Theory of Disintegration of Nuclei by Neutrons

Abstract

The large probability of nuclear disintegration by slow neutrons as well as the large cross section for the elastic scattering of slow neutrons can be explained without any new assumption. Interaction between neutron and nucleus is assumed to be only present when the neutron is inside the nucleus or very near its boundary. The rate of change of the potential energy of the neutron at the boundary of the nucleus is important for the quantitative, but not for the qualitative results; in agreement with other data, it has been assumed that the potential drops to $\frac{1}{e}$ in a distance 1.5.${10}^{\ensuremath{-}13}$ cm (range of the forces between neutron and nucleus).The large disintegration cross sections are due to two factors. The first is elementary: the cross section is inversely proportional to the neutron velocity, because a slow neutron stays longer in the nucleus. The second factor is $\frac{1}{{sin}^{2} {\ensuremath{\phi}}_{0}}$, where ${\ensuremath{\phi}}_{0}$ is the phase of the neutron wave function at the nuclear boundary. This resonance factor explains the large differences between the cross sections of different elements. ${\ensuremath{\phi}}_{0}$ cannot be predicted theoretically, but reasonable assumptions lead to agreement with experiment. The resonance factor occurs in all phenomena with slow neutrons; therefore large capture cross sections should always be accompanied by large elastic scattering. The explanation of the large neutron cross sections on the basis of ordinary wave mechanics makes one confident in the applicability of orthodox quantum theory in nuclear phenomena.1. Elastic scattering. May be large for slow neutrons because of resonance. Magnitude is ${5.10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$ without, ${10}^{\ensuremath{-}22}$ and more with resonance. If present, large cross section persists up to neutron energies of 10,000 or 100,000 volts.2. Capture with emission of $\ensuremath{\gamma}$-rays. Cross section large for slow netrons. About half the elastic scattering cross section for gas-kinetic energy. Cross section inversely proportional to neutron velocity. All capture effects observed should be due to admixtures of slow neutrons in the incident beam. Capture only possible, if unoccupied neutron level with angular momentum $l=1$ exists in the nucleus.3. Disintegration with emission of $\ensuremath{\alpha}$-particles. Very probable for slow neutrons if exothermic process, which is usually the case. Cross section for gas-kinetic neutrons and light nuclei ${10}^{\ensuremath{-}21}$ ${\mathrm{cm}}^{2}$ without resonance, for $Z=11$ same cross sections as for fast neutrons (${10}^{\ensuremath{-}25}$ ${\mathrm{cm}}^{2}$). May be increased by resonance which may occur as well for neutrons as for $\ensuremath{\alpha}$-particle. Cross section inversely proportional to neutron velocity up to neutron energies of some 100,000 volts, then cross section increases again because faster $\ensuremath{\alpha}$-particles penetrate more easily through nuclear potential barrier. Disintegration by slow neutrons should stop at $Z\ensuremath{\approx}16$, by fast ones at $Z\ensuremath{\approx}27$, the latter in agreement with experiments.4. Disintegration with emission of protons. Always endothermic, therefore impossible with slow neutrons. With fast neutrons, cross section $\ensuremath{\approx}{10}^{\ensuremath{-}25}$ ${\mathrm{cm}}^{2}$ up to $Z\ensuremath{\approx}20$. Weak effects should be observable up to $Z=40$, in case of resonance even to 60.5. Excitation of nucleus without capture of neutron or emission of particles. Should have cross section of the order ${10}^{\ensuremath{-}25}$ ${\mathrm{cm}}^{2}$ independent of atomic number. Possible only for nuclei with suitable excited states and for fast neutrons.