P H Y S I C A L R E V I E W V O L U M E 1 0 1 , N U M B E R 3 F E B R U A R Y 1 , 1 9 5 6

Negative Pions from Neutron Bombardment of Deuterons MYRON W. KNAPP AND WILSON M. POWELL

Radiation Laboratory, Department of Physics, University of California, Berkeley, California (Received October 24, 1955)

In order to obtain information on the neutron-neutron interaction, a cloud chamber filled with deuterium gas was bombarded with the neutron beam of the Berkeley 184-inch synchrocyclotron. The spectrum of the neutron beam, which is produced by 340-Mev protons on a 2.5-inch lithium deuteride target, is peaked at 300 Mev and extends to 340 Mev. The three reactions d{n,iTp)d, d(n,w~pn)p, and d(w,7r~)He3 were studied. A total of 310 events were examined; the three reactions contributed 208, 80, and 22 events respectively. Laboratory-system angular distributions and energy spectra of the mesons are presented. Comparisons were theory indicate agreement with the predictions of the charge-independence hypothesis.

INTRODUCTION

MANY of the recent experiments1-3 on meson physics have sought information on charge

symmetry and charge independence of nuclear forces. The latter hypothesis, as formulated in the principle of conservation of isotopic spin, permits all cross sections for pion production in nucleon-nucleon collisions to be written in terms of three independent cross sections,4

whereas the weaker principle of conservation of isotopic parity relates only the neutron-neutron interactions to the proton-proton ones. Either of these hypotheses predicts that the cross section for the reaction p+p—^ir+

+d will be the same as that for the reaction n-\-n -^Tf-Jrd. This is also true for the angular distributions in both reactions. Because the latter reaction cannot be observed directly, the reaction n+d—>w~+3 nucleons has been substituted. An exact knowledge of the condi­tion of the neutron in the deuteron when it is struck by the incoming neutron should permit the calculation of the angular distribution of the pions in the center-of-mass system of the two neutrons. Ideally one would compare this distribution with the (J+cos20) obtained for 7r+ mesons by protons on protons5-7 and for ir° mesons by neutrons on protons.1 The unknown momentum of the neutron in the deuteron, however, makes a transformation to the center-of-mass system of the two neutrons impossible. Therefore the alter­native possibility was chosen, and laboratory-system distributions are compared with theoretical distribu­tions as derived from the known neutron spectrum and known momentum wave functions of the deuteron. Owing to difficulties in monitoring the high-energy portion of the neutron beam, no attempt was made to determine absolute cross sections, and the results are

1 Roger H. Hildebrand, Phys. Rev. 89, 1090 (1953). 2 Frank, Bandtel, Madey, and Mover, Phys. Rev. 94, 1716

(1954). 3 Robert A. Schluter, Phys. Rev. 95, 639 (1954). 4 A. H. Rosenfeld, Phys. Rev. 96, 139 (1954). 6 Cartwright, Richman, Whitehead, and Wilcox, Phys. Rev.

91, 677 (1953). 6 Frank Stevens Crawford, Jr., University of California

Radiation Laboratory Report No. UCRL-2187, April, 1953 (unpublished).

7 M . Lynn Stevenson, University of California Radiation Laboratory Report No. UCRL-2188, April, 1953 (unpublished).

11

presented in terms of relative angular distributions and energy spectra for the three reactions involved.

EXPERIMENTAL PROCEDURE

Experimental Apparatus

The experimental apparatus consisted of a ten-atmosphere Wilson cloud chamber operated in the neutron beam of the Berkeley 184-inch synchro­cyclotron. The cloud chamber, cyclotron lithium deuteride target, and neutron energy spectrum are identical with those described by De Pangher8 except for the fact that the chamber was filled with ten atmospheres of deuterium gas instead of hydrogen.

Analysis of Film

Description of an Event and Sample Picture

The three types of events possible in this experiment are shown in Table I together with their Q values. The first is referred to as a d or deuteron type, the second as a p or proton type, and the third as a He3 type event.

Because there is no unseen particle in either the d or He3 type events, they must show a total forward momentum equal to that of the incident neutron, and their transverse momenta must balance. The p type event has an unseen neutron, therefore the particles that are seen need not have as much total forward momentum as in the other two types, and their trans­verse momenta need not balance. I t also follows from momentum considerations that the pion, being light, can have any direction relative to the neutron beam and that the proton in a d-type or one of the protons in a ^-type event can come off in a backwards direction, if its energy is fairly low.

An event consists, therefore, of one lightly ionized track of negative curvature and one or two positive tracks that have considerable forward momentum. Figure 1 contains two easily visible ir~ events and one 7r+ event. The 7r+ events were not studied because they were difficult to find with certainty, as indicated by the difficulty of seeing the one in Fig. 1.

