A Monte Carlo program to design a transition radiation detector

Computer Physics Communications 51(1988) 431—441 North-Holland, Amsterdam

431

A MONTE CARLO PROGRAM TO DESIGN A TRANSITION RADIATION DETECTOR M. CASTELLANO, C. FAVUZZI, N. GIGLIETFO, E. NAPPI and P. SPINELLI Dipartimento di Fisica dell’Uniuersità and Sezione INFN, 1-70126 Ban, Italy Received 15 December 1987; in revised form 16 March 1988

A Monte Carlo program to design a transition radiator detector is described. The program provides the possibility to calculate the X-ray yield from radiators of different materials and structures, and analyzes the transition radiation energy release in various gaseous detectors.

PROGRAM SUMMARY Title of program: TRD_ SIM Catalogue number: ABDI Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this issue) Computer: VAX 11/780; Installation: INFN-Bari, Dip. di Fisica, Università degli studi di Ban, Italy Operating system: VMS Version 4.4 Programming language used: FORTRAN 77 Virtual memory: 148 Kbytes Number of bits in a word: 32

yield of ultrarelativistic charged particles both from multilayered regular radiators and foam slabs is calculated. The program evaluates the number of photons emitted by the radiator, the number of the photons converted in the following gaseous detector and the relative energy distributions. Method of solution Monte Carlo simulation. Restrictions on the complexity of the problem For each set of input parameters, the program typically produces a 23 Kbytes output file. The choices of the scanning parameters “menu” should take into account the file size to avoid problems for the user disk space allocation. Attention should be paid by the user also in the choice of the input design parameters (for this purpose one may use simple orientative prescriptions given in ref. [1]) so that the energy of a single transition radiation X-ray does not exceed 100 keV.

Peripherals used: disk, video terminal VT series or compatible Number of lines in combined program and test deck: 3331 Keywords: transition radiation, foams Nature of physical problem We have developed an interactive software package suitable to design a transition radiation detector. The transition radiation

Typical running time Depending on the kind of radiator selected (regular or foam), the typical VAX-11/780 CPU time in seconds is, respectively, about 15 times the number of runs and 70 times the number of runs for 5000 events. Reference [1] J. Cobb et al., Nucl. Instr. and Meth. 140 (1977) 413.

OO1O-4655/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

432

M. Castellano et al.

/

Design of a transition radiation detector

LONG WRITE UP 1. Introduction dW h d~dQ

Transition radiation detectors (TRDs) are cx-

9

—

~

—

tensively used in high energy experiments to discriminate electrons from hadrons [1~3] of the same energy. Sometimes they have been used to identify hadrons in the final states of high energy interactions [4]. In cosmic ray physics there are also several applications for particles identification or for particle energy evaluation: these methods are based on the Lorentz factor y measurement [5,6]. A TRD in its simplest configuration consists of a low Z material radiator emitting soft X-rays which are detected by a wire chamber filled by a high Z gas. The radiator is typically made of several hundred foils regularly spaced in a low Z gas, or may consist of foams of light materials like polyethylene. The wire chamber generally works in the proportional region and detects at the same time the transition radiation (T.R.) photons and the ionization energy released by the charged primary particle, The photon conversion capability depends on the type of the gas used and on its thickness determined by the chamber intercathode gap.

—

—

~

2

2

4 sin

—~

_F~0h(

4l

I

~2

FCOh

2

I + exp( Na) 2 exp( Na/2) cos N4 1 + ~~D( a) 2 exp( a/2) cos ~

=

—

—

—

—

—

—

and a + ,.t2d2 is the absorption coefficient for X-rays; the linear absorption coefficients ~t1, ~2 are derived for each energy from compilations [9], =

_____ ~‘

=

~,

=

2c

,

~

+

=

i=

~2

+

1, 2,

w, is the plasma frequency in medium i and w is the frequency of the emitted quantum; 6 is the angle of emission with respect to the particle trajectory; d1 and d2 are the foil thickness and spacing, respectively. This equation can be integrated over the angle approximately, yielding: dW 4a =

~e~(

2. Analytic procedures for transition radiation yield determination

~

—

~

x(1 —cos(p~+6~)),

2.1. Regular multilayer stack

We have used the differential energy distribution for X-ray emission from a particle with a Lorentz factor y interacting with a radiator of N foils taken from ref. [1]

(1)

where

hdw

Depending on the type of radiator used, whether regular multilayer stack or irregular structure (foam), we have used different analytic approaches according to the prescription of various authors [7,8].

