shown in Fig. 9.10 when no plexiglas layer was inserted in similar conﬁgura-

tions.

However, the overall change in the electron visible-energy is best observed (and

shown in Table 9.2) when the energy ²

vis

(R + P) deposited in R-conﬁgurations,

for the 3 mm thick passive sampler in which plexiglas layers [(1.6 + 0.8) mm]

are inserted, is compared with the energy ²

vis

(F) deposited in corresponding F-

conﬁgurations (with no plexiglas layer). The value of

D ≡

vis

(F) − ²

vis

(R + P)

vis

(R + P)

(9.17)

is as large as (41.0 ± 1.0)% for 15 mm of Fe and 15 mm of Pb in the passive sam-

pler. Taking into account that from Eq. (9.17) ²

vis

(R + P) = ²

vis

(F)/ (1 + D), the

ratio e/mip(R + P) with plexiglas layers and 15 mm Pb +15 mm Fe absorbers (R+P

conﬁguration) is given by

e/mip(R + P) =

vis

(R + P)

vis

(F)

(1 + D)

(R + P)

. (9.18)

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Principles of Particle Energy Determination 639

Table 9.2 Pb thickness versus the ratio D ≡ [²

vis

(F) − ²

vis

(R + P)]/²

vis

(R + P) in

percentage, where ²

vis

(R + P) is the energy deposited in the R-conﬁgurations for the

30 thick samplers and plexiglas layers [(1.6 + 0.8) mm], ²

vis

(F) is the corresponding

energy deposited in F-conﬁgurations (with no Plexiglas) from [Leroy and Rancoita

(2000)].

Pb thickness (mm) Ratio D (%)

5 32.9±1.0

10 34.1±1.0

15 41.0±1.0

Since D is ≈ 41%, and E

(R + P) only ≈ 1.2% lower than E

(R) = E

(F) (namely

the E

value for the F- and R-conﬁguration for 15 mm Fe and 15 mm Pb absorbers),

the ﬁnal result is:

e/mip(R + P) ≈

vis

(F)

(1 + D)

≈ 0.71 e/mip(F). (9.19)

As discussed in Sect. 9.2.3, the insertion of low-Z plates (like polyethylene, plexi-

glas, aluminium, G10 plates or others) leads to similar eﬀects when these absorbers

are inserted in between the thick passive sampler and the readout detector.

A large e/mip ratio reduction, of about 18%, was obtained by combining the

two eﬀects in a calorimeter with plastic scintillator active samplers, and Pb and Fe

passive absorbers [Beretvas et al. (1993)]. In this case the local hardening eﬀect was

achieved by inserting low-Z plates in front of and behind the active media, i.e., by

cladding the scintillator with 1.6 mm thick aluminum sheets [Beretvas et al. (1993)].

The possible use of polyethylene, a hydrogen-rich material, to achieve the tu-

ning of the e/mip ratio presents the advantage that it plays the role of a neutron

moderator, as indicated by activation studies in [SICAPO Collab. (1991d)], and

may then contribute to reinforcing the radiation hardness of calorimeters, whose

readout detectors are not too sensitive to very slow neutrons.

A further increase of the calorimeter radiation hardness is obtained, when low

(or medium) Z absorbers, like Fe, are employed as passive samplers. In fact (see

Sect. 3.3 on Hadronic Shower Development and Propagation in Matter), during the

hadronic cascading process, fewer neutrons are generated in low-A (which are also

low-Z) materials than in high-A (which are also high-Z) materials.

Indeed experiments at the LHC collider, for instance, will face an environment

of high-level radiation challenging the survival of the calorimeters. The neutrons

with ﬂuences estimated to reach up between 10

and 10

−2

year

−1

are at the

core of the problem. The large cross section of neutrons on hydrogen nuclei suggests

introducing hydrogeneous material in calorimeters, in order to moderate the eﬀect of

neutrons and reduce the damage inﬂicted by neutrons on the calorimeter materials

and equipment, esp ecially the detectors and their readout electronics. Preliminary

results were reported on experiments involving the exposure to very intense beams

at the CERN PS of Na, In, and Rh foils, with and without polyethylene foils in a

dump calorimeter [SICAPO Collab. (1991d)]. These results indicate that the low-

energy neutron ﬂux should be reduced by as much as an order of magnitude with