From the Current Literature

Photograph of the Decay of Heavy Mesotrons in a Wilson Chamber

The investigation of the composition of cosmic radiation, carried out under the direction of A. I. Alikhanian and A. I. Alikhanov over recent years, has shown that, in addition to “ordinary” mesotrons with a mass of \(200\,m_e\), particles of greater mass are present in cosmic radiation at an altitude of 3250 meters. The magnetic analysis of the charged component of cosmic radiation, performed on Mount Alagez in Armenia in 1946, showed that, in order to explain the observed set of values of momenta and ranges, it is necessary to assume the existence of at least three particles with masses of about \(500\,m_e\), \(1000\,m_e\), and \(2000\,m_e\).[^1] The same result was obtained by comparing the ionizing power and absorption of particles included in the composition of the so-called “soft component.”[^2] In 1947 these conclusions were confirmed and extended owing to an increase in the accuracy of the magnetic analysis: the presence of a powerful magnetic field made it possible to establish the existence of a discrete mass spectrum extending to mass values several times greater than the proton mass.[^3]

Fig. 1.

The existence in cosmic radiation of particles with a mass of about \(1000\,m_e\) finds new confirmation in the work of Rochester and Butler,

published in Nature on 20 December 1947.^4 These authors, over the course of several years, studied showers of penetrating particles that arise in lead under the action of cosmic radiation. Using the usual method of a controlled Wilson chamber placed in a magnetic field, they obtained 50 stereoscopic photographs of penetrating showers formed in a lead plate located above the chamber. The paper under review presents two such photographs (see Figs. 1 and 2), on the basis of which the conclusion is drawn that there exist spontaneously decaying neutral and charged particles with a mass of about \(900\,m_e\). In the first photograph two tracks \(a\) and \(b\) are clearly visible, emerging from a common point located below a lead plate \(3\ \mathrm{cm}\) thick, which divides the chamber into two parts. In the second photograph the tracks \(a\) and \(b\) are visible, sharply kinked at a point located in the upper part of the photograph, above the lead plate. In Table 1 experimental data are given that characterize both “forks” of the tracks.

Table 1

The authors give convincing evidence that the “forks” of the tracks in both photographs cannot be explained by strong scattering of the particle by a nucleus. Indeed, if the tracks \(a\) and \(b\) had been caused by strong scattering of the particle, a recoil-nucleus track would have been visible in the photographs. In addition, the supposition that the “fork” in Fig. 2 is caused by scattering encounters the following difficulty: at the apex of the fork, as a result of a single collision, the particle is scattered through \(19^\circ\), then passes through \(3\ \mathrm{cm}\) of lead and is scattered in it by only \(2.4^\circ\). Such a case seems almost improbable. With regard to the fork in Fig. 1, one might further suppose that it represents the track of an electron–positron pair formed in the field of the nucleus by a photon of high energy entering as part of the penetrating shower. This possibility is completely excluded for two reasons: 1) for an electron and positron with the momentum indicated in Table 1, the angle of divergence should be of the order of tenths of a degree, whereas in reality it is \(66^\circ\), and 2) a high-energy photon passing through a \(3\ \mathrm{cm}\) lead plate should have been accompanied by a large number of cascade electrons. Thus it is obvious that both forks cannot be explained by collision processes. The authors suppose that in both cases they are dealing with the decay of a moving particle into two particles, similar to what occurs in the decay of a mesotron into an electron and a neutrino. From this point of view the photograph in Fig. 1 represents a case of decay of a neutral particle, entering as part of the penetrating shower, into two particles, one of which has a positive charge,

the other is negative, and the photograph in Fig. 2 is the case of the disintegration of a positively charged particle into a particle with the same sign of charge and into a neutral particle.

Let us consider the conclusions concerning the masses of the disintegrated particles at which the authors of the paper arrive on the basis of applying the laws of conservation of energy and momentum to the observed tracks.

Fig. 2.

Let us denote by \(M\) the mass of the primary (disintegrated) particle, by \(m_1\) and \(m_2\) the masses of the products of the disintegration, and by \(P, p_1, p_2\) the corresponding momenta of these particles. Let \(\vartheta\) and \(\varphi\) be the angles formed by the directions of flight of the particles \(m_1\) and \(m_2\) with the direction of the primary particle. The laws of conservation of energy and momentum in this case have the following form:

\[ \sqrt{M^2 c^4 + P^2 c^2} = \sqrt{m_1^2 c^4 + p_1^2 c^2} + \sqrt{m_2^2 c^4 + p_2^2 c^2}, \tag{1} \]

\[ P = p_1 \cos \vartheta + p_2 \cos \varphi, \tag{2} \]

\[ p_1 \sin \vartheta = p_2 \sin \varphi . \tag{3} \]

