EFFECTIVE NUCLEAR CROSS SECTIONS FOR HIGH-ENERGY NEUTRONS

In recent years a number of works have appeared devoted to the determination of effective nuclear cross sections for high-energy neutrons.

Two reactions served as sources of high-energy neutrons—the disintegration of deuterons upon bombardment of various targets, and the exchange interaction of protons with neutrons in the nuclei of the targets being bombarded.

In the first of these reactions, neutrons arise with an average energy equal to half the energy of the deuterons. In the second reaction, neutrons arise with a very broad energy spectrum, the maximum of which lies somewhat below the energy of the initial protons.

According to theory¹, total effective nuclear cross sections for high-energy neutrons are composed of the cross sections for elastic (diffraction) scattering $\sigma_d$ and the cross sections for inelastic collisions $\sigma_a$, and, at relatively low energies, $\sigma_a = \sigma_d = \pi R^2$ and the total cross section $\sigma_t = 2\pi R^2$, where $R$ is the nuclear radius. On the basis of experiments to determine total cross sections for neutrons with energies of 14–25 MeV, the approximate relation² was derived

\[ R = \left(1.3 + 1.37 A^{\frac{1}{3}}\right)\cdot 10^{-13}\ \text{cm}. \]

The energy

Total effective nuclear cross sections

for neutrons of various energies

Table 1

dependence of effective nuclear cross sections for high-energy neutrons was considered theoretically,^3 and the conclusion was drawn that the total cross sections and, especially, the inelastic-collision cross sections should fall rather rapidly with energy. This conclusion was obtained on the basis of the assumption of an increase in the “transparency” of nuclei for high-energy neutrons, following from experiments that showed a rather strong decrease of the \(np\)-scattering cross section with increasing neutron energy.^4,5,6 However, studies of the \(pp\)-scattering cross section at various proton energies showed that this cross section remains practically constant over a wide energy interval: from 120 to 340 MeV.^7 Thus the basic assumption concerning “transparency,” which lay at the basis of the theoretical predictions about the energy dependence of the effective nuclear cross sections for high-energy neutrons, was seriously shaken.

Table II

Ratios of the inelastic-collision cross sections and total effective nuclear cross sections \(\left(\dfrac{\sigma_a}{\sigma_t}\right)\) for neutrons of various energies

Experiments to determine these cross sections confirmed the disagreement with the theoretical predictions. It turned out that the cross sections for the interaction of high-energy neutrons with nuclei fall rather rapidly with increasing neutron energy up to 150–180 MeV, but at higher energies they change very little. A summary of all the data is given in Tables I and II. The determination of total cross sections was carried out with the detector placed away from the neutron absorber, when any collisions removed neutrons from the beam. The determination of inelastic-collision cross sections was carried out with the detector placed directly behind the absorber, when elastic collisions did not remove neutrons from the beam. For a number of elements the cross sections were determined from the differential effect of attenuation of the beam by compounds containing atoms of the given elements. Such elements are marked in the table with asterisks. The cross sections and the quantities \(2\pi R^2\) are given in units equal to \(10^{-24}\ \text{cm}^2\). The quantities \(2\pi R^2\) were calculated from the formula given above,

\[ R=f\left(A^{\frac{1}{3}}\right). \]

G. I.

CITED LITERATURE

1. A. I. Akhiezer and I. Ya. Pomeranchuk, Some Problems of Nuclear Theory, Gostekhizdat, 1948.
2. R. Sher, Phys. Rev. 61, 734 (1942).
3. S. Fernbach, R. Serber, T. Taylor, Phys. Rev. 75, 1352 (1949).
4. J. Hadley, E. Kelly et al., Phys. Rev. 75, 351 (1949).
5. A. Taylor, T. Pickavance et al., Phil. Mag. 42, 20 (1951).
6. E. Kelly, C. Leith et al., Phys. Rev. 79, 96 (1950).
7. O. Chamberlain, E. Segrè, C. Wiegand, Phys. Rev. 81, 284 (1951).

1. T. Pickavance, I. Cassels, T. Randle, Phil. Mag. 42, 328 (1951).
2. R. Hildebrand and C. Leith, Phys. Rev. 80, 842 (1950).
3. L. Cooc, E. McMillan et al., Phys. Rev. 75, 7 (1949).
4. J. De Juren and N. Knable, Phys. Rev. 77, 606 (1950).
5. J. De Juren and B. Moyer, Phys. Rev. 81, 919 (1951).
6. J. De Juren, Phys. Rev. 80, 27 (1950).
7. R. Fox, C. Leith et al., Phys. Rev. 80, 23 (1950).
8. A. Bratenahl, S. Fernbach et al., Phys. Rev. 77, 597 (1950).