Experimental results on elastic scattering of protons on the light nuclei 2H, 3H, 3He and 4He at 600 MeV

Ntrcfear PI@cs

A262 (1976) 413 -432;

@ North-Holla~

P~~~hin~ Co., Amsrerdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

EXPERIMENTAL RESULTS ON ELASTIC SCATTERING OF PROTONS ON THE LIGHT NUCLEI ‘H, 3H, 3He AND 4He AT 600 MeV J. FAIN, J. GARDE& A. LEFORT, L, MERITET, J. F. PAUTY, G. PEYNET, M. QUERROU and F. VAZEILLE ~borato~re de Physique Corp~~~u~re, University de Cdermont, 63f70 Aubiere, France and B. ILLE Institut de Physique Nuckfaire, lJniversit6 de Lyon, 69621 Villeurbanne, France Received I December 1975 Abstract: Differential cross sections for the elastic scattering of protons on “H, 3H, 3He and 4He have

been measured at 600 MeV. Proton-d~ut~i~ elastic scattering is investigated in a four-momen~m transfer square t-range corresponding to ~~ornb-nucl~r interference in order to determine the nucleon-nucleon amplitudes at 600 MeV. For the other nuclei, we investigate the t-range corresponding to the first and second maximum, in order to determine the mechanism of the nuclear process. A few physical comments on the results are made.

E

NUCLEAR

REACTIONS

‘, 3H, ‘2 4He(p, p), E = 600 MeV; measured (r(6); deduced reaction mechanism.

1. In~~uetion High-energy elastic scattering of hadrons on light nuclei is studied mainly in two ranges of four-momentum transfer square t: first, the Coulomb-nuclear interference region; second, the region of nuclear multiple scattering. We describe here several experiments performed at the CERN synchrocyclotron in order to measure the differential elastic cross sections of 600 MeV protons on various gaseous targets of light nuclei (‘H, 3H, 3He, 4He), for the values of ItI listed in table 1. The t-range for deuterium corresponds to the Coulom~nuclear interference region. The aim of this particular experiment is to determine the nucleon-nucleon amplitudes at 600 MeV in order to make possible the analysis of other experiments. For 3H, 3He and 4He, the t-range corresponds to the nuclear process. In term of Glauber’s formalism ‘), we are in the region of single and double scattering. The aim of these experiments is to determine the true mechanism of the nuclear process. The experimental method consists in detecting the recoil nucleus with a AE-E telescope made with semiconductor detectors. Such a method makes possible the identification of the recoiling nucleus and the accurate measurement of its energy 413

J. FAIN et al.

414

TABLE 1 Values

Target nucleus min momentum transfer square (GeVjc)’ max momentum transfer square (GeVM2 Type of interference observed Range of measurements

of ItI (see text) 2H

3H

‘He

4He

0.003

0.08

0.09

0.12

0.029

0.45

0.69

0.51

Coulomb-nuclear

Single-double nuclear scattering

at different angles. Thus, we select directly the elastic channel by identification of the recoiling nucleus and measure directly the four-momentum transfer square of the elastic process which is related very simply to the energy of the recoil (see eq. (3)). At high energy, above 100 MeV, and relatively low ItI [less than 0.8 (GeV/c) 2)1, this method has several advantages 2, over the usual one, which relies upon measurements made on the fast light particle scattered in the forward direction: (i) The energy and angular ranges in which the recoiling nucleus is produced are changed very little with the energy of the incident beam; consequently, the same experimental set-up can be used for higher energies. (ii) The energy fluctuations of the incident beam which are very troublesome for selecting the elastic events, when the scattered particle has to be measured in the forward direction, have practically no influence on the energy of the recoiling nucleus. (iii) The elastic events are easily identified if one knows the nature of the recoiling nucleus and its energy. This identi~~tion eliiinates the cases involving light nuclei where the nucleus is produced in an excited state, since it disintegrates before reaching the telescope. The very good energy resolution given by the semiconductor detectors competes with the very sophisticated and sometimes impossible angular measurement one would have to make at very high energies if one looked at the fast forward scattered particle. (iv) One can make the measurements rather far from the main beam and avoid a large part of the background brought by the tail of the beam. 2. Experimental details 2.1. The beam. The beam was the ejected proton beam of the 600 MeV (+ 3 MeV) CERN synchrocyclotron as used for the isotope separator ISOLDE; its diameter (FWHM) was 2.2 cm with a maximum intensity of about 2.5 x 10”’ protons/set, and a duty cycle ranging from 10 % to 30 %_ 2.2. General set-up cfis. I>. The gas target is a cylindrical box of z 10 liters volume (for tritium, a special box has been built and is described later). An arm, which can be moved horizontally through a vacuum tight spherical knee-

ELASTIC

PROTON

41.5

SCATTERING

oroton

beam

(66OMC3ti

knee-joint t.500) preamplifiers to electronics Fig. 1. General

Fig. 2. Details

lay-out.

of the telescope.