+ 42)~

2

(2)

where

~

2c (7

=

2’rrn

—

2

+

~),

k

=

d2/d1,

(p1 + kp2) 1+k

So far we have considered the system ‘particle plus radiator’ as a classical electromagnetic source. Since the number of photons is typically a few units, _

N~

a(1 (1

— —

exp( Na)) exp(—a)) —

M. Castellano et at

/ Design of a

the electromagnetic field must remain quantized [10]: this implies that W has the meaning of average energy radiated by many particles of the same Lorentz factor traversing the radiator and producing some photons. The number of the produced and the detected quanta should follow Poisson distributions. We assume that the mean number of photons is KNX~ W/h~ (~3is the mean of ca as deduced by (2)), if we restrict to a photon energy range where there is significant X-ray yield, namely 0.5w~d1 2.5ca.~d1(d1 is the foil thick=

—

ness in microns and w1, is the plasma frequency of the medium in eV).

2.2. Irregular structure (foam) In this case in order to evaluate the average number of transition radiation X-rays we used the procedure suggested from Garibian [8] where the irregular structure of the foam can be parametrized in terms of N plates of average thickness
29~ =

137’~rw 1

1 —

~

1 +

~2

—

1

—

~2 + ~2

2

I. (3)

transition radiation detector

433

2) to each photon is assigned an energy according to the distribution (2): this means that for the foams we assume the same energy distribution as for regular radiators; 3) the T.R. energy (ETR) released in the chamber is deduced summing up all the energy contributions from the (Ne) photons converted in the gas; (N,~’>is derived from
—

ficient of the gas, which depends on the photon energy, GAP is the gas thickness; 4) the total energy released is calculated adding to ETR the ionization contribution in the gas from the particle, extracted from experimental Landau distributions included in the program data. These distributions have been derived using the data of different authors [11] for most gases used in the program. To extrapolate the data to situations where the gas thickness GAP is different, we just scaled the distribution means according to the ratio GAP/g, where g is the gas thickness of the experimental distribution. For less common gases such as the quenchers we deduced the distributions starting from the most probable values of (dE/dx) 10~ compilations [12] according to parametrizations of the Landau distnbution. Fig. 1 shows the logical flow used to design a TRD.

For the symbols explanation one can refer to ref. [8]. 4. Input parameters The input parameters are requested by the pro3. Program descnphon

gram using menu and mask techniques. Some

When the particle Lorentz factor ‘y is assigned, depending on the radiator structure, type choice and on the chamber gas selected, the program evaluates the average number of transition radiation photons produced, . At this point starts the Monte Carlo procedure to simulate the energy released in the chamber following these steps: 1) the actual number of T.R. quanta is extracted for each event according to a Poisson distribution of average ;

examples will be shown in section 6 (fig. 4a—l). The program asks for the kind of structure of the radiator: then one has to select the radiator material and gas type in between the foils according to the list displayed. This menu also gives the possibility to define a new kind of material (with respect to those already inserted) selecting the item “USER DEFINED”. In this case an alternate path is followed and after the insertion (fig. 2a—c) of the new material parameters it will return to the principal path.

a

I~

Ia

~ cI~

I/ I/

i; ~ a.

~

/~

g __ II__~‘~ fl~ /“~\tI ~d ~fl un I/~ ~ :~____ I1K.v”II \ Ii p 1<~! U Zo ~t

Xn.~

U!

M. Castellano et aL

/ Design of a

transition radiation detector

The input parameters for the regular radiator in

User Defined System

the next mask are: the Lorentz ‘y of the incident particle, foil thickness in microns, k d2/d1 (d2 is the foil spacing),

Available/Available

Aluminum / Neon Available/Available

Available/Available

Available/Available

Available/Available

—

Available/Available

Available/Available

—

Available/Available

EXIT

—

—

__________________________________ Rows (Up,Down~flight,Left)

435

—

F9-Default CrAcquisition

—

(a)

=

=

N1 number of foils, GAP intercathode chamber gap in cm (gas thickness), Nev number of events generated. =

=

=

For the irregular radiator they are:

Distribution from 1 to 100 Key ALUMINUM. [1] 7] [13] [19] [25] [31] [37] [43] [49] [55] [61] [67] [73]

