FROM CURRENT LITERATURE

FIRST EXPERIMENTS PERFORMED AT THE COSMOTRON

In 1952 a proton synchrotron came into operation at Brookhaven (USA), accelerating protons to an energy of 2300 MeV. This accelerator, which made it possible artificially to obtain particles with energies above a billion electron volts (BeV), i.e., with energies of the order of cosmic-ray energies, was given the name cosmotron.

In recent months several reports have appeared in the literature on the first physical experiments performed at the cosmotron. With the aid of a Wilson diffusion chamber 40 cm in diameter, placed in a pulsed magnetic field with an induction of 11,000 gauss, a preliminary study was made of charged particles emitted by beryllium and aluminum nuclei at an angle of 57° to the bombarding beam of protons with an energy of 2.3 BeV¹. It was found that about 90% of the particles with momenta exceeding 200 MeV/c are positive. The positively charged particles have a broad momentum distribution with a maximum near 900 MeV/c, which corresponds to the momentum expected for elastic scattering of protons by nucleons at a laboratory angle of 57°.

The negative particles—apparently mainly \(\pi^-\)-mesons—are characterized by a maximum of the momentum distribution near 350 MeV/c. For these particles the values 900 MeV/c correspond to the upper limit of the momentum distribution. At relatively small momenta \((<550\ \text{MeV}/c)\) protons could be distinguished from other positive particles by ionization density. In this way it was possible to estimate the number of light positive particles with momenta from 200 to 550 MeV/c—mainly, apparently, \(\pi^+\)-mesons—which proved to be \(1.8 \pm 0.5\) times greater than the number of \(\pi^-\)-mesons. Assuming that in the region \(>550\ \text{MeV}/c\) the spectrum of \(\pi^+\)-mesons is similar to the spectrum of \(\pi^-\)-mesons, it turns out that protons constitute about 85% of the yield of all positively charged particles; moreover, in the proton spectrum the region of higher energies is represented more strongly than in the meson spectrum.

Thus, in work¹ it was shown that even at energies of about 2 BeV elastic \(pp\)- and \(pn\)-scattering plays a large role in the general picture of nuclear interaction. We note that this fact is not connected with the choice of the angle of observation, for a laboratory angle of 57° corresponds to an angle of 133° in the center-of-mass system, a differential cross section for which at energies of 350–400 MeV does not exceed the average value both for \(pp\)-scattering, almost isotropic in the center-of-mass system, and for \(pn\)-scattering. Let us recall that, according to a recent paper by Fermi², in which the probabilities of multiple production of \(\pi\)-mesons were calculated (on the assumption that the effec-

effective volume in which the energy of the colliding nucleons is released

\[ \Omega_0=\frac{4}{3}\pi\left(\frac{\hbar}{\mu c}\right)^3, \]

where \(\mu\) is the mass of the \(\pi\)-meson), the following probabilities are obtained for different processes of nucleon–nucleon interaction at an energy of \(2.3\) Bev:

It is evident that the results of work \(^{1}\) indicate an unexpectedly large fraction of elastic scattering in comparison with \(\pi\)-meson production. It would, of course, be premature to draw any quantitative conclusions. It is possible that a considerable fraction of the produced mesons perishes without leaving the nucleus, with the formation of stars. Such a conclusion can, in particular, be drawn on the basis of work \(^{3}\), in which the products of nuclear reactions in lead and copper under the action of protons with an energy of \(2\) Bev were investigated. As is known, at an energy of the particles bombarding lead of the order of \(300\)—\(400\) Mev, among the scattering products, as \(Z\) and \(A\) increase, one first observes a characteristic maximum of the yield due to fission fragments (\(Z \simeq 40;\ A \simeq 100\)), then a sharp decrease in the yield and, finally, a new increase in it (at \(Z > 75,\ A > 190\)) due to processes of deep spallation. In the bombardment of lead by protons with an energy of \(2\) Bev, however, a very large yield of light elements is observed, situated in the “gap” between fission products and deep-spallation products at \(300\)—\(400\) Mev. In this case isotopes with a deficiency of neutrons predominate. At an average beam intensity of \(10^{3}\)—\(10^{9}\) protons/sec, the saturated activity of some reaction products amounted to \(10^{6}\)—\(10^{7}\) decays per minute per gram.