joint, allows the positioning of the BE-E telescope at angles between 90” and 57” with respect to the beam direction in steps of OS”, with a relative accuracy of 0.1”. A copper diaphragm placed in front of the telescope limits the angular aperture to about 1”. The mechanical details of the telescope are shown in fig. 2. A permanent shielding of concrete, 2 m thick, stops a large part of the background coming from the tail of the main beam; a movable lead shielding, adjustable according to the arm position, stops the background particles coming directly from the walls and from the windows of the box. 2.3. Experimental lay-out for different gaseous targets. For the cases of the 3He and 4He targets, the pressure inside the box was atmospheric pressure; the arm, in which the vacuum was made, was isolated from the gas by a mylar window 9 pm thick. In the case of the deuterium target, the pressure inside the box and the detecting arm was the same and equal to 100 Torr; there was no mylar window, and we found

416

J. FAIN et QI. solid

angle

of

detaction

metal-glass(pyrex)

_,

connsct sealing

knee-joinl,

of

ion the

,

to

detectors

Fig. 3. Tritium gas target - details of the general lay-out.

that with such an arrangement the influence of the absorbtion and multiple scattering was less disturbing. The tritium target was carefully studied. The use of solid tritium targets lead to difficulties, mainly due to the background produced by the support, so for this reason we decided to build a gaseous target (fig. 3) corresponding to the following requirements: (i) Walls should be thin enough to make the background as low as possible but strong and tight enough to insure a satisfying safety; (ii) a volume as small as possible in order to reduce the total amount of radioactivity; and (iii) a shape such that the region where the walls are crossed by the proton beam is not seen by the detectors. The stainless steel box had a volume of 120 cm3 with walls 100 pm thick and slightly thinner (35 pm) on the path to the detectors and was inclosed in the bigger chamber normally used for the helium and deuterium target and which holds the detecting arm. The tightness of the box was tested by putting it in a vacuum after it was filled with hydrogen or helium at atmospheric pressure. The rate of leakage was measured and

ELASTIC

PROTON

417

SCATTERING

found to be less than 10-l’ Torr * liter/set for hydrogen, and lo-l1 Torr * liter/set for helium. The target was filled at the Centre d’Etudes Atomiques de Saclay using a Pyrex tube and was sealed afterwards. The tritium pressure was 733 Torr at 26 “C and the total radioactivity equal to 270 Ci. A very efficient ventilation was necessary in the experimental area to limit the danger in case of breakage. 2.4. The AE-E telescope. The recoil detector was a telescope made with two semiconductor detectors ; the first measured the energy loss AE and the other the remaining kinetic energy E. The identification of the light nuclei was done according to the method described by Goulding et al. 3). Between the two parameters E and AE there exists the relation (E+AE)@-ED

= Ax/a = J,

(1)

where Ax is the thickness of the first detector and a is a parameter depending only on the nature of the particle measured; this relation is true in any region where the range R of the particle in the stopping material can be written as R = aE@. For light nuclei (:H to iHe) and for an energy range from 10 to 100 MeV, one can take B = 1.73. Below 10 MeV, which is the energy range of the deuteron corresponding to the p-d Coulomb-nuclear interference, one can see from fig. 4 how the identification parameter J varies experimentally “) as a function of the kinetic energy E, for various values of /3. It appears in particular that this method cannot be used

13

3

t 1.2.

1.0

1.5

2.0

Fig. 4. Variation of the identification

2.5

3.0

parameter as a function of fi.

E (Meti

J. FAIN et al.

418 Ax

a

X10’

Ax=lOO,m

Ax=

1 mm

t

5 4

3

1

2 1 0’

1

3H *H ‘H 1’0

$0

30

40

50

do

7’0

8.0

‘

e

1’0

10 30

40 50

Fig. 5. Particle separation as a function of dx. The dashed areas correspond identi~~ation peaks.

60 70

80

90

E;cA E bAeq

to the FWHM of the

below I MeV, and between 1.5 and 10 MeV p must be varied from 1.60 to 1.73. The choice of the thickness Ax of the AE detector is related to the minimum energy that one wishes to measure and to the ~uctuation SJ of the identi~~ation parameter. The parameters J and 6J increase proportional to Ax and ,,& respectively. The separation between two types of particles increases with increasing Ax. The optimum thickness Ax is not the same, at a given energy, for particles of charge one and particles of charge two because of their different ranges. The influence of the Ax value on the particle separation is shown in fig. 5 where the dashed areas correspond to the FWHM of the identification peaks [the two thicknesses, taken as an example, correspond to the extreme values used for 3He and 3H, ref. *)I. The criterion for the choice of Ax is that the incident particle has to lose between 0.2 and 0.5 times its initial energy in the AE detector. TABLE2 The detector arrangements and energy ranges for each target Target v mm energy recorded (MeV) max energy recorded (MeV) dE@m) thickness of the E(pm) detectors used (surface barrier Si) Comments

2H 1.2 10 10; 50 1000

3He 16 124 100; 150; 200; 300; 1000 300; 1000; 1000 additional use of Al absorbers (from 1 to 4 mm)