[79] (85] [97]

550.00 2454.56 67.75 46.57 13.67 11.38 4.81 4.13 1.79 1.64 0.97 0.92 0.70 0.66 049 0.48 0.39 0.38 0.33 0.32 0.28 0.28 0 26 0 25 0.24 0.23 0.22 0.21 0.20 020 0.19

0.18

871.11 35.95 9.63 3.53 1.50 0.87 0.61 0.46 0.37 0.32 0.27 0 25 0.23 0.21 0.20 0.18

Rows ~Up Down RightLeft)

406.83 29.13 8.07 3.05 1.36 0.83 0.58 0.44 0.36 0.31 0.27 0 25 0.23 0.21 0.20

229.67 22.96 6.69 2.60 1.22 0.78 0.54 0.42 0.35 0.30 0.27 0 24 0.22 0.20 0.20

108.75 17.32 5.53 2.16 1.09 0.74 0.51 0.41 0.34 0.29 0.26 0 24 0.22 0.20 0.19

0.18 ~,=2.70~=33.g0

F9-Default

Cr~Acquisition

)b) Distribution from 1 to 100 KeV NEON. [1] 4310.00 1145.20 [7 1 33.19 22.39 [13] 5.71 4.58 [19] 207 175 [25] 0.85 0.79 [31] 0.51 0.49 [43]

~ [61] [67] [73]

[79] [85] [91] [97]

—


—

crons, ad the dispersion around the mean in mi-

—

=

mean value of plate thickness in mi-

=

crons,
‘

— —

.

=

=

.

,

ator (typically one can calculate radiator thickness to
it

dividing the

The following menu gives the possibility to run in ‘scanning mode’ modifying one or more parameters step by step. Then the gas specifications are required type of primary noble gas, i.e., argon, krypton or xenon, with relative percentage, the quencher (with relative percentage), i.e., carbon dioxide (C02),

369.82 16.99 3.85 149 0.73 0.47,

165.07 13.54 3.26 131 0.67 0.45

88.31 10.42 2.81 1.15 0.61 0.43

49.91 7.57 2.40 099 0.56 0.41

methane (CH4), isobutane (C4H10). Temperature and pressure of the gas are required at last.

0.27

0.27

Lastly is given the possibility to modify the

0.24 0.20 0.19 0.18 0.17 0.16 0.16 0.63

histogram parameters (number of channels, lower and upper limits). Selecting the item “PROCESSING...” in the next display the job

0.31

0.30

0.29

0.28

~ 0.21 0.20 0.19 0.18 0.17 0.16 0.16

0.21 0.20 0.18 0.17 0.17 0.16 0.16

0.25 0.21 0.19 0.18 0.17 0.17 0.16 0.16

0.25 0.24 0.20 0.20 0.19 0.19 0.18 0.18 0.17 0.17 0.17 0.17 0.16 0.16 0.16 p=9E-4 w=

It is also possible to select a nuxture of two noble gases (same as before including helium) with a quencher to have a ternary mixture.

Will start.

5. Output list flows (Up Down RIght l.eft)

F9—Oefault Cr.Acquisitlon

(c) Fig. 2. (a) Selection list for new radiator materials; (b) List of the mass absorption coefficients for a user defined radiator material; i.e. alumini (c) List of the mass absorption coefficients for a user defined chamber gas; i.e. neon,

,

The program provides: d

1)

and (N~>which may be used for studies of TRD performances with “cluster counting” techniques [3];

436

M. Castellano et a!.

/ Design of a

transition radiation detector

Multilayer RADIATOR form Regular

.

Irregular

.

—Definition

Detector Parameters—

NOBLE GAS QUENCHER

Processing

_______________________________________ (a)

XENOI’J CH4

% 100.00 % 000.00

TERNARYGAS Helium % 000.00 >>>>>>> Temperature (°C) 20.00 >>>,>>> Presure ( Atm) 1.00

Definition of the Radiator Rows (UpDown,Right,Left)

-

Polyethylene / Air Mylar / Air Lithium / Air Beryllium / Air User Defined

Polyethylene / Helium . Mylar / Helium LIthium 1 Helium . Beryllium / Helium . Not Available

F9~Default Cr~Acquisition

-

(t) 5_Bins Fst_Bin

Total _____________________________________________________ ROWS (Up Down Right Left)

