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From Current Literature
Fission Neutron Spectrum of U$^{235}$
For the calculation of reactors, for estimating the thickness of radiation shielding, and for a number of other problems of nuclear power engineering[^1], it is important to know the spectrum of fission neutrons. Until now no data on this question had been published in the literature. It was known that the maximum neutron yield corresponds to an energy of about 1 MeV. The paper under review[^2] investigates the spectrum of fission neutrons of U$^{235}$, both prompt and delayed, by the photographic-plate method. Plates of the Ilford C2 type, 100 microns thick, were irradiated.
Fig. 1.
The arrangement of the apparatus and its dimensions are shown in Fig. 1. Uranium-235 oxide (UO$_3$) was deposited on an aluminum plate in a layer measuring $10 \times 2.5 \times 0.025$ cm. The inclination at $3^\circ$ relative to the vertical gave the specimen in order that the fission neutrons striking the photographic plate should not pass through the aluminum backing. The photographic plates were in a cadmium cassette to prevent their exposure by reactions in the emulsion due to thermal neutrons. Especially undesirable was the reac-
tion \(N^{14}(np)C^{14}\), in which protons with an energy of about \(0.5\) MeV are emitted.
The source of thermal neutrons was a boiler with heavy water as moderator. The neutron flux in the beam was about \(6\cdot10^5\) neutrons/\(\text{cm}^2\cdot\text{sec}\) at a boiler power of \(5.5\) kW. With such a flux, about \(4\times10^7\) neutrons per second were emitted from a uranium layer. Irradiation lasted 15 hours at the indicated boiler power.
The background was observed by replacing the sample with an aluminum plate without uranium. It amounted to no more than \(5\%\) of the observation result, and was not taken into account in the calculations.
The neutron spectrum of fission was determined from the recoil-proton spectrum; moreover, proton tracks were selected that made an angle of not more than \(10^\circ\) with the median line of the photographic plate. This made it possible to resolve maxima with a half-width of 60 keV at \(0.5\) MeV and with a half-width of 120 keV at a neutron energy of 2 MeV. This method was developed in the work of [3, 4].
Fig. 2.
The number of measured tracks was multiplied by the factor
\[ \frac{1}{1-P}, \]
where \(P\) is the average probability for a proton to leave the surface of the plate at any point of the emulsion.
The corrected number of recoil-proton tracks with a given energy is proportional to the neutron scattering cross section on protons \(\sigma_p(E_n)\) and to the fission-neutron flux \(N(E_n)\).
However, it is desirable to have the energy spectrum of fission neutrons as a function of neutron energy, and not of the energy of recoil protons. The transition was made both theoretically and using the experimental value of \(\sigma_p(E_n)\). In both cases the conversion coefficient proved to be of the order of 1.06, i.e. \(E_n \simeq 1.06E_p\).
The data were obtained for 4700 recoil-proton tracks. The measurements were carried out independently by two microscopists. No large discrepancies were noted.
On the basis of the data obtained, the graph shown in Fig. 2 was constructed.
Along the ordinate is plotted the corrected number of recoil-proton tracks per interval of 0.1 MeV of neutron energy, divided by \(\sigma_p(E_n)\times10^{24}\). This number is proportional to \(N(E_n)\). Along the abscissa is plotted the neutron energy in MeV. In the upper right corner the fission-neutron spectrum of \(U^{235}\) is shown on a semilogarithmic scale.
The neutron spectrum was observed for energies in the range \(0.4 \div 7\) MeV. The lower limit is set by the sensitivity of the photographic plate, and the upper by the small number of observed tracks.
From the graph it is clearly seen that the spectral curve has a maximum in the neutron-energy region \(0.7 \div 0.8\) MeV. For energies greater than 2 MeV
the curve falls exponentially, \(N(E_n)\sim \exp(-E/1.7 \pm 1)\). The slope is \(3.9 \pm 0.2\) MeV per tenfold change in intensity. The semiempirical formula \(N(E_n)=Ae^{-E_n}\cdot \operatorname{sh}\sqrt{2E_n}\), where \(A\) is a constant and \(E_n\) is in MeV, agrees well with the experimental points.
L. K.
References
- Scientific and Technical Foundations of Nuclear Power Engineering, edited by K. Goodman, vols. I and II, Foreign Literature Publishing House, 1948 and 1950.
- N. Nereson, Phys. Rev., 85, 600 (1952).
- H. Richards, Phys. Rev., 59, 796 (1941).
- N. Nereson and F. Reines, Rev. Sci. Instr., 21, 534 (1950).