MESONS PRODUCED IN A CYCLOTRON*)

E. Gardner, V. Barkas, F. Smith, and G. Bradner

The nature of the forces that hold protons and neutrons in the atomic nucleus has attracted the attention of physicists for many years. It is obvious that these forces differ from the electrostatic forces usually demonstrated with charged balls. Since protons are positively charged, according to the laws of electrostatics they should repel one another and the nucleus should fly apart. In reality, protons and neutrons are so firmly bound to one another in the nucleus that to knock one of them out of the nucleus requires an energy of millions of electron volts. The true nature of nuclear forces has still not been precisely established. An attempt to solve this problem was made with the aid of the meson theory of nuclear forces, proposed in 1935 by Yukawa \(^{33}\). According to this theory, every neutron or proton is bound to a “meson cloud.” It is assumed that mesons are something like quanta of the electromagnetic field, with the difference that they possess charge and a finite rest mass. Nuclear forces are explained as the interaction of protons and neutrons with the meson cloud, and not as “long-range” forces. Under certain conditions it is possible to extract a meson from the nucleus and study it as an independent particle. The meson component of cosmic radiation is formed in collisions of high-energy particles with atomic nuclei in the atmosphere.

In the process of meson production, the incident particle loses some amount of kinetic energy. This energy then appears in the form of energy associated with the rest mass of the meson.

In the same way, i.e., by bombarding a target with protons, \(\alpha\)-particles, or neutrons, mesons are produced in a cyclotron. In a synchrotron, mesons are formed by bombarding a target

*) Science 111, 2878 (1950). Translated from the English by V. A. Troitskaya.

E. GARDNER, V. BARKAS, F. SMITH, AND G. BRADNER

γ-rays of high energy. The fundamental processes of formation and decay of mesons were discovered in investigations of cosmic radiation,^3 but at present additional information is beginning to come in from experiments with mesons obtained in cyclotrons and synchrotrons. In the present article we shall describe a number of methods used for detecting mesons, and shall also present some results obtained with high-energy protons produced in the 184-inch cyclotron at Berkeley.^4 It has been established with certainty that there exist two kinds of mesons—π and μ—whose properties have been carefully studied. Both are unstable particles, with masses intermediate between the mass of the electron and the mass of the proton. Usually they are investigated on one and the same apparatus and are often encountered in one and the same experiment. Nevertheless, they are in fact very different types of particles. The most conspicuous difference between them is that π-mesons interact strongly with nuclei, whereas μ-mesons interact only weakly with nuclei. According to present-day ideas, π-mesons are primary particles produced in nuclear collisions occurring in cosmic radiation and in accelerators. In all probability all μ-mesons observed in the cyclotron are, by their nature, secondary particles arising as a result of the decay of π-mesons. Thus it is possible that nuclear forces are due to π-mesons. There exist both positively and negatively charged π-mesons. It is also possible that neutral mesons exist,^4,15,19 but in the present article we shall not consider them. When π^+- and π^−-mesons decay in free space, their decay gives rise respectively to μ^+- and μ^−-mesons. This process, known as (π—μ)-decay, will be considered in one of the following sections. In the decay of μ^+- or μ^−-mesons in free space they emit a positron or an electron. The energies possessed by the positron and the electron indicate that in each splitting of a μ-meson two neutrinos are also emitted.^18 If π-mesons are stopped in matter, they are absorbed by a nucleus and disappear. In this process their rest energy is converted into excitation energy of the nucleus. This phenomenon is observed on photographic plates in the stars arising at the ends of the tracks of π^−-mesons. The tracks emerging from the center of the star belong to charged particles ejected from excited nuclei. μ^−-mesons rarely, and possibly never, form such stars.^9 The penetration into nuclei of slow π^+- and μ^+-mesons is hindered by electrostatic forces. Thus, when positively charged mesons are stopped in matter, they decay in the same way as they decay in free space.