In the case of copper, at a proton energy of \(2\) Bev the yields of \(\mathrm{Ni}^{57}\), \(\mathrm{Co}^{55}\), \(\mathrm{Fe}^{59}\), \(\mathrm{K}^{42}\), \(\mathrm{Na}^{24}\), and \(\mathrm{Na}^{22}\) are comparable; whereas at \(300\)—\(400\) Mev the yield of the last three isotopes is approximately 50 times smaller than the yields of Fe, Co, and Ni. It is evident that at an energy of \(2\) Bev the processes of deep spallation are represented much more strongly than at \(300\)—\(400\) Mev, i.e., a much larger number of heavy secondary particles (\(n,\ p,\ d,\ \alpha\)) escapes from the bombarded nuclei. Precisely such facts should be observed when the produced mesons are absorbed in the nucleus.

The results of work \(^{3}\) agree with the direct observation of stars formed by protons with an energy of \(2.2\) Bev in Ilford G-5 emulsions of \(400\)-micron thickness \(^{4}\). In all, 294 such stars were observed, distributed according to the number of rays as follows:

It is evident that the average number of rays is almost three times higher than at an energy of the bombarding particles of \(300\)—\(400\) Mev.

For 130 stars, the rays were classified according to specific ionization, and the angular distribution of light (ionization \(I<1.2\) minimum) and gray (\(I=1.2\)—\(3\) minimum) tracks was investigated. Of these stars, 55% have at least one light track and 77% one gray track. The average number of light tracks proved to be 0.7, of gray tracks 1.3, and of black tracks (\(I>3\) minimum) 7.6. The ratio of intensities in the forward and backward hemispheres was \(16:1\) for light tracks and \(10:1\) for gray tracks. Since, however, in \(^{4}\) it was not possible to distinguish the light tracks of protons and mesons, it is also impossible to conclude what fraction of the gray tracks was connected with scattering and what fraction with meson production. In this sense

more indicative results of work\(^5\), in which the interaction range of protons with an energy of \(2.2\ \text{Bev}\) with nuclear photoemulsions was determined. Ilford G-5 plates were introduced inside the cosmotron chamber and exposed during one pulse under such conditions that about \(3\cdot10^4\) protons fell on \(1\ \text{cm}^2\) of emulsion. To expose the plates, it was necessary to reduce the total intensity (of the order of \(10^8—10^9\) protons/pulse) by several orders of magnitude. Therefore, an insignificant part of the beam injected by the Van de Graaff generator was admitted into the cosmotron chamber. The background was reduced by means of a special pneumatic device, which introduced the particles from the shelter into the chamber and, after several milliseconds, switched off the high frequency. This operation was carried out after the passage of the maximum of the magnetic field, and therefore, after the high frequency had been switched off, the protons, continuing to spiral out, struck the plates.

Proton tracks in the emulsion with a total length of about \(10\ \text{m}\) were examined. The interaction range was found to be \(\lambda = 33\pm6\ \text{cm}\), which corresponds to \(\sigma \simeq 0.8\,\sigma_{\text{geom}}\). About 30% of all cases proved to be indisputably elastic scattering: a single track of minimum ionization was observed, and sometimes also a short (\(<10\) microns) track of the recoil nucleus. Thus, the range for elastic scattering is about \(110\ \text{cm}\), and the range for inelastic collisions is about \(47\ \text{cm}\).

Let us note that, judging from the magnitude of the effective nuclear cross sections for nucleons with energy \(300—400\ \text{Mev}\), both these ranges are approximately equal and amount to about \(50\ \text{cm}\).

Thus the elastic-scattering cross section decreases from \(300\ \text{Mev}\) to \(2\ \text{Bev}\) by only a factor of 2, whereas the inelastic-collision cross section remains practically constant, although the character of these collisions changes strongly in connection with the strong increase in the cross sections for meson production and the appearance of multiple meson production, as well as the birth of other particles. The latter two processes have already been observed at the cosmotron.\(^{6,7}\)

