Spallation neutron spectra measurements Part II: Proton recoil spectrometer

Nuclear Instruments and Methods in Physics Research A 385 ( 1997) 345-353

lNSTNUMENTS f

Mii:

RESEARCH Section A

EISEVIER

Spallation neutron spectra measurements Part II: Proton recoil spectrometer E. Martinez a-*, J. Thun b*e, Y. Patin a, S. Leray b,c, M. Beau a, A. Boudardc, F. Bou6 a, P. Bouyer b, J.L. Boyard b, F. Brochardb, S. Crespin ‘, D. Drake ‘, J.C. Duchazeaubeneix b, J.M. Durand b J. FrChaut a, L. Kowalski f, R. Legrain ‘, J.P. Lochard a, S. MCnard d, G. Milleretb, E. Petibon”, F. Plouin b, Y. TerrienC, M. Uematsu b, S. VuillierC, D.M. Whit&lb a DPTMSPN, CEA BruyPres-le-Chiitel, France b Labomtoire National SATURNE, Saclq France ’ DAPNWSPhN. Saclap France * IPN. Orsq France ’ IJ pala Univewity Uppsala. Sweden P Montclair State Universir?: USA Received 2 September

1996

Abstract We present the experimental method conceived to measure high energy neutrons in the range (200 5 E 5 1600 MeV) The neutrons produce recoil protons in a liquid hydrogen converter. Momentum evaluation and identification of these protons are made by using a magnetic spectrometer equipped with plastic scintillators and three double-plane (X-I’) wire chambers. The response functions of the apparatus are determined using quasi-monoenergetic neutron beams produced by the break-up of deuterons or 3He on a Be target. The performance of the apparatus is illustrated in the form of a preliminary neutron spectrum. PAC.9 25.4O.S~; 07.07.-a;

07.75.+h:

29.30.-h

1. Introduction A program is in progress at the Laboratoire National Satume to measure energy and angular distributions of spallation neutrons produced by high energy protons or deuterons (800 5 E 5 1600 MeV) on thin targets. The preceding paper [ 1] (Part I) describes the experimental method used to study the low energy part of the spectra (3 5 E 5 400 MeV). The time of flight technique employed is limited to a maximum energy of 400 MeV because of poor time-offlight resolution for higher energies. For high energy neutrons, we have used the experimental technique, reported by Bonner [2], based on the use of a recoil proton magnetic spectrometer. Neutrons impinge on a liquid hydrogen convener and the energy of recoil protons is determined by trajectory reconstruction. This technique allows the measurement of neutron energies from 200 MeV up to the beam energy with a momentum resolution of 3%. * Corresponding author. Tel. +33 e-mail maninez~bruyeres.cea.fr. 0168-9002/97/$17.00 PI1SO168-9002(96)01

I

69 26 68 31, fax +33 1 69 26 70 63,

Therefore, the two independent methods used to measure the overall neutron spectra overlap in the energy range 200-400 MeV thus providing a useful check on their consistency. The response functions of the spectrometerare determined by using quasi-monoenergetic neutron beams [ 31 produced by the break-up of deuterons or “He on Be. We evaluate the neutron flux by using the cross sections of the elastic scattering [ 71 in the hydrogen converter. Subsequently, a comparison of the spectrometer response with the calculated neutron flux provides the apparatus efficiency. A deuteron beam at energies from 100 to 1150 MeVIA and a ‘He beam at energies from 1150 to 1600 MeV/A were used to produce the quasi-monoenergetic neutrons. The spectrometer response functions thus obtained, including the inelastic contributions in the converter, were parametrized to allow reconstruction of incident neutron spectra from the measured proton spectra. This paper is organized as follows: Section 2 is devoted to the description of the experimental setup. In Section 3 we present the data reduction. Section 4 focuses on the evaluation of the spectrometer efficiency. In Section 5, we describe

Copyright @ 1997 Elsevier Science B.V. All rights reserved 147-6

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Instr. and Meth. in Phs.

the response functions used in Section 6 to unfold the experimental data. Finally we present the cross section evaluation in Section 7.