Lot_Bin]

Hist. Param.s [n

F9—Default Cr.Acquisition (b )

Energy

Distribution

38.00

000.00

90.00

Differential

T.R, Intensity

38.00

000.00

90.00

Pure

Energy Distribution

3800

00000

9000

38.00

000.00

90.00

TP

Ionization Energy

Dis. in the Gas

Regular Radiator Param.S Enter Enter Enter Enter Enter Enter

GAMMA Dl K NE GAP NEV

Omega 1

value value value value value value

14.40

(10000.00) ( 25 00) ( 20.00) ( 500.00) ( 0.96) ( 5000.00)

Omega_2

--> , .-> --> ..> -.>

2740.00 51 00 10.00 1000.00 2.08 10000.00

Rows (Up Down Right Left)

REGULAR RADIATOR -ss LITHIUM / HELIUM PARTICLE

0.40

GAMMA

FOIL THICKNESS Dl OMEGA PLASMA 1

F9~Default Cr~Acquisition

(c) Scanning of parameters

GAMMA 2740.00 Dl 51.00 K 10.00 NE 1000.00 GAP 208 NEVENT 10000.00

N of Runs N. of Runs N. of Runs N of Runs N. of Runs N. of Runs

1 1 1 1 1 1

Step Step Step Step Step

DI

Left

0 274000 E

.

0510000 E

02

+

0144000 E

OMEGA PLASMA2

..s

O4SS000 E

FOiLS SPACING K

..,

0 1000S0 E

+

02

0208000 E

o

SI

EVENTS NUM~R

0000.00 0000.00 0000.00 0000.00 0000.00 0000.00

04

s

NUMBEROFFOILS

..>

10000

.>

005

02 00

_______________________________________________ GAS MIXTURE. XENON 100 % GAS PRESSURE GAS TEMPERATURE

.Row~ .

..>

DETECTOR GAP I Cs~I

___________

Step

Cr~Acquisition

(9>

______________________________________________________________

Rows (Up,00wn,Right,Left)

F9.Default

FY-De ~àuIt~. Gr.Acquisibon~..

(atm)

)~C)

---> --.>

1.00 20.00

AVERAGE NUMBER OFTR pRoDuc:D PHOTONS

3.99

(d) —Definition

Detector Parameters )tEN~ 0/ 100 00 QUENCHER CH4 % 000 00 TERNARYGAS Helium % 000.00

NOBLE GAS

Rows (Up,Down,Righi,Left)

F9.~DefauIt CAcquisitton e)

.

.

Fig. 3. (a) List of the options for the kind of TRD radiator; (b) List of the choices for the radiator materials; (c) Input parameters list for a lithium/helium regular radiator followed by a wire chamber; (d) Input parameters list for an eventual multiple run, where any parameter can be varied. In this particular case a single run is chosen with no parameter change; (e) Gas choice list for the detectcr; (f) Gas temperature and pressure setting; (g) Distributions list issued by the Monte Carlo with histogram parameters choice. (h) Summary of the TRD selected parameters issued by the Monte Carlo.

M. Castellano et a!.

/

Design of a transition radiation detector

437

450

(i)

p

~ DIFVERENTI’~. TRANS1TI0N RADIA11ON INIENSITY D(W)/D(OMEGA) (KEy)

TOTAL ENERGY DSTRIBLJT1Ce t*4/~ (KEv~

Fig. 3. (i) Total energy distribution of the TRD as defined in the previous tables: (j) Differential transition radiation intensity.

2) dn/dW01: total energy distribution; 3) dW/d h w: differential transition radiation intensity; 4) dn/dWTR: pure transition radiation energy distribution; 5) dn/dW10~:ionization energy distribution in the gas (Landau distribution). The user can decide how to obtain these histograms editing the PRINT.XTR file as follows: — — — —

Print ASCII file (Y or N) Capture file for laser pnnter output HBOOK file by Hstore TeKtromc Video output

=

N =; Y eo; N~

The identifier of the ASCII file follows the syntax “Polyethyl Air OUT.XTR” if, for example, the choice has been Polyethylene/Air. The user can store subsequently the histograms onto disk file “Polyethyl_Air_ HBK.XTR” in order to be able to restore them in memory by the HBOOK output selection. In the same way the disk file “Polyethyl Air_ LAS.xtr” produces an output printable for the laser wnter in GD3 format. —

-

-

6. Some examples In the following tables we show two examples of Monte Carlo runs relative to a regular (peri-

438

M. Caste!lano et a!.

/ Design of a

transition radiation detector *10

6001-

r

)k)

2. 1.75b

500r

1,5

fl

—

ii 44

1.25r

H

300~

1.