DETECTION OF MESONS PRODUCED IN A CYCLOTRON

The problem of detecting mesons created in a cyclotron consists in finding a small number of mesons formed together with a considerably larger number of protons and other heavy particles. If mesons are produced by bombarding a target with protons of energy 345 MeV, then the number of these background particles is thousands of times greater than the number of mesons. In solving this problem it is convenient to use two types of detectors, namely: Wilson chambers and photographic plates. In both of these methods charged particles are studied from the tracks they leave. If the background of unwanted tracks is large, then in order to detect the track of the particle of interest to the investigator one has to examine a large number of extraneous tracks. However, if a track has been found, the presence of other tracks has little effect on the measurements made along this track. Detection of mesons produced in a cyclotron has been carried out with the aid of photographic plates^12, and also with the aid of a Wilson chamber^13. The greater part of the work on the study of mesons produced in a cyclotron has been carried out with photographic plates. This circumstance is partly explained by the fact that the first work was done inside the cyclotron, where it is extremely difficult to operate a Wilson chamber. Recently Alvarez and his co-workers have developed a method for detecting positive mesons produced in a cyclotron by means of scintillation counters.

This method makes it possible to save a considerable amount of time and effort, and it is quite probable that these counters will replace photographic plates in many meson investigations. Although photographic plates have been used as detectors of charged particles for a very long time^5, the photographic plates now widely used were created only during the last three or four years. Some of these plates are made by the investigators themselves.

These special plates, used for the detection of charged particles, contain a higher density of silver bromide than ordinary photographic plates, and the emulsion layer on them is thicker. If a charged particle passes through the emulsion, it leaves behind a track in the form of developable silver grains. After the plate has been developed, under the microscope there is visible a line consisting of silver grains, which indicates the path of the charged particle.

The diameter of the silver grains is 0.2–0.4 micron; therefore the track is studied under a microscope with a magnification from 100 to 2000, depending on the requirements of the problem being solved.

One of the advantages of the method of detecting charged particles by means of photographic plates is the availability in our

at our disposal plates of almost any desired sensitivity. This means that, for the study of strongly ionizing particles—such as, for example, low-energy particles or fragments formed in fission—one can use such insensitive plates that will record only strongly ionizing particles, and the observer will not have to examine the tracks of electrons or other weakly ionizing particles. On the other hand, there are plates with such sensitivity that they make it possible to record the tracks of quite weakly ionizing particles.

For rapid identification of meson tracks, plates similar to Ilford C-2 plates are used; their sensitivity is such that the grain density in a meson track changes noticeably over the last several hundred microns of the meson’s range. This gives meson tracks a characteristic appearance, making it easy to distinguish them from all other tracks. Meson tracks are also recognized by the curvature associated with scattering through small angles. This change in grain density and the curvature of the track are visible in the photograph shown in Fig. 1.

For comparison, Fig. 1 shows the track of a proton. Along the proton track the scattering is not as noticeable as along the meson track. In addition, the grain density along the track changes only slightly.

Fig. 1. On the right: a photomicrograph of the track of a $\pi$-meson. This meson stopped in the emulsion and produced a star with four tracks.
On the left: the track of a proton, shown for comparison.

The \(\pi^-\)-meson, whose track is shown in the figure, moved from top to bottom. After it had slowed down and stopped in the emulsion, it entered a nucleus, and its rest energy was transformed into the excitation energy of the nucleus. Then four ionizing particles flew out of the excited nucleus, forming four tracks clearly visible in the photograph. Phenomena of this kind are called “stars.”

The search for meson tracks is very laborious; therefore, when photographic plates are exposed, every measure is taken to make the ratio of the number of meson tracks to the number of background tracks as high as possible.

Figures 2 and 3 show two methods of exposing photographic plates intended for the study of mesons. The photographic plates are exposed either wrapped in black paper or with the cyclotron room darkened.

Fig. 2. Sketch of a cyclotron with an arrangement for studying \(\pi^-\)-mesons. (Not to scale.)

Fig. 3. Sketch of a cyclotron with an arrangement for studying \(\pi^+\)-mesons. (Not to scale.)

As shown in these figures, mesons are produced when a beam of protons with an energy of \(345\) MeV strikes a target located inside the cyclotron. Figure 2 shows an arrangement for detecting \(\pi^-\)-mesons. The \(\pi^-\)-mesons leaving the target in the direction of the beam motion are deflected by the magnetic field and leave the region bounded by the high-energy proton beam. Protons and heavier nuclear fragments, likewise produced in the target and moving in the direction of the beam, have the opposite charge; as a result, they are deflected toward the center of the cyclotron and do not strike the photographic plate.