To observe multiple production of \(\pi\)-mesons\(^6\) and the appearance of \(V^0\)-particles\(^7\), a Wilson diffusion chamber was used, placed in a pulsed magnetic field with an induction of 11,000 gauss, filled with hydrogen (pressure 18 atm) and operating on methyl alcohol vapors. Neutrons were directed into this chamber; they were formed in the cosmotron on a 3.2-cm or 6.4-cm graphite target and emerged through a collimator (of size \(2.5\times5\ \text{cm}\)) in the protective wall surrounding the cosmotron, approximately at an angle of \(0^\circ\) to the initial direction of the protons. The neutron beam passed through a gap between the poles of a permanent cleaning magnet, which deflected charged particles, then through a lead filter \(3.8—5.6\ \text{cm}\) thick, and entered the chamber. The number of neutrons entering the chamber has not yet been estimated with sufficient reliability. The spectrum of these neutrons is also unknown, except for the upper limit \(2.2\ \text{Bev}\), equal to the energy of the initial protons. Therefore the data obtained are of a purely qualitative character.

In work\(^6\), more than 100 cases of \(\pi\)-meson production in neutron-proton interaction in the diffusion chamber were photographed. Two such cases are schematically reproduced here from the stereoscopic photographs presented in\(^6\) (case \(A\) in Fig. 1 and case \(B\) in Fig. 2). The tracks of the particles were identified by momentum and ionization density. Tracks of particles with minimum ionization are shown in Figs. 1 and 2 by dashed lines.

A summary of the data for cases \(A\) and \(B\) is given in Table 1.

For both cases, a rough estimate of the masses of particles \(a(-)\) and \(b(+)\) leads to the conclusion that these particles are, most likely, \(\pi\)-mesons (in case \(A\), mass \(a\), \(m_a < 400\,m_e\), mass \(b\), \(m_b < 240\,m_e\); in case \(B\), mass \(b\), \(m_b < 450\,m_e\)). The heavy particle \(c\) in case \(A\) is a proton; in case \(B\), the momentum and ionization density for this particle are compatible only with the assumption that

Table I

Data on the \(\pi^+ - \pi^-\) pairs shown in Figs. 1 and 2

particle \(c\) is a deuteron. Thus, case \(A\) is evidently the process
\(n + p \to \pi^+ + \pi^- + n + p\), while case \(B\) is
\(n + p \to \pi^+ + \pi^- + d\). These assumptions are also confirmed by the data on the total momenta in the direction of the incident neutron forward \((P_z)\) and perpendicular to this direction—sideways \((P_\perp)\).

Fig. 1.

Thanks to stereophotography, the authors\(^6\) measured six angles between the tracks of particles \(a\), \(b\), \(c\) and the direction of the incident neutron and determined:

\(P_z\) and \(P_\perp\). As is apparent from Table I, in case A the impulse \(P_\perp \ne 0\), which is possible only if there is at least one more neutral particle not visible in the picture. Knowing the quantities \(P_\perp\) and \(P_z\), and also the sum of the energies of the particles \(a, b\), and \(c\), the authors\(^6\) calculated the energy of the initial neutron \(E_n\), given in Table I. In case B, as is seen from Table II, \(P_\perp \simeq 0\), which indicates the absence of neutral particles. In this case \(P_z\) is evidently equal to the momentum of the initial neutron, and the energy of the initial neutron \(E_n\), calculated from the value of \(P_z\), practically coincides with the sum of the energies of the charged particles \(E_m\).

At the kinetic energy of the bombarding neutron \(E_n\), and with a proton at rest in the laboratory system, the total energy of both nucleons in the center-of-mass system is thus evidently equal to

\[ W=\sqrt{2mc^2(E_n+mc^2)}, \]

where \(m\) is the mass of a nucleon. Thus, at the birth of mesons in an \(np\)-collision, the kinetic energy that can go into their production is

\[ T=\sqrt{2mc^2(E_n+mc^2)}-2mc^2 \]

(in the center-of-mass system), equal to \(830\) Mev in case A and \(810\) Mev in case B.

Fig. 2.

Knowing the magnitudes and directions of the momenta of the \(\pi^+\)- and \(\pi^-\)-mesons in the laboratory system, the authors\(^6\) determined their total energy in the center-of-mass system, equal in case A to 320 and 300 Mev respectively. Thus, in case A the mesons received about 75% of all the excess energy of the colliding nucleons. In case B the mesons received still more—about 90%, and in the center-of-mass system both mesons flew forward, while the deuteron flew almost strictly backward. This proves the presence of a very highly excited state after the collision of the nucleons.

