SOME INFORMATION ON THE PROPERTIES OF HEAVY NUCLEI

Recently a number of papers have appeared in the literature devoted mainly to various questions connected with the fission of uranium nuclei. Below the principal content of these papers is briefly considered.

I. ENERGY DISTRIBUTION OF FRAGMENTS IN FISSION BY NEUTRONS OF DIFFERENT ENERGIES[^1]

A thin layer of uranium \((0.14\ \mathrm{mg}/\mathrm{cm}^2)\), enriched in the isotope \(U^{235}\), was deposited on the high-voltage electrode of an ionization chamber and irradiated with neutrons of energies \(2.5\ \mathrm{MeV}\) and \(14\ \mathrm{MeV}\). Neutrons of the indicated energies were obtained by bombarding deuterium and tritium targets with deuterons.

The ionization pulses in the chamber, caused by fission fragments, were first amplified and then fed to a 10-channel amplitude analyzer and counted. The form of the spectra obtained is shown in Fig. 1. For monitoring the apparatus, the energy spectrum of fission fragments produced by thermal neutrons was also recorded.

The form of this spectrum, shown in Fig. 2, agrees well with the data of other authors.

Similar measurements were carried out by Jungerman and Wright[^2] at neutron energies of 45 MeV and 90 MeV. They found that the curve of the energy spectrum of fission fragments from neutrons with an energy of 45 MeV

Fig. 1. Energy spectrum of fission fragments.
a) From neutrons with an energy of 2.5 MeV (abscissa axis: energy in MeV, ordinate axis: number of counts (in relative units)).
b) From neutrons with an energy of 14 MeV (abscissa axis: energy in MeV, ordinate axis: number of counts (in relative units)).

has a very small “dip” between the two maxima, while the curve for neutrons with an energy of 90 MeV has only one maximum.

Comparison of all these data again confirms the increase in the probability of symmetric fission with increasing energies that induce fission of particles.

II. ENERGY SPECTRUM OF SECONDARY NEUTRONS IN THE FISSION OF U\(^{235}\) BY THERMAL NEUTRONS[^3]

An aluminum plate, on which a layer of U\(^{235}\) in the form of oxide U\(_3\)O\(_8\), 150 g thick, had been deposited, was placed in a beam of thermal neutrons emerging from a nuclear reactor.

The neutrons emitted in the fission of uranium nuclei were recorded with the aid of a thick-layer photographic emulsion irradiated by protons of recoil.

Fig. 2. Energy spectrum of U\(^{235}\) fragments in fission by thermal neutrons. (Abscissa axis: energy in MeV, ordinate axis: number of counts (in relative units).)

The experimental background, reduced as much as possible by the choice of the experimental geometry and the use of various shields, was monitored by an exposure carried out under the same conditions, but with the uranium plate replaced by an aluminum plate without uranium.

When examining the emulsion, only those tracks were analyzed that formed an angle with the mean direction of neutron motion not exceeding 10°. Corrections were introduced into the results for the escape from the emulsion of some tracks and for the “shrinkage” of the emulsion. The experimental background was not taken into account, since it was less than 5%.

A total of 4700 tracks were processed. From the distribution of recoil protons and the known values of the cross sections for the collision of hydrogen with neutrons, the energy distribution of secondary neutrons was obtained, as presented in Fig. 3.

These data, covering the neutron-energy interval from 0.4 MeV to 7 MeV, are in good agreement with the semiempirical formula given in 4:

\[ N(E)=e^{-E}\cdot \operatorname{sh}\sqrt{2E} \]

and represented by the dashed curve in Fig. 3.

Fig. 3. Spectrum of secondary neutrons in the fission of U²³⁵. (Abscissa axis: \(E\) (MeV), ordinate axis: \(N(E)\).)

Both experiment and the semiempirical formula indicate that the maximum of the secondary-neutron spectrum is located at an energy of 0.7–0.8 MeV.