Neutrons arising in the target and in other parts of the cyclotron collide with nuclei in the emulsion and in the plate and produce a background of recoil protons, \(\alpha\)-particles, and nuclear fragments. Up to the present time, in the most successful exposures, the ratio of the number of meson tracks to the number of background tracks has been approximately \(1/50\).

Plates are arranged in such a way that the mesons produced in the target enter the plates through the upper surface of the emulsion, and their trajectories make an angle of approximately \(5^\circ\) with the plane of the emulsion. With a 10-second exposure, about 1000 tracks of \(\pi^-\)-mesons are observed on a photographic plate measuring \(2.5\ \mathrm{cm}\) by \(7.5\ \mathrm{cm}\). One of the methods used for detecting \(\pi^+\)-mesons is shown in Fig. 3. This device is similar to that which was used for the study of \(\pi^-\)-mesons, with the difference that in this case the \(\pi^+\)-mesons recorded are those which leave the target in the direction opposite to the direction of motion of the beam. In this case protons and other positively charged particles flying out of the target may move along the very same trajectories as the \(\pi^+\)-mesons; however, the heavy particles moving along these trajectories have such low energy and, correspondingly, such a short range that their tracks do not constitute a significant obstacle in the study of \(\pi^+\)-mesons.

MEASUREMENT OF MESON MASSES

At present, a series of experiments on measuring the masses of \(\pi\)- and \(\mu\)-mesons is being carried out in our laboratory. The apparatus we use is analogous to the apparatus developed by Brode\(^7\) and others in connection with the measurement of the masses of cosmic-ray mesons. Using the apparatus shown in Figs. 2 and 3, we can measure the momentum and range of a meson. Knowledge of these two quantities is sufficient for determining the mass of the meson.

If the magnetic field were homogeneous, then the trajectory would be part of a circle, and the momentum could be found from the magnetic-field strength and the radius of curvature of the meson trajectory. The radius of curvature of the trajectory can be determined by knowing the coordinate of the point at which the meson strikes the photographic plate, the position of the target, and the angle formed by the track with the edge of the plate. In reality, the magnetic field of the 181-inch cyclotron decreases slightly as the radius increases and, consequently, the meson trajectory is not exactly a circle. In this case the momentum is found by calculation taking this change of field into account\(^8\). The range of the meson in the emulsion is determined by measuring the length of the track under a microscope. The exact formula giving the relation between the kinetic energy of the meson and the radius of the circle along which it moves in the magnetic field has the following form:

\[ E\left(1+\frac{E}{2mc^2}\right)=\frac{e^2}{2mc^2}(B\rho)^2, \tag{1} \]

where \(E\) is the kinetic energy of the mesons (in ergs), \(m\) is the rest mass of the mesons (in grams), \(e\) is the charge of the meson, taken to be equal to the charge of the electron (CGSE), \(c\) is the velocity of light (cm/sec), \(B\) is the magnetic induction (in gauss), and \(\rho\) is the radius of curvature of the trajectory (in cm).

The range \(R\) and the kinetic energy of a meson are related by an empirical formula which, as was found\(^6\), gives a sufficiently good representation of the range–energy relation in the region of energies investigated by us:

\[ E = k m^{1-n} R^n, \tag{2} \]

where \(E\) is the kinetic energy of the meson (in MeV), \(m\) is the rest mass of the meson (in proton masses), and \(k, n\) are constants determined from experiment. The numerical values of these constants are: \(k = 0.250\); \(n = 0.581\).

With the aid of (1) and (2) one can eliminate \(E\) and solve the resulting equation for the meson mass \(m\).

In this method of measuring meson masses we use the fact that the trajectories of the mesons begin at the target. Thus, this method is applicable for measurements of the masses of \(\pi^+\)- and \(\pi^-\)-mesons, since these mesons are formed at the target. As a result of the decay of \(\pi^+\)-mesons stopping in the target, \(\mu^+\)-mesons are formed. Consequently, the target is a source of mesons that can be used to measure the mass of the \(\mu^+\)-meson. The \(\pi^-\)-mesons stopping in the target are captured by nuclei and, consequently, the target is not a source of \(\mu^-\)-mesons; therefore our method cannot be applied to measuring the mass of the \(\mu^-\)-meson.

