“Total” proton-proton cross sections

Nuclear Physics 55 (1964) 463--470; ( ~ North.Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

"TOTAL" PROTON-PROTON

CROSS SECTIONS

R. GOLOSKIE Department of Physics, Worcester Polytechnic Institute, Worcester, Massachusetts, U.S.A and

Cyclotron Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A. t and J. N. PALMIERI Department of Physics, Oberlin College, Oberlin, Ohio, U.S.A. and Cyclotron Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A. * Received 24 February 1964 Abstract: The cross section for the scattering of protons by protons into the angular range of 6° to 84° (laboratory system) has been measured for several proton energies using a "good-geometry" absorption technique. The results are Average energy (MeV) 147 134 122 108 91 70 E]

Cross section (mb) 23.7=[=0.1s 24.94-0.2 25.94-0.2 28.34-0.3 32.74-0.4 38.54-0.5

NUCLEAR REACTION H'(p, p) Ep = 70-153 MeV; measured a(E).

1. I n t r o d u c t i o n

At the present time considerable effort is being devoted to the analysis o f nucleonnucleon scattering. While p-p differential cross sections have been measured 1-4) with relative precisions o f a b o u t 4- I ~ in the range f r o m 60 to 160 MeV, the uncertainties in the absolute values are often m u c h greater. The absolute uncertainties can usually be attributed to several effects which do not significantly influence the relative cross sections: (i) calibration o f the absolute beam m o n i t o r 5), (ii) corrections for absorption in the counter telescope, (iii) measurement o f target thickness (particularly t This work was supported

by

the U.S. Office of Naval Research. 463

]

464

R. GOLOSKIE AND

J. N. PALMIER[

for liquid hydrogen targets), (iv) determination of the solid angle subtended by the telescope. To provide a more reliable determination of the absolute value of some differential cross sections, we have measured the "total" cross section for protons to be scattered by protons into the angular range of about 6° to 84° (laboratory system). A "goodgeometry" absorption technique was used.

2. Experimental Arrangement The unpolarized external beam of the Harvard University Cyclotron was used (fig. 1). Slits A, B and C were adjusted to produce a beam about 2 cm diam. in the experimental area. The energy of the beam was varied by placing brass and/or lead absorbers between slits B and C. The bending magnet removed from the beam any protons of undesired energy. This magnet, slit C, and the acceptance angle of the counter telescope limited the energy spread of the incident beam to less than -t-½%.

rlLrr•EXTERNAL BEAN PIPE

T CN

t57.5

+

r~COUNTER

t

923 CN

+

I-g

i!

31.1 CN

4

•,.-------~eOUNI'ER2 IN

9.1 CN ACUUN CHAMBER

22.2 CH

HEAT RAOIATION SHIELO RGET

61,9 CN

2 Fig. 1. Source of unpolarized proton beam used in:this experiment. Slits D did not affect the beam in any way.

~COUNTER 3

Fig. 2. Experimental arrangement.

IO cM

p-p CROSS SECTIONS

465

The intensity of the beam reaching the experimental area was reduced to about 200 protons/see by means of a carbon block ("carbon clipper") placed at a radius of 27 em inside the cyclotron vacuum tank. The arrangement of the detectors and the target is shown in fig. 2. All detectors were plastic scintillators (Pilot B), used with RCA 6810A photomultiplier tubes. Counters 1 and 2 were identical discs, each 0.66 cm diam. and 0.17 era thick. These two counters, separated by 123 can, defined a wellcollimated beam and served, in double coincidence, as the incident beam monitor. Counter 3 was 15.143+0.005 era diam. and 0.64 can thick. It was located 73.0-t-0.3 cm from the centre of the target. This counter, in coincidence with detectors 1 and 2, monitored the transmitted beam, detecting protons leaving the target at angles less than 5.95*, measured with respect to the target centre. As shown in fig. 2, several brass collimators (3.8 cm thick with 1.2 em apertures) were placed along the direct beam to reduce the number o f non-beam protons reaching the various counters. ~'COINCIOENCECIRCUITS

1 I r l

i I EXPERINENTAL AREA

l

[]

[]

CONTROL AREA

Fig. 3. Arrangement o f electronic circuits. All signal cables were type RG 62/U.

The target was a right circular cylinder with its axis along the beam. As a compromise between good energy resolution and a reasonable signal-to-background ratio, the target was made about 12 MeV thick for 153 MeV incident protons. The liquid hydrogen in the target scattered about 1.5 ~ of the incident 153 MeV protons out of the angular range of counter 3. The end windows of the target were made of berylliumcopper, with a total thickness of 0.008 cm. A vacuum chamber with 0.008 cm Mylar windows enclosed the target. In additional a total thickness of 0.003 cm of aluminium (part of a heat shield) was in the direct beam. At liquid nitrogen temperature, the target was 15.392+0.008 cm long and 9 cm diam. (The target length was measured with liquid nitrogen at 2 atm pressure in the target and the "vacuum" chamber open to air.) A dummy target which contained the same materials (except for hydrogen) as the real target was used for background measurements. The dummy and real targets were alternately placed in the proton beam by remote control without interrupting the cyclotron operation.