2. Experimental

setup

The method is based on the detection of recoil protons produced by the scattering of neutrons on a hydrogen converter. Identification and evaluation of the proton momentum are made by using a magnetic spectrometer with trajectory reconstruction and time-of-flight measurement. The spallation measurements were made by using the proton beam of the Laboratoire National Satume synchrotron which delivers pulses of approximately 0.5 s duration with a 1 Hz recurrence depending on the proton energy. This beam passes through the target and is then deflected by a magnet (Mimosa) into a concrete beam stop. A view of the experimental setup is shown in Fig. 1. The neutrons emitted at 0” are collimated through an 8 m concrete shielding to an angular aperture of f 0.25” and interact with a liquid hydrogen converter of 1 g/cm* thickness and of 7 cm radius, placed in front of the spectrometer. The spectrometer contains a dipole magnet (Venus) and three double-plane (X-Y) wire chambers (Cl, C2, C3) to reconstruct the deflected trajectory of the protons, which takes place in the air. The magnet Venus can provide a field of about 0.5 T on a 160 x 60 cm’ aperture and along a 140 cm length. The first chamber covers a 20 x 20 cm2 surface whereas the other ones cover a surface of 80 x 40 cm2 for C2 and 100 x 80 cm2 for C3. These chambers give a 1 mm accuracy on the position measurement. From the reconstruction of the trajectory, it is possible to deduce the momentum of the particles which are emitted within the spectrometer acceptance. The two chambers placed in front of the magnet measure the emission angle. The neutron momentum is thus deduced assuming the proton is created by an elastic scattering reaction in the converter. A scintillator placed behind the hydrogen converter (Tl ) and a plastic scintillator hodoscope (200 x 200 cm2) placed behind the spectrometer (T2) are used in coincidence to provide the trigger. The two scintillators Tl and T2 are also used to measure the time-of-flight of the particles crossing

Fig. 1. High energy experimental setup

Rrs. A 385 (1997)

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the spectrometer in order to identify the protons from other charged particles produced in the hydrogen converter. The beam intensity is limited to about 10”’ protons/s (giving an average number of 400 triggers/s) by dead times (20%) for reading out the wire chamber information. To measure this intensity, two triple-element scintillator telescopes view a 50 pm Mylar foil placed upstream in the beam. Absolute calibration of these telescopes is obtained by irradiating a disk of carbon and counting the beta decay rate of “C, for which the production cross section is known [ 4-61. To veto stray charged particles which are emitted in the forward direction or created in the collimator, two scintillators (SA and ST) are placed in front of the hydrogen converter. Events for which particles are detected by either one of these scintillators are rejected. This contribution is typically 30% of the total number of identified trajectories.

3. Data acquisition and reduction Data are recorded in event mode and acquisition is triggered when signals are received in coincidence in the two scintillators placed at the beginning (Tl) and at the end (T2) of the spectrometer. For each event, data recorded include: the time-of-flight of particles between Tl and T2, the addresses of active wires for each plane of the three chambers and the signals received in the two scintillators SA and ST, used to remove charged particles. Events are recorded without any conditions on what is detected in the chambers. The selection of physical events is made during the data reduction. To ensure consistency of the measurements, all the data have been recorded with a single setting of the magnet field (0.4 T). The current of the magnet and the positions of the chambers have been chosen to optimize the detection rate of the spectrometer. The geometric acceptance of the spectrometer is limited vertically by the magnet pole pieces to an emission angle of 4.5“ and horizontally, by the third chamber placed behind the magnet. The results of a Monte Carlo calculation which simulates the particle trajectories in the spectrometer are presented in Fig. 2. The limits for the left and right horizontal angles depend on the incident momentum for a given current in the magnet. The dependence of the spectrometer detection rate on the particle momentum is taken into account by the response functions measured with monoenergetic neutron beams, presented in Section 5. The calculated coordinates in each chamber allow the reconstruction of the particles trajectory, assuming there is only one cluster of active wires in each plane. 30% of the total events are rejected because of insufficient information in the chambers to allow trajectory reconstruction. These events are due to uncorrelated signals detected in coincidence by Tl and T2 or to particles emitted outside the spectrometer acceptance region. This rejection rate is quite stable from one run to another and is taken into account by the

E. Martinez

t

I

I

ct al./Nuci.