Suppose that, as a result of the disintegration observed in Figs. 1 and 2, light particles arise, whose rest energies \(m_1 c^2\) and \(m_2 c^2\) may be neglected in comparison with \(p_1 c\) and \(p_2 c\). Then from the law of conservation of energy (1) one obtains a lower limit for the mass of the primary particle

\[ M_{\min} c^2 = c \sqrt{(p_1 + p_2)^2 - P^2}. \tag{4} \]

In the case shown in photograph 1 (see Table I), \(p_1\) and \(p_2\) are known, and since \(p_1 \simeq p_2 = p\), it follows that \(\vartheta \simeq \varphi\) and the momentum \(P\) of the primary neutral particle is equal to \(P = 2p \cos \vartheta\), where \(p = 3.4 \times 10^8\ \mathrm{eV}/c\), and \(\varphi = \vartheta = 33^\circ\). Substituting the values of \(p_1, p_2\), and \(P\) in (4), we obtain

\[ M_{\min} = (770 \pm 200)\, m_e . \]

In the case of the decay shown in photograph 2, the unknown momentum \(p_2\) of the neutral particle that arose in the decay can be determined from equations (2) and (3). Substituting \(p_1\), \(p_2\), and \(P\) into (4), the authors obtain for the minimum value of the mass:

\[ M_{\min}=(1700\pm150)\,m_e . \]

If the masses of the particles produced as a result of the decay are equal, \(m_1=m_2=m\), then \(p_1=p_2=P\), and from (1, 2, 3) the following expression is obtained for the mass of the primary particle:

\[ M=2m\left(1+\frac{p^2c^2}{m_0^2c^4}\sin^2\vartheta\right)^{1/2}. \]

The first part of Table II gives the values of \(M\) for the case of photograph No. 1, obtained on the assumption that \(m_0\) is equal to 0, 200, and 400.

Table II

Mass of the primary particle as a function of the mass of the secondary particle

We see that when the mass of the secondary particles is varied from 0 to \(400\,m_e\), the mass of the primary particle \(M\) changes only slightly: from 770 to \(1110\,m_e\).

The mass of the particles in photographs 1 and 2 can also be determined from the magnitude of the specific ionization and the momentum. An exact determination of the specific ionization from the photographs is impossible; however, the authors indicate that in both photographs \(\beta>0.7\). If the lower limit for \(\beta\) is known, the value of the momentum makes it possible to determine an upper limit for the magnitude of the mass. In the case of photograph 1, the authors determine the upper limit for \(m_1\) and \(m_2\), and then, from formulas (1), knowing \(m_1\), \(m_2\), and \(P\), determine the upper limit for \(M\). It is obtained that \(M<1600\,m_e\). Thus, the mass of the neutral particle lies within the limits

\[ (770\pm200)\leq M\leq 1600\,m_e . \]

For the mass of the decaying particle in photograph 2, the estimate of the mass from \(\beta\) and \(P\) gives:

\[ M<1200\,m_e . \]

We see that the upper limit obtained in this case for \(M\) is smaller than the lower limit \((1700\,m_e)\). The reason for such a discrepancy is, first of all, the large inaccuracy in determining the momentum of the primary

particle, due to the fact that in photograph 2 the length of the trajectory of the primary particle suitable for determining the radius of curvature is small. From Tables I it is clear that the momentum of the decay particle in this case was measured with far greater accuracy.

Therefore the authors consider it most correct to estimate the mass of the primary particle \(M\) on the assumption that this particle decayed into two particles of equal mass, whose momenta are known. Table 2 gives the values of \(M\) obtained under this assumption. The smallest value of \(M\), corresponding to the case \(m_0 = 0\), is obtained equal to \(980\,m_e\). We note that in this case the momentum of the primary particle should have the value \(14.5 \times 10^8\ \mathrm{eV}/c\) instead of the measured value \((6 \pm 3)\cdot 10^8\ \mathrm{eV}/c\). The authors consider it most probable that photograph 2 corresponds to a mass of the primary particle lying between \(980\,m_e\) and the mass of the proton.

A. Weisenberg

CITED LITERATURE

1. A. Alikhanyan, A. Alikhanov and A. Weisenberg. DAN, 55, No. 8 (1947).
2. S. Nikitin. J. of Phys. 11, 196 (1947).
3. A. Alikhanyan, A. Alikhanov, V. Morozov, G. Muskhelishvili, A. Khrimian. DAN, 58, No. 7, p. 1391 (1947).
4. G. D. Rochester and Butler. Nature 160, No. 4077, 855 (1947).