III. DATA ON THE EFFECTIVE NEUTRON CROSS SECTIONS OF URANIUM NUCLEI

1. For thermal neutrons having a Maxwellian velocity distribution with the most probable velocity \(2200\ \text{m/sec}\), the following values of the effective cross sections of uranium nuclei are given in 5 (in units of \(10^{-24}\ \text{cm}^2\)):

1. The dependence of the fission cross section of a natural mixture of uranium isotopes on the energy of fission neutrons, according to 4, is given in Fig. 4.

The curve corresponds to the most reliable data, covering the neutron energy interval from 0.7 to 5 MeV. In addition, in 4 and 5 a number of data are given relating to the fission of \(U^{238}\) in a natural mixture of isotopes. The cross section for such fission by neutrons with the spectrum of secondary fission neutrons is \(0.29\cdot 10^{-24}\ \text{cm}^2\). Averaged over the spectrum of secondary neutrons, the radiative-capture cross section is \(0.04\cdot 10^{-24}\ \text{cm}^2\).

The number of neutrons emitted in the fission of \(U^{238}\) by above-threshold neutrons is 2.55, i.e., practically equal to the number of secondary neutrons in the fission of \(U^{235}\) by thermal neutrons \((2.5\pm 0.1)\).

The total effective cross section of \(U^{238}\) nuclei with respect to secondary fission neutrons is \(4.3\cdot 10^{-24}\ \text{cm}^2\), the elastic-scattering cross section being \(1.5\cdot 10^{-24}\ \text{cm}^2\), and the inelastic-collision cross section (excluding fission and radiative capture) \(2.47\cdot 10^{-24}\ \text{cm}^2\). In 5 an approximate experimental formula is given for the integral cross section of resonance absorption:

\[ \int \sigma_c(E)\,\frac{dE}{E} = A\left[1+aT+\mu\frac{S}{M}\right], \]

where \(S\) \((\text{cm}^2)\) is the surface area of the uranium block; \(M\) \((g)\) is its mass; \(a\simeq 10^{-4}\ 1/\text{degree}\), and the temperature \(T\) is expressed in degrees C.

Fig. 4. Dependence of the fission cross section of a natural mixture of uranium isotopes on neutron energy. (Abscissa axis: neutron energy (MeV); ordinate axis: fission cross section (in units of \(10^{-24}\ \text{cm}^2\).)

The constants \(A\) and \(\mu\) are different for the cases of metallic uranium and uranium oxide. Thus, for metallic uranium \(A=9.25\cdot 10^{-24}\ \text{cm}^2\), and \(\mu=2.67\ g/\text{cm}^2\). For \(U_3O_8\), \(\mu=1.67\ g/\text{cm}^2\). The limiting value of the integral cross section at the greatest “dilution” of uranium is \(240\cdot 10^{-24}\ \text{cm}^2\).

The logarithmic width of the resonance absorption band \(\ln \dfrac{E_0}{E}\) is about 5.6 for the metal and about 7.3 for the oxides. The reciprocal diffusion length \(K_0\) for resonance neutrons is \(K_0=0.022\rho\ \text{cm}^{-1}\), where \(\rho\) \((g/\text{cm}^3)\) is the density of uranium.

IV. CROSS SECTION OF PLUTONIUM AND XENON FOR THERMAL NEUTRONS 5

1. The fission cross section of \(Pu^{239}\) is . . . . . . . \(664\cdot 10^{-24}\ \text{cm}^2\).

2. The capture cross section (without fission) of \(Pu^{239}\) . . . . \(361\cdot 10^{-24}\ \text{cm}^2\).

3. The number of secondary neutrons per one fission of \(Pu^{239}\) . \(3.0\pm 0.1\).

4. The absorption cross section of Xe . . . . . . . . . . \(3.5\cdot 10^{-18}\ \text{cm}^2\).

References

1. Stephen S. Friedland, Phys. Rev. 84, 75 (1951).
2. J. Jungerman, S. C. Wright, Phys. Rev. 76, 1112 (1949).
3. Norris Nereson, Phys. Rev. 85, 600 (1952).
4. Nucleonics, 8, 78 (1951).
5. Nature, 169, 871 (1952).

Yu. I.