I

-5

I

I

I

instr. and Mrth.

,

1

0

Fig. 2. Acceptance

region

and the two rectangles.

of the spectrometer. steps in the energy

The calculations

From

left to right:

and the horizontal

have been performed

I

I deg

-10

cxIJl~x2-y2.xz.h,

c

x2 . y2 X? Y3

-5

the contour

(vertical) for energies

0

5

lines indicate

-5

1

0. I deg

1

response function measurements. After this selection, we treat those cases where there is more than one signal in one chamber plane. For horizontal positions, only events for which there is one cluster in each plane can be taken into account in the analysis. They represent 88% of the selected events. On the contrary, for vertical coordinates, as they must be on a straight line, a selection between the several possible trajectories is made using a x2 value criterion. This selection takes into account the vertical focussing of the magnet which is about -0.3 mrad/cm for 200 MeV protons and decreases for higher energies. This procedure also allows the recovery of events where the information is missing in the vertical plane of one chamber. The vertical trajectory is reconstructed for 97% of the selected events. The overall process thus enables us to recover the trajectory for 85% of the selected events. The overall chamber detection efficiency is determined as follows: for the first chamber, for example, we select the events for which one cluster is detected in the central zones of the second and third chambers. By this selection, we determine the number of events that should be correctly detected in the first chamber. The efficiency is obtained by comparing the number of events for which one cluster is effectively detected in the first chamber to the number of selected events. Thus the efficiency is defined as: EI(Cl)=

A 385 (19971 345-353

I

5 0.

angle plane and by 20%

\

in Phys. Ra.

the detection

0

rates, by I070

angle plane. The full acceptance

3’

5

0, 1 deg 1 steps in the horizontal

and vertical

aperture cone is also represented

by the circle

higher than 200 MeV.

rection also takes into account the vertical direction of the trajectory. Furthermore the momentum is corrected for the energy lost by the particle when it crosses the spectrometer. This correction evaluates the energy lost in the air and in all the detectors crossed by the particles (converter window, wire chambers, scintillator Tl). According to the simulation, the resolution of the momentum measurement, defined as APjP, is about 3%. The proton energy spectrum obtained from accepted events is then corrected for the overall chamber detection efficiency. Some of the particles detected in the spectrometer are created in the materials which surround the hydrogen target. To get rid of this background, software cuts are applied on the trajectory reconstruction to eliminate protons which do not originate from the hydrogen. These cuts define the solid

Pb(p,xn)X at 1200 MeV

(1)

X,(X) means one cluster is selected in the corresponding plane of chamber i. This efficiency is about 95% for each chamber and thus the overall efficiency of the chambers is typically about 85%. The momentum is deduced from the trajectory of the particles in the horizontal plane, assuming the directions before and after the deflection cross each other in the center of the magnet. A simulation of the particle path in the spectrometer, knowing the measured map of the magnetic field, is used to determine a correction to this first evaluation. This cor-

O.ozo

.'.'I'.

0.5

. .'. I

.'.I.'. 15

Momentum Fig. 3. Typical

two-dimensional

of pions (bottom,

left).

protons

.'.'. 2

.,

( GeV/c )

spectrum

which

(middle)

and deuterons

enables

the identification (top,

right).

348

E. Martinez

er al./Nucl.

Insrr. and h4eth. in Phg.

Res. A 385 (1997) 345-353

p(n,p)n at 800 MeV

0

500

p(n,d)n’ at 800 MeV

1000 1500 2000

so0 loo0 1500 2ooo Momentum ( MeV/c )

Momentum ( MeV/c )

Fig. 4. Typical proton and deuteron spectra measured with quasi-monoenergeticneutronsat 800 MeV. in the angular range 0-3O. Two peaks appear on the deuteron spectrum. They correspond

to the two kinematic solutionsfor the emission angle.

angle (0.063 msr) which is used to evaluate the spallation neutron cross sections. The measurement of the time-of-flight of the particles combined with the momentum calculation enables good identification of the various charged particles detected in the spectrometer. The mass resolution is adequate to provide identification of protons, deuterons and pions, as shown in Fig. 3. The error on the proton identification is negligible ( SO.1 %) for energies lower than 1200 MeV and reaches 0.4% for higher energies.