°,75r 2~

10o~

O0~

0,2~

110

~O

t~O

607080

~

PORE TRA.MsrloN RAOA11ON ENERGY DISTRIBU11O$4 (EEV)

0,110210

~ ICIN1ZAT1ON ENERGY DISTRIBUTION IN THE GAS

~ lKeVl

Fig. 3. (k) Pure transition radiation energy distribution; (1) Distribution of the ionization energy released from the particle in the gas.

odic) radiator (fig. 3) and to a foam radiator (fig. 4). In the first case we have derived the design parameters both of the radiator and of the associated chamber from a transition radiation detector described in ref. [13]. The simulated dn/dW~ 08and dn/dW10~distributions have been plotted with the same scale as those shown in fig. 12b of ref. [13]; the agreement with the experimental distributions looks reasonable. The number
photons (fig. 3h) is practically the same (~2) as quoted in section 4.2 of ref. [13]. In the second case we have taken the design parameters from a prototype we developed for muon energy spectra studies in underground laboratories we will publish later. The radiator was made of polyethylene foam of 30 g/l density [13] and was 28 cm long. The wire chamber was run in proportional mode with an argon (90%)/ carbon dioxide (10%) mixture and had an intercathode gap of 6 cm. Also in this case the agree-

]

M. Caste/!ano et a!. _________ -

Multilayer RADIATOR form

Regular

-

Irregular

-

/ Design of a transition radiation detector

~jj

Processing

(a _________________________________________________ Definition of the Radiator

-

Potyethylene / Air Mylar / Air

-

Polyethylene / Helium Mylar I Helium

-

u~~um Not Available

.

rT/Air

User Defined

Hist. Param.s [n°_Bins Fst_Bin Total

p ~

I,l.F9D8fa

uIt~ Ir

Energy

Distribution

Lst_Bin

46.00

000.00

67.14

Differential T.R. Intensify Pure T.R. Energy Distribution

46.00 46.00

000.00 000.00

67.14 67.14

Ionization Energy Dis. in the Gas

46.00

000.00

67.14

Rows (Up Down Rlght.Lett)

__________________________________________________

RcwS,

439

—Definition NOBLE GAS

iM~.n.

QUENCHER

~..“

(b) __________________________________________________________

>>>>>> >>>>>>

Cr*Acquisition

FO-Default (g)

Detector Parameters— ARGON % 90.00

ooo 00

Hehum Temperature (°C) Pressure ( Atm)

20.00 1.00

Irregular Radiator Param.s _____________ Enter Enter Enter Enter Enter Enter Enter Enter

GAP GAMMA NF

SIGM1 SIGM2 NEV

Omega_i

(

value value value value value value value value

19.00

0.96) (10000 00) ( 500.00) ( 25.00) ( 5.00) (1000.00) ( 100.00) ( 5000.00)

Omega_2

6.00 7000 00 280.00 32.60 14.00 965.00 294.00 10000.00

--> > --> --> --> -~> --> >

ROws (Up Down Right Left)

PARTICLE

..+

0.700000 E

+

04

..+

0.326050E

+

02

..,

0.140000 E

*

02

+02+

..+

5,965550E

+

03

SIGMA 02

..,

0 294000E

,

03

OMEGA_t

..+

0.190000 E

+

02

..+

0700000 E

+

00

+

01

sIGMA

Rows (Up Down Right Left)

F9..Detault

Scanning of parameters Gap

Gamma Nfoil

Sigmi Sigm2 Nevents

6.00 7000.00 280.00 32.6 14.00 965.00 294.00 10000.00

N. N. N. N. N. N. N. N.

Rows (Up Down Right Left)

of of of of of of of of

Runs Runs Runs Runs Runs Runs Runs Runs

1 1 1 1 1 1 1 1

__________ Step Step Step Step Step Step Step Step

0000.00 0000.00 0000.00 0000.00 0000.00 0000.00 0000.00 0000.00

(dl

~

TERNARY GAS

Helium

:IF9.DéfaU’It~ 10r_Acquisitiofl’i (e)