3H 14 86 200; 1000 1000

4He 15 68 50:200;300;1000 450; 2000

use of a Ge detector for E-measurement

419

ELASTIC PROTON SCATTERING

We used surface barrier silicon detectors with thicknesses ranging from 10 pm to 2 mm with an effective circular area of 1 cm’. For the detection of 3He above 60 MeV, we added aluminium absorbers with thicknesses varying from 1 to 4 mm. For tritium, the range in silicon was equal to 2mm for an energy of 28 MeV; at higher energies, we used a NIP type ge~ani~ detector (1 x 1 x 2 cm”) which has a higher stopping power. Unfortunately, such a detector must be handled more carefully: first, it must be kept at liquid air temperature and secondly, the beam intensity must be reduced in order to avoid saturation and damage (the beam intensity was Iowered to IO’* p/s instead of lOi p/s with a silicon detector). The various detector arrangebias

voltage

bias

voltage

E d&et

D

r_“_

____--_

I_____

identifier -__--

&i_e&l~)_

_ _

‘I 1

I

I

* *o&aiAE I

5: /

L_____.-___r__---__

i

I

1

wa -_._

i

---_--

__.__

-

____

Fig. 6. Block diagram of the electronics.

__-__--_

___i

J. FAIN et al.

420

ments that we used are listed in table 2, as well as the energy ranges measured for each target. 2.5. Block diagram of the electronics. The schematic block diagram of the electronics was of the type described by Goulding et al. 3, and is shown in fig. 6. The detectors were fohowed by charge sensitive feed-back capacitive preamplifiers (10 mV/MeV). The signals were amplified, shaped and analysed in amplitude. The time signals were provided from a bipolar signal by zero-crossing circuits. The signals were fed by fast coincidence and the single channel analyzers opened linear gates both ways. The ide~t~cat~on system gave at the same time the identi~cation parameter J defined by eq. (1) and the total kinetic energy E+BE of the particle, For a given particle, J can be choosen by a single channel analyser opening a gate on the energy channel and, in this way, the energy spectrum of the particle coming from an elastic collision is obtained. Fig. 7 gives one example of the identification spectrum obtained for charge-one particles with a tritium target and germanium detector for the measurement of the remaining energy E. 2.6. Beam monitor. To monitor the incident beam, we counted with the two scintillator counters telescope secondary particles emitted around 90” using an

200

wents

150

100 I

50

0

kt

k_F ident

if ication

parameter

Fig. 7. Identification spectrum of charge-one particles.

(arbitrary

units)

ELASTIC

PROTON

421

SCATTERING

TABLE? Differential cross sections for elastic scattering of protons on deuterium at 600 MeV

--/ (GC\

/cy tmbisr)

1.200 1.440 1.904 2.140 2.380 2.620 2.865 3.105 3.594 3.840 4.085

87.13 86.86 86.38 86.17 85.96 85.76 85.56 85.38 85.03 84.86 84.70

0.0045 0.0054 0.0071 0.0080 0.0089 0.0098 0.0107 0.0116 0.0135 0.0144 0.0153

127.4 130.65 108.3 117.9 109.4 105.4 93.6 98.3 99.8 95.6 93.5

269.1 276.7 229.4 249.9 231.8 223.5 202.8 208.6 211.8 202.9 198.6

3.352 3.594 3.840 4.085 4.301 4.517 4.828 5.072 5.317 5.565 5.813 6.060 6.308 6.551 6.805 7.054 7.303 7.552 7.800

85.20 85.03 84.86 84.70 84.56 84.39 84.24 84.09 83.95 83.81 83.68 83.54 83.41 83.28 83.16 83.03 82.91 82.79 X2.67

0.0126 0.0135 0.0144 0.0153 0.0161 0.0172 0.0181 0.0190 0.0199 0.0209 0.0218 0.0227 0.0237 0.0246 0.0255 0.0265 0.0274 0.0283 0.0293

100.0 94.1 93.7 95.1 85.7 92.4 84.75 84.25 85.9 81.4 80.7 78.4 75.0 73.5 19.6 75.9 71.9 69.0 70.6

212.2 199.6 198.9 201.9 182.1 196.3 180.1 179.1 182.6 173.1 171.7 166.9 159.6 156.4 169.4 161.7 153.2 147.0 150.4

79.65 79.32 78.09 78.38 77.23

0.0581 0.0619 0.0694 0.073 1 0.0881

42.0 31.3 28.7 26.7 22.0

90.3 67.3 61.8 57.7 47.1

15.5 16.5 18.5 19.5 23.5

auxiliary target inserted in the beam (fig. 1): The geometry of this target was such that it simulated the part of the actual gas target which is seen by the BE-E telescope (for an average position of the detector arm). For this to be possible, along the path of each proton in the beam, the thickness of the monitor target has to be proportional to the probability of recording in the AE-E telescope an event coming from the gas target; thus the number of secondary particles counted by the scintillators is propor-