4. Neutron detection efficiency The neutron energy can be deduced from the proton momentum assuming that this proton has been produced by elastic scattering. However, a correction must be applied since the neutron can initiate inelastic processes in the hydrogen such as np + pnn-’ and np --+ pprr-. The detection efficiency of the spectrometer, which is the rate of protons detected for each incident neutron, must also be taken into account to provide the neutron spectra. This efficiency depends on the conversion rate in the hydrogen target and, as already seen in Section 3, the spectrometer acceptance. Corrections of the spectra for inelastic reactions occurring in the converter and for detection efficiency are made at the same time by an unfolding process using the spectrometer response functions measured with quasi-monoenergetic neutrons. The break-up of deuterons on Be is used to produce quasimonoenergetic neutron beams at 100, 200, 400, 600, 800, 1000, and 1150 MeV. This last value is fixed by the maximum deuteron energy available at Satume. The break-up of ‘He on Be is used to produce quasi-monoenergetic neutron beams at 1150, 1300, 1400, and 1600 MeV. These measurements have been performed assuming the break-up of deuterons on Be produces monoenergetic neutrons by the stripping process [ 31. This hypothesis is confirmed by our time-of-flight measurements with deuterons [ 11 up to 400

MeV. We have made the same assumption for the 3He incident projectiles. In both cases, the neutron energy is spread by the Fermi motion of the neutron inside the incident particle. The proton spectra measured with quasi-monoenergetic neutron beams are obtained via the same data reduction as explained in Section 3. They are normalized by the incident neutron flux on the hydrogen converter. To determine the number of incident neutrons, a cut at 3” is applied to the proton scattering angle. This value has been chosen according to the trajectory simulation which confirms this choice. The selected domain is represented by the circle and the two rectangles in Fig. 2. It is inside the region where the spectrometer acceptance is maximum. Therefore this cut ensures a well defined solid angle where the proton detection is 100%. Two typical proton and deuteron spectra measured with 800 MeV neutrons and used to calibrate the spectrometer are shown in Fig. 4. For the proton spectrum, an integration over the elastic scattering peak gives the number of particles detected and, combined with the elastic scattering cross section, provides the neutron flux. These cross sections are obtained by integrating the angular distributions of the p( n,p)n reaction [ 71 between 0 and 3’. The values obtained for each neutron energy are indicated in Table 1. Table 1 (n,p) elastic scatteringcrosssectionsintegratedover the angular range O-3’ Energy [ MeV I

Cross section [ mb]

too 200 400 600 800 1000 1150 1300 1400 1500 1600

0.5059 0.4390 0.4166 0.3715 0.3570 0.3421 0.3283 0.32 I9 0.3231 0.3289 0.3388

E. Muriinc: et al./Nucl. Instr. and Met/t. in Phw Res. A 385 (1997)

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349

5. Response functions l

Be(d.n)X

l

p(n.d)n’, I” solufion

l

p(n,d)n’, 206solution

A Ptn*P)n

5

.

1

:

t

:

i

“:

i

1. 300

500

7M)

900

1100

Energy (MeV) Fig.

5.

kinematic

Neutron

flux

solutions)

800, and 1000 MeV has been applied

calculated

with

and Be(d,n)X normalized

the

p(n,p)n,

reaction

by the incident

on the calculated

p(n,d)n’

cross sections deuteron

(the

two

at 400.

600,

flux. A factor

IO’

values.

