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Determination of the Charge of Heavy Particles Formed During Explosive Fission of the Nucleus
There have already been several reports in print on the discovery, on photographic plates exposed to cosmic radiation, of heavy nuclear “fragments” emitted during explosive fission of nuclei \(^{2,5,6}\).
By exposing Kodak NT4 “electron-sensitive” plates at Jungfraujoch (3300 m) and at high altitudes with the aid of balloon sondes, the author of the paper under review \(^{1}\) also succeeded in detecting, among cosmic-ray “stars,” several tracks of heavy nuclear fragments with energies of about 500 MeV, which he identified as nuclei of lithium, beryllium, and boron. To determine the charge of these particles, the author used the method of \(\delta\)-electrons developed in papers \(^{3,4}\) for studying the heavy component of primary cosmic radiation.
In the case where a particle with charge \(Ze\) moves with nonrelativistic velocity \(v\), the number of \(\delta\)-electrons per 1 cm of track length with energies in the interval from \(w_1\) to the maximum energy \(w_2 = 2mv^2\) that the particle moving with velocity \(v\) can transfer to an electron is given by the formula
\[ \nu(w_1, v)=\frac{2\pi Ne^4 Z^2}{mv^2}\left(\frac{1}{w_1}-\frac{1}{2mv^2}\right), \]
where \(m\) is the electron mass, and \(N\) is the number of electrons in 1 cm\(^3\) of emulsion. From this equation it follows that, at points where particles with different charge \(Z\) have the same velocity, \(\nu(w_1, v)\) will vary in proportion to \(Z^2\). The number of \(\delta\)-electrons with energy exceeding \(w_1\) reaches a maximum when the heavy fragment has velocity
\[ v=\sqrt{\frac{w_1}{m}}. \]
These considerations can be used to determine the charge \(Z_2\) of an unknown particle. In equal length intervals (for example, 100 \(\mu\) each), the number of all \(\delta\)-electrons is counted whose tracks contain more than a prescribed number of grains (corresponding to the \(\delta\)-electron energy \(w_1\)). The resulting distribution rises to a maximum and then slowly decreases.
The maximum value of the quantity \(\nu\) for particles with the sought charge \(Z_2\) can then be compared with the maximum value \(\nu_1\) obtained from similar observations for tracks of particles with known charge \(Z_1\), for example, with the maximum \(\nu\) for protons or mesons. Then the sought charge \(Z_2\) is determined from the relation
\[ \frac{\nu_2(w_1)}{\nu_1(w_1)}=\left(\frac{Z_2}{Z_1}\right)^2 . \]
As particles with known charge the author used \(\mu\)-mesons, which stop in the emulsion and for which a track of the decay electron can be detected.
The presence of the decay-electron track confirmed that the track under consideration was indeed that of a \(\mu\)-meson. The use of mesons and protons for calibration encounters a certain difficulty, consisting in the fact that the tracks of \(\delta\)-electrons, made up of only a few grains (from 4 grains and more), are poorly noticeable if they are associated with the track of light particles (mesons, protons), but they have a tendency
“lost” if they are associated with the thicker tracks of heavy fragments. It has been established, however, that this effect is insignificant for particles with \(Z<6\), if the \(\delta\)-electrons knocked out for registration have a sufficiently long range.
The material studied consists of one track of a boron nucleus emitted from a star with nine rays of energy about 250 MeV, one track of a beryllium nucleus emitted from a star with 14 rays of energy about 140 MeV, and five tracks of lithium nuclei emitted from various stars with energies up to 500 MeV.
The maximum values of \(v\), obtained in experimental distributions of \(\delta\)-electrons along the tracks of heavy fragments, coincided within the limits of error with the values \(v_{\max}\) calculated for the corresponding values of \(Z\). In the analysis described above, the author did not take into account the effect of scattering of particles, whose role increases as the particle velocity decreases. This is permissible, since in the case of nuclei with \(Z<6\) such an effect is limited to the last 25 \(\mu\) of the range. In this interval the particle reaches such a velocity that it can no longer produce \(\delta\)-electrons with energy exceeding the minimum value \(w_1\) accepted for measurement—16 keV. However, this condition is not valid in the case of nuclei of heavier elements. The figure (see the insert at the end of the issue) shows a greatly enlarged track of a heavy nucleus of primary cosmic radiation, discovered on plates exposed at an altitude of about 40 km. The charge of this particle proved to be
\[ Z=(35\pm 4)e. \]
The author points out that the \(\delta\)-electron method can also be applied to determine the mass of heavy fragments, since the position of the maximum of the \(\delta\)-electron distribution depends on the magnitude of the fragment mass.
Discussing the results, the author notes that the formation, within stars, of heavy fragments with energies of 300–500 MeV apparently should be explained by the knock-on effect caused by fast nucleons.
A. Gorbunov
CITED LITERATURE
- S. O. C. Sörensen, Phil. Mag. 40, 947 (1949).
- Bonetti a. Dilworth, Phil. Mag. 40, 585 (1949).
- Bradt a. Peters, Phys. Rev. 74, 1828 (1948).
- Freier, Lofgren, Ney a. Oppenheimer, Phys. Rev. 74, 1818 (1948).
- Heitler, Powell a. Fertel, Nature 144, 283 (1939).
- Hodgson a. Perkins, Nature 163, 439 (1949).
CRYSTAL COUNTERS
In article 1, which is a continuation of the review devoted to crystal counters published in Uspekhi Fizicheskikh Nauk,² questions connected with the experimental investigation of their most important characteristics are considered.
The determination of the mobility of electrons in a crystal by experiment is based on measuring the rise time of the pulse caused by the entry of an ionizing particle into the crystal. This time is equal to the “transit” time, i.e. the time taken by the electrons to pass from the negative
Determination of the charge of heavy particles formed during explosive fission of the nucleus (see p. 153). Track of a bromine nucleus \((Z = 35 \pm 3)\), passing through plate 21 and ending in the emulsion of plate 22 at point \(e\). The region of maximum ionization was located in the glass of plate 21. Some distortion of the emulsion is present.