422

J. FAIN et al. TABLE 4

Differential cross sections for elastic scattering of p on 3H at 600 MeV

Wisr) 14.00 15.00 16.00 17.00 18.00 19.00 13.00 24.00 25.00 26.00 26.50 27.00 23.50 34.50 35.50 36.50 37.50 38.50 39.50 40.50 41.50 42.50 43.50 45.00 46.50 47.50 48.50 49.50 50.50 51.50 52.50 53.50 54.50 56.00 61.00 66.25 71 .OO 76.00 83.00 86.25

79.76 79.40 79.04 78.70 78.37 78.05 76.84 76.35 76.27 75.99 75.86 75.72 74.06 73.82 73.59 73.35 73.12 72.89 72.66 72.44 72.22 72.00 71.78 71.46 71.15 70.94 70.74 70.53 70.33 70.13 69.93 69.74 69.54 69.25 68.31 67.36 66.52 65.67 64.51 63.99

0.0786 0.0842 0.0898 0.0955 0.1013 0.1067 0.1292 0.1346 0.1494 0.1488 0.1488 0.1516 0.1742 0.1794 0.1846 0.1898 0.1950 0.2002 0.2054 0.2106 0.2158 0.2210 0.2262 0.2340 0.2418 0.2470 0.2522 0.2574 0.2626 0.2678 0.2730 0.2782 0.2834 0.2912 0.3172 0.3445 0.3692 0.3952 0.4316 0.4485

‘) Statistical errors only.

27.6 20.0 17.6 14.5 11.9 9.37 4.48 3.66 3.35 2.51 2.19 2.13 0.733 0.569 0.554 0.531 0.386 0.300 0.237 0.216 0.180 0.197 0.103 0.0919 0.0545 0.0612 0.0501 0.0551 0.0535 0.0537 0.0583 0.0539 0.0565 0.0540 0.0865 0.120 0.0566 0.0555 0.0776 0.0619

0.4 0.3 0.3 0.2 0.2 0.20 0.13 0.12 0.09 0.09 0.22 0.08 0.072 0.045 0.044 0.061 0.051 0.032 0.028 0.037 0.034 0.035 0.019 0.0134 0.0132 0.0144 0.0112 0.0120 0.0132 0.0120 0.0127 0.0086 0.0089 0.0088 0.0125 0.012 0.0103 0.0083 0.0091 0.0087

-

(mb/sr) 12.9 9.33 8.23 6.77 5.60 4.40 2.12 1.73 1.59 1.19 1.04 1.Ol 0.352 0.274 0.267 0.257 0.187 0.146 0.121 0.105 0.0879 0.0961 0.0503 0.0480 0.0268 0.0301 0.0248 0.0272 0.0315 0.0267 0.0290 0.0269 0.0282 0.0271 0.0437 0.0612 0.0446 0.0289 0.0409 0.0328

(mb/sr) 0.2 0.12 0.14 0.1 0.11 0.09 0.06 0.06 0.04 0.04 0.11 0.04 0.035 0.022 0.021 0.030 0.025 0.015 0.013 0.018 0.0163 0.0173 0.0095 0.0066 0.0065 0.0071 0.0055 0.0059 0.0066 0.0060 0.0063 0.0043 0.0045 0.0044 0.0063 0.0063 0.0053 0.0043 0.0052 0.0046

[mb/(GeV/c)‘] 59.7 41.1 36.2 29.8 24.6 19.4 9.33 7.63 6.99 5.25 4.59 4.45 1.56 1.24 1.18 1.14 0.830 0.646 0.510 0.461 0.330 0.426 0.223 0.213 0.119 0.134 0.110 0.121 0.140 0.119 0.129 0.120 0.125 0.120 0.195 0.273 0.199 0.129 0.180 0.147

,

I

[mb/(GeV/c)‘] 0.8 0.5 0.6 0.4 0.5 0.4 0.27 0.24 0.19 0.20 0.48 0.18 0.15 0.1 0.09 0.13 0.110 0.068 0.059 0.080 0.072 0.077 0.042 0.029 0.029 0.032 0.029 0.026 0.029 0.027 0.028 0.019 0.020 0.020 0.028 0.028 0.024 0.019 0.023 0.021

ELASTIC

PROTON

423

SCATTERING

TABLE5 Differential cross sections for elastic scattering of p on 3He at 600 MeV

WW 16.40 17.37 18.34 19.32 20.29 21.27 22.25 23.23 24.22 25.20 26.18 27.17 28.16 29.15 30.10 31.12 32.11 53.10 34.09 35.09 36.08 37.07 38.05 38.60 38.61 39.60 40.59 41.59 42.58 43.57 44.57 46.56 47.28 48.27 49.76 51.75 53.25 54.25 56.24 57.24 58.23 60.23 63.22 67.71 70.21 73.19 78.18

78.91 78.58 78.20 77.95 77.85 77.35 77.06 76.77 76.49 76.21 75.94 75.68 75.41 75.15 74.90 74.65 74.41 74.16 73.92 73.68 73.45 73.22 72.99 72.87 72.87 72.64 72.42 72.20 71.98 71.77 71.56 71.14 70.99 70.78 70.48 70.08 69.78 69.59 69.21 69.01 68.83 68.45 67.90 67.10 66.66 66.15 65.31