466

R. GOLOSKIE AND J. N. PALMIERI

A block diagramme of the electronic circuitry is shown in fig. 3. The configuration was arranged to record all protons passing through counters 1 and 2 (12), through 1, 2 anff 3~ (123) and through 1 and 2 but not through 3 (123). The fact that (123) always agreed with the difference between (12) and (123) provided a constant indication of the stability of the circuits. The outputs of the coincidence circuits were fed to discriminators which had dead times of less than 0.2 #see. The 10 MHz sealers were Hewlett-Packard model 520 A. The first step in the experiment was the alignment of the counter telescope. Counter 1 was centred on the beam photographically. Counter 2 was positioned to give a maximum coincidence rate (12) with counter 1. To aid in the alignment of counter 3, a collimator with a 1.3 era aperture was attached to counter 3 such that the aperture was centred on the counter. This counter was positioned to give a maximum triple coincidence (123) rate, and then the collimator was removed. The voltages on the photomultipliers and the lengths of the cables from the detectors to the coincidence circuits were adjusted for optimum conditions to provide stable operation throughout the measurements. Because the scattering due to the hydrogen in the target was Rot much greater than that due to counter 2, air and the windows in the target, background measurements had to be made for almost as long as the hydrogen measurements. At each energy approximately 12 runs were made with the hydrogen target in place and 9 runs with the dummy target in place. The latter runs were spaced among the 12 hydrogen runs to eliminate spurious effects from possible changes in the responses of the various circuits. In fact, no such variations were observed. To check the effects of misalignments, some data were taken with intentional mistakes: (i) bending magnet current incorrect by 3 %; (ii) target axis 0.6 era from the beam centroid; (iii) centre of counter 3 located 1.3 cm from the beam centroid. In each case the results agreed within their statistical uncertainty of +. 2 % with the result for proper alignment. The energy of the beam for each measurement was obtained from a range-energy measurement using brass abosrbers 6). 3. Calculations

The total cross section a for scattering an incident particle into the angular range between 0 o and 01 in the laboratory system is defined by the equation F =

exp (-pNoa/A),

(1)

where A is the atomic weight of the target material, p its areal density, No Avagadro's number, and F the fraction of protons incident on the target which are n o t scattered into the range 0o to 01 . Hence . = ( ~ / N o p ) In ( I / F ) .

(2)

p-p CROSS SECTIONS

467

To determine F, assume that Mt is the number of protons incident on the hydrogen target, as measured by the (12) coincidences. Call Art the number of (123) counts recorded for Mt incident particles. Let Md and Nd be the corresponding numbers for the dummy target. Then we obtain

F = (1-Nt/Mt)/(1-Nd/Md).

(3)

a = (A/Nop) In [(1--Nd/Md)/(l-NdMt)].

(4)

Therefore Since Na/M d and Nt/M t are both small (<0.04), the logarithm may be expanded so that

In calculating a, a value of 0.0709 g/era 3 was used for the density of liquid hydrogen 7); No was taken as 6.025 x 1023 mole- 1 and A as 1.008. Since N a and N t are distributed binomially from 0 to Md and M t, respectively, the standard deviation in a due to statistical fluctuations is given by 8, 9) N,

Nd

Aa = (AINop) [-(Mt_~,)M ' + (M.-Nd)M;]

+ (6)

It was necessary to make two corrections to ~ as calculated from eq. (5). The dummy measurement Na/Ma did not exactly represent the scattering by the windows of the target. With hydrogen in the target, the beam protons reaching the exit windows and the air beyond have a different energy from the corresponding beam protons with the dummy target in place. Hence a small correction ( < 2 % of a) based on the measured energy dependence of p-carbon and p-copper absorption cross sections 1o) had to be made. A much smaller correction was required due to multiple scattering l i, 12). Some protons which left the target having apparently been singly scattered through an angle 0 had actually been scattered many times. If a is to represent the total single scattering cross section, a correction must be made for the multiply scattered particles. It has been shown 13) that, for the conditions existing in this experiment, the ratio of the differential cross section for both single and multiple scattering at the angle O to that for single scattering alone can be written approximately as (1 +a/02), where a is a positive constant depending on target material, target thickness and incident proton energy. If the differential cross section (laboratory system) for p-p scattering is assumed to be b cos 0, then the fraction of multiply scattered particles included in a is given by

fus =

fo

' b cos 0(1 +a/O 2) sin 0 dO o - 1. ~'b COS 0 sin 0 dO 0

(7)

4~

TAaLE 1 Results

Energy at target (MeV)

tr (mb)

enter

exit

av.

uncorrected

153

141

147

23.83+0.12

Corrections (%) background multiple energy a) scattering

--0.48

--0.12+G.02

Angular range

a(mb) final b)

lab

23.694-0.15

5.95-83.57

12.36-167.64 12.30-167.70

c.m.