~+

EVENTSNuI~ER

-+

0.600000 E 10000

(atm) (°C)

---> -.->

1.00 15.00

AVERAGE NUMBER OF T R PRODUCED PHOTONS

1 52

AVERAGE NUMBER OF T.R. DETECTED PHOTONS

0.60

ters list for a polyethylene foam radiator followed by a wire chamber; (d) Input parameters list for an eventual multiple run, where any parameter can be varied. In this particular case a single run is chosen with no parameter change; (e) Gas choice list for the detector; (0 Gas temperature and pressure

00000

___________________________________

Rbwé (Up,Doin,Right,Leit)’

DETECTOR GAP ICml

Fig. 4. (a) List of the options for the kind of TRD radiator; (b) List of the choices for the radiator materials; (c) Input paranoe-

1 90.00

~

290

..+

(hI

Detector Parameters—

NOBLE GAS

OMEGA_2 FOILS NU~R

GAS PRESSURE GAS TEMPERATURE

Cr—Acquisition

F9-Default

ot

GAS MIXTURE: ARGON 90.00 % C02 10.00 %

_________________________________

—Definition

GAMMA

Cr..Acguusltlon

Ic)

Cr..Acpuisltion

(f) *0 IRREGULAR RADIATOR..>> POLYETHYL/AIR _______________________________________________

sot +

0.70

F9—Default

1

setting; (g) Distributions list issued by the Monte Carlo with histogram parameters choice. (h) Summary of the TRD param-

eters issued by the Monte Carlo.

440

M. Caste!lano et a!.

/ Design

of a transition radiation detector 320

(j

MONTE CARLO DATA 600

-

280

500

240

-

200 400

160 300

200

120

-

80

-

40

-

-

100

0~ 10

20 TOTAL ENERGY

I

I

I

30

40

50

DeTRIBU11ON DH/DW (KEV)

0

60

I

1)

It

20

30

4..,

40

50

60

DIFFERENTIAL TRANSITION RADIATION INTENSITY 0(W)/D(OUEGA) (KEy)

Fig. 4. (i) Total energy distribution of the TRD as defined in the previous tables; (j) Differential transition radiation intensity.

M. Caste!!ano etaL

/

Design of a transition radiation detector

441

800’

1k)

240

(I) 700

200 600

160

500

400

120

300 60

200

40 100

00

I ID

I 20

PURE TR.ANSI11ON

I 30

I 40

IN 50

I 60

RADIATION ENERGY DISTRIBuTiON (KEy)

00 _____________________________________________________________ 10 20 30 40 50 60 IONIZATION

ENERGY DISTRIBIJTION IN TIlE GAS I KeyI

Fig. 4. (k) Pure transition radiation energy distribution; (I) Distribution of the ionization energy released from the particle in gas.

ment of the dn/d W01 distribution with the experimental one (overimposed) looks reasonable (fig. 4a). We measured also (Ne) with “cluster counting” techniques obtaining 0.6, which is the same as calculated with Monte Carlo (fig. 4h).

References [1] J. Cobb et al., Nuci. Intr. and Meth. 140 (1977) 413. [2] C.W. Fabjan et al., Nuci. Instr. and Meth. 185 (1981) 119. [31C. De Marzo et al., Nucl. Instr. and Meth. A253 (1987) 235. [4] V. Comichau et al., Nucl. Instr. and Meth. 176 (1980) 325.

[5] M. Castellano et al., NucI. Instr. and Meth. A256 (1987) 38 [6] M.L. Cherry et al., Proc. 1986 DPF Summer Study, Snowmass, CO (1986). [7] C.W. Fabjan et al., Phys. Lett. B 57 (1975) 483. [8] G.M. Garibian et al., NucI. Instr. and Meth. 125 (1975) 133. [9] Handbook of X-rays, ed. E.F. Kaebble (McGraw-Hill, New York, 1967). [10] X. Artru et al., Phys. Rev. D 12 (1975) 1289. [11] A.H. Walenta et al., Nuci. Instr. and Meth. 161 (1979) 45. [12] Review of Particle Properties, Phys. Lett. B 170 (1986). [13] J. Fisher et al., Nucl. Instr. and Meth. 127 (1975) 525. [14] The foam (BREMBOCEL 3020.101) was provided by BAYER Italia S.P.A., wale Certosa 130, Milano.