0.0921 0.0975 0.1030 0.1085 0.1139 0.1194 0.1249 0.1304 0.1360 0.1415 0.1470 0.1526 0.1581 0.1637 0.1692 0.1748 0.1803 0.1859 0.1914 0.1970 0.2026 0.2082 0.2137 0.2168 0.2168 0.2224 0.2279 0.2335 0.2391 0.2447 0.2503 0.2615 0.2655 0.2711 0.2794 0.2906 0.2990 0.3046 0.3158 0.3214 0.3270 0.3382 0.3550 0.3802 0.3943 0.4110 0.4390

15.6 13.4 12.3 11.5 9.20 8.52 7.51 6.90 5.89 5.46 4.98 4.36 3.44 2.98 2.43 2.38 1.94 1.56 1.41 1.25 1.06 0.768 0.725 0.617 0.728 0.541 0.478 0.347 0.313 0.273 0.244 0.173 0.161 0.150 0.143 0.130 0.116 0.103 0.099 0.101 0.107 0.135 0.142 0.143 0.142 0.144 0.141

(mbisr) 0.5 0.4 0.4 0.4 0.26 0.24 0.23 0.22 0.17 0.14 0.19 0.14 0.15 0.12 0.09 0.11 0.09 0.07 0.06 0.06 0.05 0.043 0.063 0.048 0.050 0.030 0.028 0.019 0.022 0.028 0.027 0.013 0.021 0.015 0.010 0.010 0.018 0.017 0.016 0.016 0.017 0.011 0.011 0.013 0.010 0.010 0.018

(mb/sr) 7.29 6.28 5.76 5.4 4.33 4.02 3.55 3.27 2.79 2.60 2.37 2.08 1.64 1.43 1.17 1.15 0.932 0.752 0.681 0.605 0.512 0.373 0.353 0.330 0.355 0.264 0.234 0.170 0.154 0.134 0.121 0.0856 0.0800 0.0745 0.0711 0.0648 0.0583 0.0520 0.0498 0.0512 0.0542 0.0686 0.0728 0.0740 0.0737 0.0754 0.0743

(mb/sr) 0.22 0.21 0.20 0.19 0.12 0.12 0.11 0.11 0.08 0.07 0.09 0.07 0.07 0.06 0.04 0.05 0.043 0.032 0.030 0.027 0.025 0.021 0.031 0.023 0.024 0.015 0.014 0.009 0.011 0.014 0.013 0.0063 0.0106 0.0073 0.0050 0.0048 0.0090 0.0084 0.0082 0.0083 0.0086 0.0056 0.0058 0.0066 0.0051 0.0052 0.0094

[mb/(GeV/c)‘I 34.0 29.3 26.9 25.2 20.2 18.8 16.6 15.2 13.0 12.1 11.1 9.70 7.68 6.66 5.45 5.35 4.35 3.51 3.18 2.82 2.39 1.74 1.65 1.54 1.66 1.23 1.09 0.794 0.717 0.628 0.563 0.400 0.374 0.348 0.332 0.303 0.272 0.243 0.233 0.239 0.253 0.321 0.340 0.346 0.345 0.353 0.348

[mb/(GeV/c)‘] 1.1 1.0 0.9 0.9 0.6 0.5 0.5 0.5 0.4 0.3 0.4 0.31 0.33 0.27 0.20 0.24 0.20 0.15 0.14 0.13 0.12 0.10 0.14 0.11 0.11 0.07 0.06 0.044 0.050 0.065 0.061 0.029 0.050 0.034 0.023 0.022 0.042 0.039 0.038 0.039 0.040 0.026 0.027 0.031 0.024 0.024 0.044

J. FAIN et nl.

424

TABLE 5 (continued)

&%)