8 John De Pangher, Jr., Phys, Rev. 99, 1447 (1955). Also University of California Radiation Laboratory Report No. UCRL-2153, March, 1953 (unpublished).

10

N E U T R O N B O M B A R D M E N T OF D E U T E R O N S 1111

TABLE I. Types of events possible in this experiment.

Event Type Q(Mev)

n+d-+ir+p+d d 138 n+d->TT~+2p-{-n p 140 w+d->7r-+He3 He3 133

Scanning Procedure and Methods

Two scanning methods were used. One of these employed a stereoscopic viewer, of high magnifying power, through which one could examine track origins, looking for more than one track starting at the same point in space. In this manner oxygen stars from the oxygen in the water vapor, pion events of the three types mentioned above, and two-prong stars were found. The two-prong stars could be fitted into one of three categories; they could either be oxygen stars, coincidences, or pion events in which the meson was hidden or unseen for some reason. Therefore all two-prong stars had to be examined in detail to be sure that no pion events were missed, and those for which no explanation was apparent are discussed in a later section.

Also noted during scanning were any negative mesons that appeared to start in the collimated region but for which no associated tracks were apparent. These were examined more thoroughly on the projection apparatus, and in all but one case the meson was either traced back to an event or to a point outside the illuminated region.

The second scanning method involved projecting the cloud-chamber pictures to approximately twice normal size and examining one of the paired stereoscopic views at a time for tracks starting at the same point. By quickly shifting from one stereoscopic view to the other, one could decide whether or not tracks started at the same point in space. The procedure in other respects was the same as above. Only about £ of the pictures were scanned in this manner, but the fraction of events missed in the one scanning was the same as that in the other method.

Measurement Procedure

The measurement procedure was identical with that of De Pangher8 except that it was necessary also to identify the tracks as those of a pion, a proton, a deuteron, or a He3 by Bp vs ionization comparisons.

Analysis of the Data

From the measured data, the direction and energy of each particle could be obtained and momentum-energy balance could be used to check that the particles were all identified correctly and to obtain the energy of the incident neutron.

Because of measuring difficulties, meson events in

FIG. 1. Cloud-chamber photograph. This picture contains three events, two of the type n-\-d—*iT-{-p-\~d, and one of the type n-\-d—>T+-\-3n. The three origins are encircled.

which the pion had a dip angle9 greater than ao=50° were excluded from the data. For this reason a geometric correction factor,

w/r f(d,ao) = ,

sin-1(sinao/sin0)

had to be applied to each event. Two assumptions were made in the derivation and use of this factor. The first is that pion production is azimuthally symmetric about the beam direction, and the second is that for each event in which the pion has an angle 0, with respect to the neutron beam, there are [1—/(0,«o)] identical events in which the pion is in the excluded region. This geometric factor is applied to all properties of the event as a whole.

No other correction factor was needed, as it was not necessary to exclude events where the positive particles had steep dip angles. This follows because the deuterons and He3,s could not have steep dip angles, and those protons having steep dip angles had low energies, making accurate measurements on them unnecessary.

EXPERIMENTAL CHECKS AND DISCUSSION OF ERRORS

In order to obtain data at a reasonable rate it was necessary to run the chamber so that each picture was very full of neutron produced events. This made it difficult to find pion events. Particular care was taken in analyzing the data to make certain that this confusion in the individual pictures did not bias the data in favor of any particular type of event.

An azimuthal division of the mesons into eight equal azimuthal groups showed twenty percent more events with the mesons going up than those going down. The energy distribution, angular distribution,

9 Dip angle is denned as the angle between the plane of a track and the horizontal plane.

1112 M . W . K N A P P A N D W . M . P O W E L L

TABLE II. Scanning efficiencies.

Run No.

Number scanned Number missed Efficiency % Number scanned Number missed Efficiency % Number scanned Number missed Efficiency %

l

8 0

100 8 3

62 0 0

2

83 5

94 83 14 S3 0 0

3

66 8

88 47

6 87 19

1 95

4

60 4

93 2 0

100 58

3 95

5

93 11 88 72 10 86 19 4

79

Total

310 28 91

212 33 84 96

8 92

a Rescanning.

and division into types of events of both groups appear the same within statistical errors and therefore it was concluded that this variation with azimuth did not affect relative cross sections.

A similar comparison was made between regions along the path of the neutrons traversing the chamber. Events appearing over the first and last two inches of the chamber were counted but discarded in the analysis because of difficulty in seeing the mesons near the entrance window and measuring curvatures on the very short tracks near the exit window. When the data was divided into two equal groups along the neutron beam or across the neutron beam a comparison of the two sets of data agreed within the statistics.