The background created by the windows of the hydrogen converter is evaluated by measuring the contribution obtained with the converter empty and represents 15% of the total data. To determine the incident neutron flux, it is necessary to subtract this contribution from each response of the spectrometer limited to 3’. We have compared the neutron flux obtained by using the elastic scattering cross sections with those obtained with the cross sections of the np -+ d7r” [8] reaction. For neutron energies varying from 400 to 1000 MeV, the calculations performed confirm the results obtained with elastic scattering cross sections. The differences do not exceed 10% as shown in Fig. 5. For higher energies, it becomes difficult to separate the deuterons created by the np -+ d&’ reaction from those created by reactions such as np + dm+r-. Therefore, the comparison is not possible for energies higher than 1000 MeV. The comparison is also made with the neutron flux calculated with the Be( d,n) X reaction cross sections [ 31 for neutron energies varying from 400 to 800 MeV. In this case the deuteron flux is evaluated by using the two triple-element scintillator telescopes placed in the beam and calibrated with an activation measurement of an irradiated disk of carbon. The agreement between the results obtained with the elastic scattering and the Be(d,n) X cross sections, is better than 20%. This result confirms that the spectrometer acceptance does not compromise the neutron flux calculation with the elastic scattering cross section. This comparison also demonstrates that the trigger efficiency (detection efficiency of Tl and T2) is high enough to enable a correct neutron flux evaluation. Finally, the neutron flux is systematically calculated by using the (n,p) elastic scattering cross sections. The other cross sections are only used to confirm this method when it is possible.

The underlying physical process which takes place, is the folding of the neutron spectrum by the response functions of the spectrometer for each neutron energy. The problem of unfolding is to deduce the incident neutron distribution from the measured proton spectrum. Therefore, a good knowledge of these response functions is necessary. The response functions are measured with quasi-monoenergetic neutron beams within the global acceptance of the spectrometer and are normalized by the incident neutron flux as evaluated in Section 4. It should be remarked that these responses as well as the proton spectra used to deduce the spallation cross sections include the contributions of the windows of the hydrogen target which are considered as a part of the converter. To confirm our hypothesis about the monoenergetic nature of the neutron beams produced by the break-up of ‘He, we have measured the spectrometer responses with deuterons and ‘He at the same energy of 1150 MeVIA. We have observed a difference of 65 MeV/c (FWHM) between the width of the elastic peak of the two functions. This is due to a higher Fermi motion of the neutron inside the ‘He which widens the neutron distribution. By subtracting this width from the measured response with ‘He, we can recover a function similar to the one obtained with deuterons. In order to calculate the response functions at those energies where there are no experimental data, the known responses are described as a superposition of four Gaussian peaks as shown in Figs. 6 and 7. Two Gaussians are used to reproduce the quasi-elastic peak and the other ones reproduce the proton emission associated with A production and disintegration. A linear background is also introduced. Each parameter of the Gaussian peaks is plotted as a function of neutron momentum and fitted with polynomial functions. The results of this parametrization give the calculated response functions which are compared with the measured ones in Figs. 6 and 7. Table

2

Calculated break-up

FWHM

for monoenergetic

of deuterons

Momentum

neutron distributions

I MeVlcl

FWHM

645

56.74

955

65.50

1219

75.3

1464

85.92

I696

96.80

Momentum

1866 1866 2033 2142 2251 2359

produced

or .‘He on Be

[ MeVlcl

FWHM

(MeV/c]

d + Be

I

(MeV/c) 'He+Be

105.08 170.08 178.23 183.60

188.78 193.84

by the

350

E. Martinez et al./Nucl.

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and Meth. in Phys. Rex A 385 (1997) 345-353

Fig. 6. Spectrometer responsesmeasured with quasi-monoenergeticneutrons (IO’)

at 200,400, 600, 800, 1000. and 1150 MeV produced by the break-up

of deuterons (gray curves) and the calculated responsesat the same energies (black curves). The several Gaussianswhich composethe calculated responses are also represented (dotted curves).

We need the spectrometer response functions for monoenergetic neutrons. Therefore, we have to subtract the width of the incident neutron momentum distribution from the calculated responses. This width is evaluated from the elastic peak, considering its width as the quadratic sum of the neutron distribution and of the spectrometer resolution (3%). The values calculated for several neutron energies are indicated in Table 2. The final response functions are obtained by subtracting this calculated neutron beam width from the width of every Gaussian peak used to reproduce the measured responses. This process enables us to calculate a matrix G which columns are the response functions of the spectrometer. It links the neutron ($n) and proton (@p) distributions as follows: (2) where P,, and PP are the neutron and proton momentum.