$z)

~~~),c)~

($)*, (mb/sr)

79.68 81.68 85.67 87.67 90.67 94.66 98.65 102.65 106.65 111.64 115.64 119.63 123.63

65.06 64.73 64.08 63.77 63.29 62.67 62.07 61.47 60.87 60.15 59.57 59.01 58.45

0.4474 0.4587 0.4811 0.4923 0.5091 0.5316 0.5540 0.5764 0.5989 0.6269 0.6494 0.6718 0.6942

0.137 0.136 0.115 0.101 0.0946 0.0860 0.0821 0.0669 0.0630 0.0612 0.0496 0.0317 0.0278

d (~),~~ (mbjsr)

($j..,.

A(S)..,’

(mb/sr)

0.012 0.012 0.007 0.~7 0.0064 0.0060 0.0046 0.0055 0.0051 0.0050 0.0045 o.po35 0.0028

(mb/sr)

0.0728 0.0722 0.0617 0.0545 0.0513 0.0470 0.0452 0.0372 0.0353 0.0347 0.0284 0.0183 0.0162

[tib/(GeV/c)‘]

0.0065 0.0063 0.0040 0.0037 0.0035 0.0033 0.0025 0.003 1 0.0029 0.0029 0.0026 0.0020 0.0016

0.341 0.338 0.289 0.255 0.240 0.220 0.212 0.174 0.166 0.163 0.133 0.0860 0.0760

d (g) [mb~(GeV/c)‘] 0.080 0.030 0.019 0.017 0.016 0.015 0.012 0.014 0.014 O.Of3 0.012 0.0094 0.0075

“) Statistical errors only.

tional to the number of ‘“effective” protons in the beam, independent of the beam setting. In practice, three aluminium foils, each 100 pm thick, stacked together and cut in an appropriate manner provided a suitable monitor target. The absolute number of effective protons in the beam is known by measuring the proton induced activity in this monitor target. The reaction 27Al(p, 3pn)24Na which takes place is known to have a cross section of 1l.Ot0.5 mb at 600 MeV [ref. “)I. 3. Numerical evaluation of different cross sections For each angular position (3of the detector arm we recorded an energy spectrum, giving the number 6n of events in energy steps of 6E. The solid angle under which the detectors are seen is dete~ined by the radius R Af the collimator placed in front of the detectors at a distance 1> from the target. For an incident pencil beam, the expression for the elastic scattering differential cross section at the angle 8 can be written from the geometry of the system in the form do

6ta Dsin2B

dr = 6E m2

1 (1-B’

(21 GO?

@

'

where M is the mass of the recoiling nucleus, B is the velocity of the c.m. (expressed as a function of the velocity of light), p is the number of target nuclei per unit length and I is the number of incident protons. This formula can still be used for the actual beam which has a cross section of about 4 cm2, the error introduced being less than 0.5 o? [ref. “)I. Its validity is dependent on the choice of 6E, since it is assumed that the effective length of the target

ELASTIC

PROTON

425

SCATTERING

TABLE 6 Differential cross sections for elastic scattering of p on 4He at 600 MeV

15.62 16.56 17.51 18.46 19.42 20.38 21.34 22.31 23.28 24.25 28.16 29.14 30.12 31.11 32.09 33.57 34.56 35.55 36.54 38.02 39.01 39.99 40.98 41.97 42.96 43.95 44.94 45.94 46.93 47.92 48.91 53.89 54.88 55.88 56.87 57.87 58.86 59.86 60.86 61.85 62.85 63.85 64.84 65.84 66.84 67.83

78.61 78.27 77.93 77.60 77.28 76.96 76.66 76.35 76.05 75.76 74.63 74.36 74.10 73.83 73.57 73.19 72.94 72.69 72.44 72.08 71.84 71.61 71.37 71.14 70.91 70.69 70.47 70.24 70.02 69.80 69.59 68.53 68.33 68.12 67.92 67.72 67.52 67.22 67.13 66.93 66.74 66.54 66.35 66.16 65.97 65.78

0.1164 0.1234 0.1305 0.1376 0.1448 0.1519 0.1591 0.1663 0.1735 0.1808 0.2099 0.2172 0.2245 0.2319 0.2392 0.2502 0.2576 0.2650 0.2724 0.2834 0.2908 0.2981 0.3055 0.3128 0.3202 0.3276 0.3350 0.3424 0.3498 0.3572 0.3646 0.4017 0.4191 0.4165 0.4239 0.4314 0.4387 0.4462 0.4537 0.4610 0.4685 0.4759 0.4833 0.4908 0.4982 0.5056

“) Statistical errors only.

(mb/sr)

(mb/sr)

(mb/sr)

18.1 14.5 12.8 11.0 8.87 7.69 5.50 4.45 3.28 2.69 1.33 0.779

0.3 0.3 0.2 0.2 0.20 0.18 0.15 0.14 0.12 0.10 0.07 0.053 0.044 0.043 0.033 0.030 0.029 0.033 0.031 0.037 0.040 0.039 0.041 0.039 0.045 0.048 0.045 0.048 0.047 0.051 0.049 0.045 0.042 0.040 0.041 0.040 0.042 0.039 0.038 0.036 0.035 0.034 0.033 0.031 0.028 0.028

9.90 7.94 7.02 6.05 4.87 4.24 3.03 2.46 1.82 1.49 0.745 0.437 0.316 0.305 0.199 0.170 0.160 0.192 0.174 0.231 0.264 0.250 0.277 0.249 0.327 0.356 0.316 0.359 0.353 0.407 0.372 0.328 0.291 0.262 0.280 0.258 0.294 0.249 0.247 0.223 0.212 0.208 0.185 0.162 0.140 0.138

.0.563 0.543 0.353 0.301 0.282 0.338 0.306 0.405 0.462 0.436 0.482 0.433 0.567 0.617 0.547 0.619 0.607 0.698 0.639 0.557 0.492 0.443 0.473 0.435 0.493 0.418 0.413 0.373 0.353 0.345 0.308 0.267 0.231 0.227

(mb/sr) 0.16 0.14 0.13 0.12 0.11 0.10 0.08 0.08 0.06 0.06 0.040 0.030 0.025 0.024 0.019 0.017 0.017 0.019 0.018 0.021 0.023 0.022 0.024 0.023 0.026 0.028 0.026 0.028 0.028 0.030 0.028 0.027 0.025 0.024 0.025 0.024 0.025 0.023 0.023 0.022 0.021 0.021 0.020 0.018 0.017 0.017

[mb/(GeV/c)‘] 39.5 31.7 28.0 24.2 19.5 16.9 12.1 9.83 7.26 5.97 2.98 1.74 1.26 1.22 0.794 0.680 0.637 0.767 0.696 0.922 1.06 0.998 1.11 0.995 1.31 1.42 1.26 1.43 1.41 1.62 1.49 1.31 1.16 1.05 1.12 1.03 0.117 0.996 0.988 0.893 0.848 0.830 0.742 0.646 0.559 0.550