Scanning Errors

The film scanning was accomplished by two observers, one of whom (referred to as No. 2) scanned only part of the film, whereas the other (No. 1) scanned all the film and rescanned that part not scanned by No. 2. Table II lists by run numbers the known number of events in the section of film scanned by each observer, the number of these events which that observer missed, and the scanning efficiency calculated thereby. It also illustrates the totals of each of these quantities for all runs.

As the run-by-run efficiency of each observer does not differ appreciably from their total efficiency, and as the efficiencies of both observers are approximately equivalent, these results have been combined to yield Table III. If the probability of missing an event in scanning is purely random, the probability that it will be missed in two independent scannings is the product of the two individual probabilities. Therefore the scanning and rescanning inefficiencies are also listed in Table III, as is their product, the total inefficiency.

TABLE III. Combined scanning and rescanning efficiencies.

Efficiency Inefficiency

Scanning 9 1 % 9% Rescanning 87% 13% Combined results 98.8% 1.2%

This result indicates that probably only one meson in a hundred was missed. This is of course a negligible number but it is still necessary to ascertain whether the events missed were simply overlooked or were missed because of a peculiar property. The former would not prejudice the results, whereas the latter would. As a check, the angular and energy distributions of those pions missed were compared with those not missed. No significant difference was observed.

On breaking down this scanning efficiency into the different types of events, however, it was found that approximately 11% of the He3 types could have been missed. This is not surprising when the fact that only two tracks show for He3 types and three for all others. This error is completely dwarfed by the statistical error in the 22 events observed and is therefore of little importance.

Errors in Measurement of Pion Energy

The errors in pion-energy measurements arise from shortness of tracks and turbulence. The lengths of the pion tracks were such, on the average, as to give an

TABLE IV. Classification of events.

Type event

d P He3

Totals

Unques­tionable

185 74 19

278

Question­able

23 6 3

32

Ratio of question­able to unques­tionable

0.12 0.08 0.16 0.12

Total question­able and unques­tionable

208 80 22

310

uncertainty in the pion momentum of about ± 5 % . The assumption of 1-reciprocal meter turbulence, which was the worst value in this cloud chamber as determined by De Pangher8 for steep tracks, would yield only a ± 2 % error in the momentum of a pion of mean energy. This means that the pion energy errors are of the order of 10% on the average.

Errors in Measurement of Neutron Energy

From the degree of balance or unbalance of each event of the d-type, it was possible to estimate the errors involved in the neutron energy determination, and these errors were found to fit a Gaussian of 8.3% standard deviation. The errors in the other two cases are assumed to be similar.

Classification of Events

Table IV shows a division of the events into types and a further division of the types into unquestionable and questionable events. The unquestionable events could be made to satisfy the momentum and energy balance required if turbulence caused an additional curvature of not more than 0.05 reciprocal meter. By

NEUTRON B O M B A R D M E N T OF DEUTERONS 1113

z <

UJ

on UJ CL

FIG. 2. Distribu- £j tions for the protons ^ in n-\-d—>ir~4-p-hd. j§

UJ

>

UJ

or

2 0 h

h

I6h

J-

,2r F

8 h

4r

oL

•"•"""i r r i" - i r 1 1

-

-

* * •

"

T i l i i

1 1 1 . ^ f e f e ^ H a , 1 ... 1

50

UJ s 40 UJ CL

a:

2 z t i i

REL

ATI

V ro

o

10

0

1 1 T r

T J 1

"I 4

1 "I 1 1 -1 1

T T |

tri T

rt !

p. \ 1

Jf^-f^t^

r 1 1 1

H

H

H

—| H

H

*

H

-j

K^XfX X L L_ J 0 40 80 120

PROTON LAB ANGLE

relieving this stringent requirement all the events could be classified as shown. A comparison of the angular and energy distributions of the d-type question­able events with the unquestionable ones showed no significant difference and therefore all events were used in compiling the data.

All events were measured twice, and those having

160 40 80 120 160 PROTON LAB ENERGY (MEV)

important disagreements between the measured values were measured a third time before the calculations were performed. Weighted averages of these measure­ments were used in the calculations.

Eleven two prong stars appeared where the momenta and energies of the prongs were such as could have occurred in a meson event. It is quite likely that several

PION ANGULAR DISTRIBUTIONS

FIG. 3. Pion labor­atory-system angular distributions for the t h r e e r e a c t i o n s studied.

PION ANGLE IN LABORATORY SYSTEM

FIG. 4. Pion laboratory-system energy spectra for the three reactions studied.

of these may have had a meson connected with them which was invisible because of obscuration by other tracks or deficiency of vapor. Fortunately, however, these eleven events amount to only 3.8% of the total number of events and therefore introduce a negligible error.