6. Solution of the inverse problem The correction consists in finding, by successive approximations, the best incident neutron spectrum which, convo-

luted with this matrix G, provides a good description of the measured proton spectrum. The calculation requires the introduction of a priori information about the unknown quantity. To evaluate this first approximation of the neutron spectrum @no,we simply use the measured proton spectrum, appropriately normalized with an estimation of the detection efficiency. This estimation is calculated, for each monoenergetic response function, from the elastic peak compared to the incident neutron flux. It is then possible to evaluate the corresponding proton distribution (4~‘) by using Eq. 2. The comparison between the measured (tips) and evaluated (4~‘) proton distributions, allows us to calculate a better approximation of the neutron spectrum (tin’) by using a formula which is deduced from the Bayes’ theorem: tin’ = 4~ + M’GTV-’ (+po - 4~‘) ,

(3)

where M’ = (M-’ + GTV-‘G)-’ is the covariance matrix associated with the final result, M is the covariance matrix associated with the first approximation (&ra) of the neutron spectrum and V is the covariance matrix associated with the measured spectrum (4~0). The mathematical developments of this method have been taken from Ref. [ 91. More information about this calculation is given in Ref. [ lo]. The unfolding process must not be too influenced by the first approximation of the neutron spectrum. Therefore, the

E. Maninez

et al. /Nucl.

Insrr. md Mrrh. in Phyv. Rrs. A 385 (1997)

60

60

s50

2 50

$40 i

$ 40

$

30

1 30

Z g 20

; 20

i

g 10

10 0

345-353

0

0

1000 2000 Momentum ( MeVlc )

I

60 L.,

0

1000 Momentum ( M?c

)

1

7OL,

JHe+Be, En = 1400 MeV

JHe+Be, En = 1600 MeV

2 50 aA

I

5% L

b

zem 1

f

0

Fig. 7. Spectrometer

(graycurves),the

0

responses measured calculated

IB2oli

10 1000 2000 Momentum ( MeV/c ) with

responses (black

1000 2twl Momentum ( MeVk )

quasi-monoenergetic

neutrons 10 at 1150. 1300, ( ‘> and the several Gaussians (dotted curves).

curves)

error bars associated with this first neutron spectrum are chosen large enough to reduce the influenceof the first iteration. As a test of the unfolding method, the calculation is applied to the proton spectra measured with quasimonoenergetic neutrons. In these cases, we must recover a neutron distribution centered around the elastic peak momentum. This is what is shown in Fig. 8, where the results of the unfolding process are compared to the first approximations of the neutron distributions (normalized proton distributions), in the case of quasi-monoenergetic neutron beams of 800, 1150, 1400, and 1600 MeV. These results confirm our hypothesis about the monoenergetic nature of

produced

by the break-up

of 3He

the initial neutron distributions, especially with ‘He. These tests have been used to estimate the error which is made by the unfolding process for each neutron energy. A comparison between the inelastic contribution which remains after the unfolding process with the monoenergetic neutron peak area enables this evaluation. The results are presented in Table 3. An alternative method has been tested to confirm the results obtained with the previous method. It consists in inverting the matrix G. The problem is then reduced to solving the m linear equations with m unknowns: pi = Mi,nj,

Table

1400. and 1600 MeV

(4)

3

Estimation

of the error

due to the unfolding

process for

energies

Energy

[ MeV I

Error

200

SO.1

400

50.1

[ %]

600

0.73

800

2.14

11.50

2.88

1300

7.41

1400

7.33

1500

8.91

1600

10.25

various

neutron

where pi is the measured proton distribution, M;j is the matrix whose columns are response functions and nj is the neutron spectrum to be determined. To simplify the calculation, the elastic peak of the response functions is concentrated into one bin. Therefore, the coefficients of this set of m equations form a triangular matrix. After solving the equations, the content of these diagonal bins is distributed with a Gaussian function to obtain the final neutron spectrum. The validity of this deconvolution was tested. as was the first one, with the proton spectra measured with quasi-monoenergetic neutron beams. A comparison of the neutron distributions calculated with these two methods is shown in Fig. 9. The fluctuations

E. Muttinez et ol./Nucl.

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Instr. und M&h. in Phy. Res. A 385 (1997) 345-353

7000 d+Be, En = 800 MeV %OOO LOO &OOO i3000 hOOO % poo 0 2000 1000 Momentum ( MeVlc )

0 x 102

Momentum ( MeVlc ) Fig.