[mb/(GeV/c)‘] 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.30 0.26 0.23 0.16 0.12 0.10 0.10 0.074 0.068 0.066 0.075 0.071 0.085 0.09 0.089 0.09 0.090 0.11 0.11 0.10 0.11 0.11 0.12 0.11 0.11 0.10 0.09 0.10 0.09 0.100 0.092 0.092 0.087 0.085 0.084 0.079 0.074 0.068 0.068

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is constant from E+6E; however for 6E = 1 MeV the error is smaller than 0.2 %. The correction due to parasitic events is less than 1 % for the lowest four-momentum transfer and reaches 20 % at the minimum of the cross section. The uncertainty introduced by such a correction always remains smaller than 4 %. The absolute number of effective protons is known with a precision of about 8 %: this error includes the uncertainty in the activity measurements and the geometry of the beam monitor. The geometrical uncertainties in the recoil spectrometer are of the order of 4 %. Multiple Coulomb-scattering .subtracts from the detection channel a part of the number of elastic events. This effect is negligible for 3He and 4He, but for tritium a correction has to be made up to 40 MeV mainly because of the 35 pm window (25 % at 15 MeV, 1 % at 40 MeV). Adding quadratically all the various independant uncertainties leads to a total systematic uncertainty of about 10 % in the elastic cross section. In addition, it

120

80

60

f

r

10 em

AE

defector

50

QE

detector

40 i

em

20

.Ol

.02

Fig. 8. Differential cross sections for p-d elastic scattering at 600 MeV, in the Coulomb-nuclear region. The dotted and dashed curve are the theoretical curves of refs. 9,1o).

interference

ELASTIC PROTON SCATTERING

421

should be noted that above 30 MeV for tritium, an additional error must be included as the germanium detector efficiency can only be determined with respect to the silicon detector efficiency, giving a total systematic uncertainty of about 15 %, The statistical errors are shown in the various tables and curves. The four-momentum transfer square is directly related to the kinetic energy ER of the recoiling nucleus through the relation (3)

( 101

II

1

8.1

8

.l

.z

.3

.,

.5

.E

Fig. 9. Differential cross sections for P-~H elastic scattering at 600 MeV; the theoretical curve is calculated with j& = @u,/4n)(i+ c& exp (&zNt), $*$ = pn,?= 1 exp (- rf/R’), o,, = 37 mb, o, = 36 mb, a,,,, = -0.48, apn = -0.36, a,, = 2.5 (GeV/c)-*, a, = 2.95 (GeV/c)-2, R = 1.68 fm.

428

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-

.1

.3

.4

.D

Fig. 10. Differential cross sections for the p3-He elastic scattering at 600 MeV; the theoretical curve is calculated with the same parameters as P-~H (fig. 9) except R = I .51 fm.

The absolute values of ER are obtained from a pulse generatar calibrated with an Am source; the uncertainty of these measurements is less than 2 % for the silicon detector telescopes and of the order of 5 % for a germanium telescope.

4. Results and conclusions The experimental values of the elastic scattering differential cross sections for p-d, P-~H, p-3He and p-4He are shown together with the statistical errors in tables

ELASTIC PROTON SCATTERING

429

3,4,5 and 6, and in figs. 8,9, 10 and 1I. Fig. 12 summarizes the results obtained with different targets. The aim of this paper is not to present a discussion of these data; nevertheless we feel that a few physical comments can already be made: (a) The p-d elastic scattering was investigated in the Coulomb-nuclear interference region to verify the influence of the phase-shift values on the nucleon-nucleon amplitudes at 600 MeV. In a companion paper lo)” we described how the curve

.I

..?

.J

.,

.a

.I

.I

-

t

(tc”iei

Fig. 11. Differential cross sections for p-4He elastic scattering at 600 MeV; :;re two theoretical curves are calculated with the same.&, function as in the p-3H and P_~H~cases (figs. 9 and IO); the dashed curve is calculated with $*qb = prji4,, exp (-$/R’f, R = 1.36fm; the full curve is calculated with +b*J,= ~fl$~[exp (-a2r~)-Cexp (-y’r:)]. c? = 0.58 fmm2. C = 0.86. yz = 4.2 fme2.

430

J. FAIN et

al.

plotted in fig. 8 can be obtained with a theoretical calculation involving the five Wolfenstein parameters 7, derived from the phase-shift analysis of McGregor et al. *) and a Glauber treatment of the nuclear part of the scattering ‘) (the Coulomb part given by Bethe analysis). (b) We show the P-~H and p-3He results in figs. 9 and 10. The dark lines correspond to a Glauber calculation using very crude Gaussian forms for amplitudes and wave function (see figure captions). The given coefficient used must be considered only as a fitting parameter with very crude physical significance. This very simple representation of the proton-nucleon amplitude cannot be used to fit the experimental