Of the total number of 24 three-prong stars analyzed in detail by the authors\(^6\), there were found 10 cases of \(\pi^+ + \pi^-\), 5 cases either \(\pi^+ + \pi^-\) or \(\pi^0 + \pi^-\), 1 case of \(\pi^0 + \pi^-\) (established from the momentum balance of two protons and a \(\pi^-\)-meson), 2 cases: \(n+p \to p+p+\pi^-\), 4 insufficiently reliable such cases, and 2 cases not identified with sufficient certainty. Thus, among the indicated cases there were no fewer than \(2/3\) in which pairs of \(\pi\)-mesons were formed. The authors observed no cases of the formation of three or four mesons, for example five-prong stars of the type:

\[ n+p \to p+p+\pi^-+\pi^++\pi^+, \]

although the energy of the nucleons was sufficient for such processes. It should be noted, however, that the total number of observed cases of \(\pi\)-meson pairs was insufficient to draw a definite conclusion about disagreement of the experimental data on the probability of birth of different numbers of \(\pi\)-mesons with the above figures, based on Fermi’s theory\(^2\) (see also\(^{{11}}\)).

In paper\(^7\) it is stated that among 4000 photographs taken, several cases of production of \(V^0\)-particles were observed, and they were analyzed in detail

[[unclear: beginning of line]] two cases of production of \(V^0\)-particles, which then decayed in gas in a diffusion chamber, were analyzed. Let us recall that recently, in \(^{8}\), it was shown that, in the interaction with proton nuclei of particles of 450 MeV energy, an exchange formation of \(V^0\)-particles is not possible (if one looks for them by the subsequent decay of the type \(V_1^0 \to n + \pi^0\)). Identification of \(V^0\)-particles in \(np\)-interactions of neutrons with energies up to 2.2 Bev was carried out on the basis of an analysis of the momenta and ionization density of the tracks formed in the decay of the \(V^0\)-particle into two charged particles.

The task of identification was simplified by the fact that all processes of \(np\)-interaction of the scattering type or of meson production can give only stars with an odd number of rays, whereas in the decay of \(V^0\) two rays are observed. Stereoscopic photographs of the \(V^0\)-particle decays observed in 7 cases are reproduced schematically in Fig. 3 (case \(A\))

Fig. 3.

Fig. 4.

and Fig. 4 (case \(B\)). In both cases it followed from observations of the momenta and ionization density that the negative particle was considerably lighter than a proton and, most likely, was a \(\pi^-\)-meson. The identification of the positive particle was less certain, although the specific ionization in the tracks of these particles also exceeded the minimum. Calculations of the binding energy \(Q\) of the \(V^0\)-particle were carried out under the assumption that the positive particle is either a proton \((V_1^0 \to p + \pi^- + Q_1)\), or a \(\pi^+\)-meson \((V_2^0 \to \pi^+ + \pi^- + Q)\). Limiting values of the lifetime \(\tau\) of the \(V^0\)-particles were calculated under the assumption that production occurred in the lead filter standing in front of the chamber, or in the steel wall of the chamber. All data concerning cases \(A\) and \(B\) are given in Table II.

On the basis of observations of \(V^0\)-particles in cosmic radiation, it is accepted in the literature that for \(V_1^0\): \(Q = 35\text{--}40\) MeV, \(\tau_{\mathrm{av}} = 3 \cdot 10^{-10}\) sec., for \(V_2^0\): \(Q = 190\) MeV, \(\tau_{\mathrm{av}} = 10^{-10}\) sec. Values of the parameters characterizing these particles, \(\alpha\), are given in Table II.

Comparing the observational results with the literature data, the authors \(^{7}\) came to the conclusion that in both cases a decay of a \(V_1^0\)-particle had taken place. Although the lifetime \(\tau\) in this case proves to be greater than the \(\tau_{\mathrm{av}}\) known from the literature (as, however, also under the assumption of \(V_2^0\) decay), in favor of the identification of \(V^0\) as \(V_1^0\) speaks the agreement of the values of \(Q\) and \(\alpha\) with the literature values, as well as the fact that the ionization of the positive particles in the \(V^0\) decay was greater than the minimum.