8. Corn&son

&on

between

beams of

the results of the unfolding

800, 1150, 1400. and 1600 MeV.

process (full

curves)

at 1200

MeV

Se+06 -

Bavesian method

----

Direct method

_LL:- .*-

. . . . . . . ..?4-. 1300

800 Momentum Fig.

9. Comparison

Bayesian

method

of the calculated (full

in the case of 1.2 GeV

curve)

and with

(dotted

curves)

in the case of quasi-monoenergetic

The overall process of unfolding leads to a correction for inelastic contributions varying with the incident energy. For 800 MeV protons, the pion production is not a dominant process and the correction does not exceed 19% of the measured spectrum. For the 1200 and 1600 MeV measurements, inelastic processes represent a significant contribution, respectively 36% and 50% of the measured proton spectra. To confirm the results of the unfolding process, calculations have been performed with the proton spectrum detected in a cone of aperture 3” by using response functions measured in the same angular domain. This region is characterized by a spectrometer acceptance of 100% for each incident neutron energy. Therefore, this acceptance does not interfere in the neutron spectrum evaluation. These calculations confirm the first neutron distributions. Thus this test demonstrates that the acceptance is correctly taken into account by the unfolding process which uses the global response functions of the spectrometer.

7. Double differential cross sections

)

spectra

the direct

protons on a Iead target.

Momentum ( MeV/c ) and the first approximations

1800

( M&/c

neutron

2000 1000 Momentum ( MeVlc )

_

of these spectra are correlated to those which are already present in the proton spectrum. The agreement between the two results is better than 5%. The first calculation leads to a neutron spectrum corrected from the spectrometer resolution. This is why the first method has been chosen to perform the final calculation.

Pb(p,xn)X

0 x 102

obtained

method

(dotted

with

the

curve)

For the conversion from neutron energy spectra to absolute cross sections, we subtract the background created by the environment of the production target. To measure this

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353

8. Conclusion

0.1 IV

IUU Energy

Fig. at 0’

10. Neutmn

distribution

by the time-of-flight

measured (dotted

1uuu

(MeV) with

curve)

800

MeV

protons

and spectrometer

(full

on lead curve)

techniques.

contribution, typically 5%, several spectra were registered without the spallation target. The target thickness (z-2 cm) is a compromise between the counting rate, the energy lost in the target giving a resolution lower than 5% and an acceptable low rate of secondary reactions ( 5 10%). The thickness has also been chosen to minimize the beam intensity in order to reduce the background coming from the beam stop. The 0” neutron spectrum measured with 800 MeV protons on the lead target is presented in Fig. 10. The errors plotted are those due to statistics only. The other sources of absolute uncertainties are: beam calibration (f7%), the efficiency of the trajectory reconstruction (S%), the cross sections used for normalization ( f 10%). the parameters for reproducing the response functions (415%) and the unfolding process (see Table 3) _The quadratic sum of these errors does not exceed 17%. This neutron distribution is presented with the spectrum measured by the time-of-flight technique presented in the preceding paper [ 1] (Part I). The agreement between the two results is better than 15% thus validating our two independent normalizations.

We present here an experimental method based on the use of a magnetic recoil proton spectrometer to measure high energy neutron distributions. The energy resolution of 3% is substantially better than is possible with time-of-fight techniques in the energy range 200 5 E 5 1600 MeV. The use of quasi-monoenergetic neutron beams produced by the break-up of deuterons on Be is a major improvement in normalizing experimental data. We have demonstrated that the break-up of “He on Be is also a good method to produce quasi-monoenergetic neutron beams up to 1600 MeV. This experimental technique will be extended to the measurement of the overall neutron angular distributions. In these experiments, the spectrometer will move around a concrete shielding surrounding the target and pierced by several collimators. This new arrangement will allow a study of the systematics of neutron production for the overall angular domain at energies varying from 200 MeV to a few GeV.

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