TABLE V. Relative frequencies of the three reactions.

Number of Ratio of each events of to the total

Reaction each type number of events

n+d->TT~p+d 208 67% n+d-*Tr-+2p+n 80 26% «+<*->*--+He3 22 7% Total, all reactions 310

RESULTS AND CONCLUSIONS

Ideally the results of this experiment should be presented in the form of pion angular and energy distributions in the center-of-mass system for the two colliding neutrons.10 Because this center-of-mass system is not known it was deemed best to present the labora­tory-system distributions for comparison with similar distributions as derived from known deuteron wave functions and various assumed center-of-mass system distributions. A calculation of this type has been carried out under the impulse approximation, using the follow­ing assumptions11:

(a) Only the neutron-neutron interaction gives the pion and the deuteron, i.e., the final deuteron is formed from the initial colliding neutrons.

(b) The excitation function given by Schulz12 for proton-proton 7r+ production is valid for neutron-neutron T~ production.

(c) The only function of the initial proton is to provide a momentum distribution for the neutron in the deuteron.

10 At 400 Mev the reaction p+p->Tr++d is favored over the reaction n+p-+ir-+2p by a factor of 7.6. [S. C. Wright and R. A. Schluter, Phys. Rev. 95, 639( 1954)]. Therefore the proton in the deuteron could produce only about 10% of the events, and this would not be detectable within the statistics of this experiment.

11 Burns MacDonald (private communication). 12 Alvin George Schulz, Jr., University of California Radiation Laboratory Report No. UCRL-1756, May 22,1952 (unpublished).

NEUTRON BOMBARDMENT OF DEUTERONS 1115

Fig. 6. Comparison of the pion distributions with theory for the reaction »+<£—*ir~

I EXPERIMENTAL A THEORETICAL #. ASSUMED

C.m. DISTRIBUTION

• THEORETICAL : ASSUMED J C-IU DISTRIBUTION IS SYMMETRIC

60 80 100 120 MO 160 PION LAB ANGLE

180 ~0 2 0 4 0 60 80 100 120 PION LAB ENERGY (MEV)

(d) The deuteron momentum wave function is Gaussian.

(e) The energy of the incident neutron is 300 Mev. (f) The center-of-mass system angular distribution

either is symmetric or equals [|+cos20]. Both cases have been carried out for comparison purposes.

One fault with this theory is immediately obvious. This concerns the protons in the deuteron-type reac­tions. They should be directed essentially forward13

with energies corresponding to the momenta they would have in the deuteron, and it is noted that their angular distribution (Fig. 2) does agree substantially with this, but the high-energy protons cannot be accounted for by the model given. These proton distributions have been included in the results because they do provide a test for any theory on the deuteron-type reaction.

The pion laboratory-system differential cross sections for the three reactions are plotted in Fig. 3. Similarly Fig. 4 gives the pion laboratory-system energy spectra. The relative frequencies of the three types of events are represented in Table V. The scales are all arbitrary, as no absolute cross sections were measured, and the errors shown are the statistical standard deviations.

13 If the neutron in the deuteron were directed^ exactly toward the incident neutron the cross section would be higher because of the steep excitation function, but the solid angle would be slightly larger for a neutron directed toward but at an angle to the incident neutron. Therefore the protons would be expected to be directed forward at small angles to the beam.

The energies of the neutrons producing the events are shown in Fig. 5. For comparison purposes the total corrected numbers of ^-type and He-type events have been normalized to the total corrected number of d-type events. The errors are large (about ±8%) but the general trends are still indicative. In particular it might be noted that low-energy neutrons favor the He3-type events, as might be expected.

In Fig. 6 the pion angular distributions are compared with those obtained from theory for (a) symmetric c.m. distribution, (b) (|+cos20) c.m. distribution. It is seen that the experimental data are in good agreement with the Q+cos20) c.m. distribution but in disagree­ment with the symmetric c.m. distribution.

Figure 6 also gives a similar comparison for the pion spectra, and it is noted that the experimental data are in poor agreement with either case; but this may be due to the spread in energy of the incident neutrons.

We conclude therefore that our results are in agree­ment with the predictions of charge independence.

ACKNOWLEDGMENTS

Many people assisted in this experiment both in preparation and in the scanning. John B. Elliott and Larry O. Oswald did much of the preparatory work and Dr. C. Y. Chih measured many of the events. The theoretical curves were calculated by Burns Mac-Donald,

FIG. 1. Cloud-chamber photograph. This picture contains three events, two of the type n-\-d—*ir~+p-\-d, and one of the type n+d—*r++3n. The three origins are encircled.