141

127

134

25.114-0.19

--0.74

--0.144-0.03

24.894-0.22

5.95-83.62

129

115

122

26.144-0.15

--0.94

--0.174-0.03

25.854-0.21

5.95-83.67

12.26-167.74 12.22-167.78

116

100

108

28.754-0.20

--1.52

--0.21 4-0.04

28.254-0.29

5.95-83.70

100

82

91

33.41 4-0.25

-- 1.86

--0.29t0.06

32.71 4-0.40

5.95-83.76

12.18-167.82

38.51:t:0.48

5.95-83.83

12.10-167.90

81

59

70

39.474-0.27

--1.98

--0.474-0.09

• ) Uncertainty taken as half of magnitude of correction. b) Includes error of 4-0.3 % due to possible telescope inefficiency and random counts.

.z

p-p CROSS SECTIONS

469

For example, at 147 MeV b ~ 16 mb/sr and a ~ 1.7 x 10-4rad 2, so that fMs = 0.0012. The final results of this experiment are displayed in table 1 and fig. 4. The variation in the upper limit of the angular range in the laboratory system is due to the usual relativistic effect. The quoted errors in a (uncorrected) arise principally from counting statistics. The energy correction to the background measurement is given a possible error of _ 50 % of itself. This source of errror becomes important at the lower energies where the background changes most rapidly with energy. An additional uncertainty of _ 0.3 % has been included in the final result at each energy because o f possible dead time losses and random coincidence counts. Errors due to these effects would tend to cancel each other. 45

t

I

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I

I

I

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I

I

I 140

I

• THIS EXPERIMENT o YOUNG AND JOHNSTON

4O

35

E 30

25

I

20 60

I 80

I I I ZOO 120 AVERAGE ENERGY (MeV)

I

160

Fig. 4. T o t a l p r o t o n - p r o t o n cross section as a f u n c t i o n o f t he a ve ra ge energy of the incident proton.

Errors due to the uncertainty in the target length (+0.05 %) and to the finite size of the target ( + 0.01 ~o) are negligible. No error has been included for the uncertainty in the value of the density used for liquid hydrogen. Such an error would apply systematically to all measurements. 4. Discussion

The p-p differential cross section 3) between 6 ° and 83.8 ° (laboratory system) at 68.3 MeV has been integrated numerically by the authors of the present paper and has a value of 38.2_ 0.4 mb, in agreement with the result of 38.5-4-0.5 mb found here at 70 MeV. A similar integration 1) of the data at 147 MeV gives a value of 25.7-t- 1.2 mb, about 8 ~o higher than the value reported here. Since difficulties with the absolute

470

R. GOLOSKIE AND J. N. PALMIERI

beam monitor used in the work of ref. 1) have been found s), we suggest that the absolute values of the cross sections reported in ref. l) be ignored in any analysis and that the total cross sections in table 1 be used instead. Such a procedure would bring the 147 MeV differential cross sections into agreement with those of Caverzasio and Michalowicz 2) at 155 MeV. This experiment was performed at the Cyclotron Laboratory, Harvard University. We thank Mr. A. M. Koehler and the members of the Cyclotron staff for their invaluable help. We are also deeply indebted to Professor A. M. Cormack of Tufts University for the assistance he rendered in all phases of this experiment. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

J. N. Palmieri, A. M. Cormack, N. F. Ramsey and Richard Wilson, Ann. of Phys. 5 (1958) 299 C. Caverzasio and A. Michalowicz, J. Phys. Rad. 21 (1960) 314 D. E. Young and L. H. Johnston, Phys. Rev. 119 (1960) 313 A. E. Taylor, E. Wood and L. Bird, Nuclear Physics 16 (1960) 320 J, N. Palmieri, R. Goloskie and. A. M. Cormack, Phys. Lett. 6 (1963) 246; J. N. Palmieri and R. Goloskie, to be published W. A. Axon, B. G. Hoffman and F. C. Williams, U.S, Govt. Printing Office 0-335880 (1955) International critical tables, Vol. 1 (McGraw-Hill Book Co., New York, 1926) H. Margenau and G. M. Murphy, The mathematics of physics and chemistry (D. Van Nostrand Co., New York, 1943) R. Goloskie, Thesis, Harvard University (1961) A. E. Taylor and E. Wood, Phil. Mag. 7 (1963) 44, 95 G. Moli6re, Z. Naturforsch. 3a (1948) 78 H. A. Bethe, Phys. Rev. 89 (1953) 1256 A. M. Corrnack, Nuclear Physics 52 (1964) 286