In the interaction of a neutron of energy 2.2 Bev with a proton at rest, the kinetic energy of the two nucleons in the center-of-mass system is about 870 MeV. This energy may, however, increase or decrease substantially if the bombarded proton is not at rest in the lab-

Table II

Data on \(V^0\)-particles

FROM CURRENT LITERATURE

...laboratory system, but moves in the target nucleus. If its total energy in the laboratory system is equal to \(W_p\), and its momentum is \(\mathbf{P}_p\), then the translational velocity of the center-of-gravity system relative to the laboratory system is

\[ \mathbf{u}=\frac{\mathbf{P}_n+\mathbf{P}_p}{W_n+W_p}\,c^2, \]

and the velocity of each of the nucleons in the center-of-gravity system is

\[ V=\frac{v_0-u}{1-(v_0u/c^2)}, \]

where \(v_0\) is the velocity of the bombarding neutron in the laboratory system. Then the kinetic energy of the two nucleons in the center-of-gravity system is

\[ T=2mc^2\left(\frac{1}{\sqrt{1-v^2/c^2}}-1\right). \]

If the energy of the proton in the target nucleus is only \(20\) Mev, i.e. less than \(1\%\) of the energy of the bombarding neutron, and the proton moves in the same direction as the neutron, the total kinetic energy in the center-of-gravity system decreases from \(870\) Mev to \(700\) Mev. If, however, the proton moves toward the neutron, then the total kinetic energy increases to \(1110\) Mev. This energy would be quite sufficient for the production of a \(V_1^0\)-particle in the process

\[ n+p\to n+p+V_1^0. \]

However, in this case the kinetic energy of the \(V_1^0\)-particle in the laboratory system could not exceed the value

\[ T_{V^0}=M_{V^0}c^2\left(\frac{1}{\sqrt{1-u^2/c^2}}-1\right)\simeq 400\ \text{Mev}. \]

The experiment gave, for the energy of the \(V_1^0\)-particle, the values \(349\pm140\) Mev (A) and \(714\pm150\) Mev (B). Thus, the high kinetic energy of the \(V_1^0\)-particle in case B indicates the impossibility of the formation of this particle from the nucleons that took part in the collision. In connection with this, Ya. B. Zel’dovich recently pointed out that the \(V_1^0\)-particles should be assigned a nuclear charge equal to the nuclear charge of the nucleon, and that conservation of nuclear charge excludes the formation of \(V_1^0\)-particles otherwise than at the expense of the nucleons participating in the collision.

In the last of the papers reviewed, the case of the formation of \(V_1^0\)-particles in hydrogen under the action of \(\pi^-\)-mesons with an energy of about \(1.5\) Bev was considered\({}^{10}\). The method of this work was the same as in \({}^{6,7}\). One of the two observed cases of the production of \(V_1^0\) is shown in Fig. 5 by a diagram of two stereophotographs, in which track \(a\) corresponds to the primary \(\pi^-\)-meson, track \(b\) to the proton, and track \(c\) to the secondary \(\pi^-\)-meson formed in the decay of \(V_1^0\). Since track \(a\) is rather short, the momentum of the primary

Fig. 5.