To within the accuracy determined by our measurement errors, we did not find a difference in the masses of \(\pi^+\)- and \(\pi^-\)-mesons. The preliminary values of the masses obtained by us are\(^ {29}\):

\[ m_\pi = (276 \pm 6)m_e, \]

\[ m_{\mu^+} = (210 \pm 4)m_e, \]

where \(m_e\) is the mass of the electron. These values were found with the aid of formulas (1) and (2) by the method described above.

At present new measurements are being carried out in which the meson masses are determined by comparison with proton masses. In all likelihood, this method will give more accurate values. At present, however, the results are not yet known.

\((\pi-\mu)\)-DECAY

One of the most interesting facts connected with the process of meson decay is that all \(\mu^+\)-mesons produced in the decay of stopped \(\pi^+\)-mesons apparently have the same energy, equal to approximately 4 MeV.

This was first discovered in experiments on the study of cosmic radiation and was subsequently confirmed in cyclotron experiments[^8]. If the tracks of \(\pi^+\)-mesons end in Ilford plates or in plates of greater sensitivity, it is always seen that a \(\mu^+\)-meson track begins at the end of the \(\pi^+\)-meson track.

If the range of the \(\mu^+\)-meson ends completely in the emulsion, then the length of its track is always approximately 600 microns (apart from certain fluctuations in the track length associated with variations caused by the statistical nature of the process of energy loss). From formula (2) it follows that this range corresponds to an energy of the order of \(4M_{\mathrm{eV}}\). An example of a \((\pi-\mu)\)-decay recorded in an Ilford C-2 emulsion is shown in Fig. 4. The fact that the \(\mu^+\)-mesons produced in \((\pi-\mu)\)-decay always possess one and the same kinetic energy is convincing proof that only two particles arise in this decay. The second particle leaves no noticeable track even in the most sensitive emulsion; consequently, apparently, this particle is electrically neutral.

From the mass values given in the preceding section, we see that the \(\mu\)-meson is approximately 66 elec-

Fig. 4. Microphotograph showing the track of a \(\pi^-\)-meson which slowed down and stopped in the emulsion and then decayed with the formation of a \(\pi^+\)-meson. The \(\mu^+\)-meson, in turn, slows down and stops in the emulsion. The \(\mu^+\)-meson track has a characteristic length equal to approximately 600 microns.

meson masses lighter than the $\pi$-meson. This difference in mass is equivalent to about 34 MeV of energy, of which 4 MeV appears in the form of kinetic energy of the meson. It is assumed that the neutral particle carries away the remaining 30 MeV of energy, and its momentum is sufficient to balance the momentum received by the $\mu^+$-meson. Calculations show that these conditions are satisfied if the rest mass of the neutral particle is zero.

LIFETIME OF THE $\pi$-MESON

The lifetime of the $\pi$-meson is so short that some of the $\pi$-mesons undergo $(\pi \to \mu)$ decay before they reach the place where the plates shown in Figs. 2 and 3 are installed. If the plates did not block the path of the mesons and they could continue to move along approximately circular orbits, then, on the average, before their decay the mesons could make about two revolutions. Richardson1 and Martinelli and Panofsky2 measured the lifetime of the meson by observing how many mesons disappear from a certain group of mesons during the time required for this group to complete one revolution.

A schematic sketch of the apparatus is shown in Fig. 5. One group of mesons $(A)$ moves upward along a spiral and strikes the upper photographic plate after it has made half a revolution. The second group $(B)$ moves downward along a spiral and makes one and a half revolutions before striking the lower plate. The corresponding shielding (not shown in the figure) prevents mesons moving along any other paths than those shown from reaching the plates.

Fig. 5. Diagram of the arrangement of the target and plates, in which one group of mesons $(A)$ passes through half a revolution, while another group of mesons $(B)$ passes through one and a half revolutions. (Not to scale.)

The number of mesons that have struck the plates is determined by counting the number of meson tracks after the plates have been developed.

After the introduction of the appropriate geometrical corrections, the lifetime of the mesons is found from the number of mesons lost from group $(B)$ during the time required to complete the extra revolution.

