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DISTRIBUTION OF SLOW NEUTRONS IN THE FREE ATMOSPHERE
As is known, neutrons are decaying particles (decay \(n \to p + e\)). Consequently, they are formed within the thickness of the Earth’s atmosphere and do not come to us from outer space.
The following processes are known to lead to the formation of neutrons in the atmosphere:
1) Nuclear disintegrations—“stars”—analogous to those observed by means of photographic plates (neutrons with energies from \(1\) MeV to several tens of MeV).
2) Absorption of negative mesons by the nuclei of matter\(^1\) (neutrons with energies of the same order).
3) Formation of neutrons in penetrating (electron-nuclear) showers (neutrons with energies from \(100\) MeV and lower)\(^2\).
It may be considered that the slow neutrons registered by neutron counters (a proportional counter filled with \(\mathrm{BF}_3\)) are, in the main, neutrons formed in nuclear disintegrations and slowed down to low energies.
This is confirmed by the identical altitude dependence of the intensity of slow neutrons and of the number of nuclear disintegrations.
This dependence is described by the formula
\[ N = N_0 e^{-\frac{x}{\lambda}}, \]
where \(N\) is the intensity of neutrons, \(x\) is the depth of the atmosphere, expressed in \(\mathrm{g/cm^2}\), \(\lambda \sim 160\ \mathrm{g/cm^2}\).
The neutrons formed in the processes indicated above are slowed, in collisions with air nuclei, down to thermal velocities. In parallel with this, absorption of neutrons by air atoms takes place, and the absorption cross section has its greatest value at neutron energies802: g/cm², but ok. final ends incomplete "neutron energies" reflecting page. Good.
from 150 keV down to several tenths of an eV (the region of the law \(\sigma \sim \frac{1}{v}\) for the absorption cross section, where \(v\) is the velocity of the neutrons). Therefore neutrons are absorbed by atoms of the air before they have time to scatter. Questions of absorption, slowing down, and scattering were considered in \(^{3}\).
[Graph labels: vertical axis—“number of counts per minute”; horizontal axis—“atmospheric depth,” in cm Hg. Legend: \(A\)—lead counter; \(B\)—cadmium counter; \(C\)—difference \((A-B)\).]
This article shows that the spatial distribution of slow neutrons can be represented by the formula
\[ N \sim x e^{-\frac{x}{2L}}, \]
where \(L\) is the mean diffusion path of a neutron.
According to the authors’ data, \(L \sim 100\ \text{g}/\text{cm}^{2}\).
It follows from this formula that there must be a maximum in the intensity of slow neutrons at \(x=L\), i.e., at \(x=100\ \text{g}/\text{cm}^{2}\). This corresponds to an altitude 15 km above sea level (pressure 7.7 cm Hg).
The formula is derived under the assumption that all neutrons are produced near the surface of the atmosphere. If one assumes that neutrons are produced throughout the entire thickness of the atmosphere, then the maximum shifts toward greater depths of the atmosphere (i.e., lower altitudes).
However, until recently, measurements of the intensity of slow neutrons \(^{5}\) gave an increase in intensity up to altitudes on the order of 30 km (pressure 2 cm Hg, \(x=27\ \text{g}/\text{cm}^{2}\)).
This serious contradiction between theory and experiment should apparently be explained by the imperfection of the measurement technique (the low counting efficiency of slow neutrons by the counter and the short time during which measurements were carried out at high altitudes).
In the reviewed work \(^{4}\), the authors, using more refined measurement methods, obtained data consistent with theory.
The intensity of slow neutrons was measured by means of two proportional counters filled with BF\(_3\), with a B\(^{10}\) content of up to 96% (the efficiency of the slow-neutron counter was 13%). The apparatus was raised on balloon sondes to altitudes of 20 km.
The counters were covered: one with a cadmium covering, the other with a tin covering (0.7 mm). The results obtained are shown in the figure. Curve \(C\) gives the number of thermal neutrons with energies below 0.4 eV. (With such an arrangement, counts due to showers of high density and nuclear disintegrations in the walls of the coverings and counters are excluded.) On curve \(C\) a distinct maximum is seen at an altitude of 15 km (8 cm Hg).
As a check, a flight was made in which the greatest altitude reached was 31 km (0.75 cm Hg). The value of the maximum was obtained at the same altitude—15 km. The value of the intensity at the maximum altitude proved to be equal to \(1/4\) of its maximum value. Up to an altitude of 12 km (18 cm Hg) the curve of the difference can be represented by the formula \(N = Ne^{-x/\lambda}\), where \(\lambda = 160\ \mathrm{g/cm^2}\), which agrees with the altitude curve of the dependence of the number of nuclear disintegrations measured with photographic plates\(^6\).
It is interesting to note that the neutron flux calculated by the formula given in paper\(^3\) proved to be \(1/6\) as large as the proton flux determined from photographic-plate data\(^6\).
In the present case, evidently, resonance absorption of fast neutrons by nitrogen and oxygen nuclei is manifested.
G. M. Guro.
CITED LITERATURE
- R. D. Sard, A. Ither, Conforto and M. F. Groutch, Phys. Rev. 74 (1), 97 (1948).
- V. Tongiorgi, Phys. Rev. 76 (4), 517 (1949).
- H. A. Bethe, S. A. Korf, G. Placzek, Phys. Rev. 57, 573 (1940).
- R. Laudeberg and L. Jouan, Cosmic Radiation (Cosmic Research. Colston Papers), p. 35, London, 1949.
- S. A. Korf and A. Cobas, Phys. Rev. 73, 1010 (1948).
- Guer, Cosmic Radiation (Cosmic Research Colston Papers), p. 29, London, 1949.