of the \(\pi^-\)-meson could only be estimated approximately as \(1.63\ \mathrm{Bev}/c\), which agrees with the energy of the \(\pi^-\)-mesons directed toward the diffusion chamber. The direction of this track also coincides with the direction of the other tracks of the primary \(\pi^-\)-mesons. If the end of the primary track of the \(\pi^-\)-meson is denoted by the letter \(A\), and the vertex of the angle formed by the tracks \(b\) and \(c\) by the letter \(B\), then the distance \(AB = 0.65\ \mathrm{cm}\), and the angle between \(AB\) and the direction \(a\) is close to \(26^\circ\). All three tracks \(a\), \(b\), and \(c\) were coplanar, which indicates a connection between these tracks, sufficient proof of which was given by the still milder condition of coplanarity of \(A\) and tracks \(b\) and \(c\). In addition, the vector sum of the momentum components of \(b\) and \(c\) in the direction perpendicular to \(AB\) proved to be zero. The angle between \(a\) and \(b\) is \(16^\circ\), the momentum of the proton \(b\) was determined to be \(480 \pm 80\ \mathrm{Mev}/c\), and the ionization density \(I = 3 \times\) minimum. The angle between \(b\) and \(c\) is \(37^\circ\); for the negative particle \(c\) the momentum was \(210 \pm 70\ \mathrm{Mev}/c\), and the ionization density \(I < 1.5 \times\) minimum. The mass of this particle proved to be \(< 410\,m_e\), which confirms the identification of particle \(c\) as a \(\pi^-\)-meson. From the data listed, for the decay \(V_1^0 \to p + \pi^- + Q_1\), the binding energy \(Q_1 = 51\ \mathrm{Mev}\) was determined. If one adopts for \(Q_1\) the value cited in the literature, \(Q_1 = 37\ \mathrm{Mev}\), then the momenta of particles \(b(p)\) and \(c(\pi^-)\) for the observed emission angles are found to be: \(P_b = 460\ \mathrm{Mev}/c\) and \(P_c = 180\ \mathrm{Mev}/c\). Both of these values, within the accuracy of the measurements, coincide with the above direct determination of the momenta, and the authors\(^{10}\) used them for further calculations. The total energy of \(V_1^0\) from the figures given is determined to be \(1.26\ \mathrm{Bev}\), and the momentum \(P_{V^0} = 610\ \mathrm{Mev}/c\). For the conservation laws to be satisfied it is necessary to assume that at point \(A\), besides \(V_1^0\), at least one more neutral particle is produced. If this is indeed a single particle, then its total energy must be \(1.31\ \mathrm{Bev}\), and its momentum \(1.11\ \mathrm{Bev}/c\). With the kinetic energy of the initial \(\pi^-\)-meson equal to \(1.5\ \mathrm{Bev}\), the mass of this particle turns out to be \(1350 \pm 70\,m_e\). If it is assumed that the energy of the initial \(\pi^-\)-meson was \(1.2\ \mathrm{Bev}\) (which the authors\(^{10}\) already consider to be certainly below the possible energies of the primary \(\pi^-\)-mesons), then the mass of the additional neutral particle turns out to be \(1150\,m_e\). Thus, if, besides \(V_1^0\), only one neutral particle is formed, then it is evidently a heavy meson. The direction of its emission is shown in Fig. 5 by arrow \(d\). The lifetime of this meson must be \(< 4 \cdot 10^{-10}\ \mathrm{sec}\), for in the chamber no decay of it was observed over a distance of \(23\ \mathrm{cm}\). In the case considered, for the production, besides the \(V_1^0\)-particle (with the observed kinetic energy), of one more neutral heavy meson, it was required that the total kinetic energy of the primary meson and of the proton in the center-of-mass system be not less than \(870\ \mathrm{Mev}\). In fact, at a \(\pi^-\)-meson energy in the laboratory system of \(1.5\ \mathrm{Bev}\), the indicated energy was \(1.06\ \mathrm{Bev}\). The lifetime of the \(V_1^0\)-particle observed in the case under consideration was \(4 \cdot 10^{-11}\ \mathrm{sec}\), i.e., almost 10 times less than the average value adopted in the literature on the basis of observations of \(V_1^0\) in cosmic radiation.

The authors\(^{10}\) indicate that they observed one more case, similar to that described above, of the production of \(V_1^0\) in the interaction of \(\pi^-\)-mesons with hydrogen. In this case the total energy of \(V_1^0\) was \(1.33\ \mathrm{Bev}\), the momentum \(745\ \mathrm{Mev}/c\), and the lifetime \(3 \cdot 10^{-11}\ \mathrm{sec}\). The angle between \(AB\) and the direction

of the primary \(\pi^-\)-meson was \(30^\circ\). Assuming that here, too, in addition to \(V_1^0\), one more neutral particle is produced, the authors\(^{10}\) found for this particle a mass of \(1280 \pm 80\, m_e\) (at a \(\pi^-\)-meson energy of \(1.5\) BeV) and a lifetime \(\tau \simeq 3 \cdot 10^{-10}\) sec. Of course, instead of one heavy particle several lighter ones could have been produced (for example, two \(\pi^0\)-mesons or a \(\pi^0\)-meson and a \(V_2^0\)-particle); however, the cases described are consistent with the assumption of the production of a \(V_1^0\)-particle simultaneously with another heavy unstable particle. If this is so, then, from the considerations mentioned above,\(^{9}\) this other particle must be assigned a nuclear charge equal to zero.

V. G.

References

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7. W. B. Fowler, R. Shutt et al., Phys. Rev. 90, 1126 (1953).
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