Richardson^27 carried out measurements with \(\pi^-\)-mesons and obtained for the mean lifetime the value \((1.11^{+0.31}_{-0.22})\cdot 10^{-8}\) sec. Martinelli and Panofsky^21, who carried out measurements with \(\pi^+\)-mesons, found for the mean lifetime the value \((1.97^{+0.14}_{-0.17})\times 10^{-8}\) sec. These values do not agree within the indicated errors. However, we do not regard such a discrepancy in the values as proof that the mean lifetime of the \(\pi^-\)-meson is in fact different from the mean lifetime of the \(\pi^+\)-meson. The mean lifetime of the \(\pi\)-meson, according to data obtained in cosmic-ray experiments, is approximately one hundred times greater than the mean lifetime of the \(\mu\)-meson. According to the data of Neresson and Rossi^23, the mean lifetime of the \(\mu^+\)-meson is equal to \((2.15 \pm 0.07)\cdot 10^{-6}\) sec.

STARS EXCITED BY \(\mu\)-MESONS

Stars excited in the emulsion by \(\pi^-\)-mesons are very diverse in appearance. They differ in the number and direction of the tracks forming them, and also in the type and energies of the particles producing these tracks. The distribution of stars according to the number of tracks in them is of interest as a way of investigating the mechanism by which a \(\pi^-\)-meson gives up its rest energy to a nucleus^11,20,24, and as a method for finding the number of tracks of \(\pi^-\)-mesons in a set of tracks among which there is a small number of \(\pi\)-meson tracks.

As is seen from the table given below of the distribution according to the number of prongs, some \(\pi^-\)-meson tracks do not end in stars and therefore there is no simple way of distinguishing these tracks from the tracks of \(\pi^+\)-mesons.

If, however, the distribution according to the number of prongs is known, then the number of mesons producing stars can be calculated, and to it must be added the corresponding number of mesons not producing stars. This method was used by MacMillan, Peterson, and White^22 to determine the ratio of the number of \(\pi^-\)-mesons to the number of \(\pi^+\)-mesons produced by \(\gamma\)-rays obtained in the 335-Mev synchrotron at Berkeley.

In order to find the distribution of stars excited by mesons according to the number of tracks, it is necessary to select a group of \(\pi^-\)-mesons not mixed with other mesons. In the arrangement shown in Fig. 2, only mesons with negative charge can reach the photographic plate. However, in this case, besides \(\pi^-\)-mesons, the meson beam will contain a certain number of \(\mu^-\)-mesons formed in the decay of \(\pi^-\)-mesons in air. Applying the method described, one can make a mass measurement for each individual meson. The measured mass values of the \(\pi^-\)-mesons form a group of values with a mean value approximately equal to 276 electron masses,

and \(\mu^-\)-mesons, as a rule, will possess such ranges and masses that they cannot be confused with this group.

The study of the distribution by number of prongs can be carried out with the same mesons that were used for the mass measurements.

Distribution by number of prongs, found from 512 stars excited by \(\pi^-\)-mesons, according to Adelman and Jones[^1]

YIELD OF \(\pi^-\)-MESONS AS A FUNCTION OF THE ENERGY OF THE BOMBARDING PARTICLES

The number of mesons scattered when a target is bombarded with protons increases rapidly as the proton energy is increased. This effect is conveniently studied by placing the target and the plates shown in Figs. 2 and 3 on orbits of different radii. In this way one can observe the dependence of the meson yield on the proton energy, beginning from arbitrarily small energies up to an energy of 345 MeV, i.e., the maximum proton energy obtainable in the cyclotron. When a carbon target is used, the integral current of the proton beam can be determined by observing the positron activity of \(C^{11}\), formed in the reaction \(C^{12}(p, pn)C^{11}\). The relative meson yield at different energies is determined by counting the number of meson tracks on photographic plates. In doing this, the corresponding corrections are introduced for the integral beam current and for the relative volumes of the emulsions investigated.

Up to the present time the yield of mesons with energies from 2 to 10 MeV has been measured. In the experiment of Jones and White[^14], the relative yield of mesons scattered when a carbon target (dimensions \(1/32\) inch, or approximately 0.8 mm) was bombarded with protons was measured. We give their results.

These results are of interest to persons designing accelerators that are intended to be used for the production of mesons.

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