Fig. 12. Comparison of the various experimental results; the curves are described in the previous figures.

ELASTIC PROTON SCATTERING

431

results. For 3He, there is rather a large variation in the slope at ItI < 0.15 (GeVjc)“. To obtain a good fit, it is necessary to use more sophisticated proton-nucleon amplitudes even at low t. In particular, the change in the slope for p-3He is due to the great importance of the spin-dependent coefficient as compared to the spin-independent coefficient for t > 0.1(GeVjc)’ in the p-p case (this is less pronounced in p-n case). We are now in the process of completing the calculation ‘I) (Glauber treatment with five partial amplitudes and a Schiff wave function). (c) The p-4He data shown in fig. 11 confirm the existence of a dip at 600 MeV, with a peak/valley ratio equal to about two. The lines represent simple calculations using a Gaussian form for the proton-nucleon amplitude and a Gaussian or a difference of two Gaussian shapes for the nuclear density. The influence of the five nucleon-nucleon amplitudes has not yet been treated in a complete calculation. It is interesting to compare our results with the results of Boschitzetal.12), Palevsky et al. 13) and Baker et al. ‘“). The Boschitz experimentwas performed at an energy of the incident proton very close to our incident energy. Their results on the p-4He elastic cross sections are very similar to ours with a peak/valley ratio of about two. However their results on p-3He elastic cross section are not as refined as ours, due to a poorer angular resolution: they do not see clearly a dip at t = 0.31 (GeV/c)2 nor the shoulder at t < 0.15 (GeV/c)2. However it must be pointed out that such a shoulder (due to a spin effect) is clearly apparent in the results of Narboni 15) on 3He at lower energy (150 MeV). The recent results of Baker et al. on p-4He at different energies between 300 MeV and 1 GeV show that the apparent discrepancy between their previous results at 1 GeV [ref. ‘“)I (no dip) and the results of Palevsky (withadip) at a nearby energy is due to a rapid variation of the nucleon-nucleon amplitudes in the 1 GeV region. Their data at 600 MeV are in agreement with our results. Other results with a dip are also available on p-4He at 720 MeV [ref. 16)], and p-3He at 1 GeV [ref. ’ 7)]. As we pointed out at the beginning of this paper our method can be used without major modification at higher energy. We have recently applied it at 24 GeV to study elastic scattering of protons on 4He [ref. ‘*)I. It is cons”lrmed that at these higher energies the simplicity of the nucleon-nucleon interaction in the nuclear process is mainly due to the fact that the spin effects can be neglected (because for the same t-range of investigation the scattering angle of the incident proton is much smaller). Then at higher energies, we are in a better situation to study typical nuclear effects such as double scattering (the peak/valley ratio is much more pronounced) and correlation effects. At 600 MeV the value of our experiments is to provide inforrnation about the mechanism of the interaction. We are grateful1 to Professor J. Combe for many discussions on this subject and for a critical reading of the manuscript; it is a pleasure to acknowledge the synchrocyclotron operators for their efficient work on machine control and maintenance.

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References al., vol. 1 (Interscience, New York, 1959) M. Querrou, Universite de Clermont, these no. 122 (1970) F. S. Goulding et al., IEEE Trans. Nucl. Sci. NSll (June 1964) p. 388 A. Lefort, Universite de Clermont, these de 3e cycle no. 295 (1972) L. M&et, Universite de Clermont, these de 3e cycle no. 98 (1968) K. Goebel et al., CERN yellow report 60-3 L. Wolfenstein et nl., Phys. Rev. 85 (1952) 947 McGregor et al., Phys. Rev. 169(1968) 1149,173 (1968) 1272 B. Jargeaix, Universite de Clermont, these de 3e cycle no. 272 (1972) J. Gardh et al., Nucl. Phys., submitted L. M&et, Universite de Clermont, these, to appear E. T. Bosch&z et al., Phys. Rev. C6 (1972) 457 H. Palevsky et al.,.Phys. Rev. Lett. 18 (1967) 1200 S. Baker et al., Phys. Rev. Lett. 32 (1974) 839 Ph. Narboni, Universite Paris-Sud, these no. 1003 (1972) J. C. Fong et al., Sixth Int. Conf. on high energy physics and nuclear structure, Santa Fe and Los Alamos (1975) R. Frascaria et al., Sixth Int. Cot& on high energy physics and nuclear structure, Santa Fe and Los Alamos (1975) J. Berthot et al., Sixth Int. Conf. on high energy physics and nuclear structure, Santa Fe and Los Alamos (1975)

1) R. J. Glauber, in Lectures in theoretical physics, ed. W. E. Brittin et 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)