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Neutron cross-section

The total neutron cross section of an isotope of a chemical element is the effective cross sectional area that an atom of that isotope presents to neutron scattering and absorption.

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Scattering versus absorption

When a neutron approaches an atomic nucleus, it will be scattered or absorbed. If absorbed, the atomic nucleus moves up on the table of isotopes by one position; for instance, U-235 becomes U-236* with the * indicating the nucleus is highly energized. This energy has to be released and the release can take place through any of several mechanisms.

The simplest way for the release to occur is for the neutron to be ejected by the nucleus. If the neutron is emitted immediately, it acts the same as it would in other scattering events.
The nucleus may emit gamma or X-ray radiation. For U-236*, absorption of a thermal neutron occurs about 18% of the time, leaving the U-236 nucleus intact. About 81% of the U-236* nuclei are so energized that they fission, releasing the energy as kinetic motion of the fission fragments, also emitting between one and five free neutrons. Nuclei that fission as their predominant decay method after neutron capture include U-233, U-235, U-237, Pu-239, Pu-241. Nuclei that predominantly absorb neutrons and then emit Beta particle radiation lead to these isotopes such that Th-232 will absorb a neutron, becoming Th-233*, emit a Beta particle becoming Pa-233, which in turn emits another Beta particle to become U-233. Isotopes which undergo Beta emission transmute from one element to another element, those which undergo gamma or X-ray emission change from one isotope to another isotope of the same element.

Types of scattering cross-section

The scattering cross section can be further subdivided into coherent scattering and incoherent scattering, which is caused by the spin dependence of the scattering cross section and for a natural sample, presence of different isotopes of the same element in the sample.

Since neutrons interact with the nuclear potential, the scattering cross section varies with the atomic number of the element in question. A very prominent example is hydrogen and its isotope deuterium. The total cross section for hydrogen is over 10 times that of deuterium, mostly due to the large incoherent scattering length of hydrogen. Metals tend to be rather transparent to neutrons, aluminum and zirconium being the two best examples of this.

Types of decay

Uranium decay

The element uranium decays in the following manner: U-235+n=U-236*. U-236*(-gamma ray)=U-236. U-236+n=U-237*. U-237*(-Beta)=Np-237.

Actinide decay

Because a large number of the isotopes of the elements in the actinide series are fissionable via neutron absorption, the higher an element is on the table of isotopes the more rarely it is formed by these reactions. As an example Th-232 has a half life on the order of 14 billion years and is the most common of the actinide series on Earth. Adding neutrons and allowing for beta decay and fission events you can build from Th-232 up to any arbitrary member of the Actinides like Pu-242. This chain moves through one of the following decay sequence:

Th-232+n=Th-233*; Th-233*(- Beta)=Pa-233; Pa-233(-Beta)=U-233; U-233+n=U-234*(fission 91%)
{Pa-233+n=Pa-234; Pa-234(-Beta)=U-234};
U-234*(-X-ray)=U-234; U-234+n=U-235*; U-235*(-X-ray)=U-235; U-235+n=U-236*; U-236*(fission 81%)
U-236*(-gamma)= U-236; U-236+n=U-237*; U-237*(-Beta)=Np-237; Np-237+n=Np-238*; Np-238*(-Beta)=Pu-238; Pu-238+n=Pu-239*; Pu-239*(fission 10%)
Pu-239*(-X-ray)=Pu-239; Pu-239+n=Pu-240*(fission 64%);
Pu-240*(-X-ray)=Pu-240; Pu-240+n=Pu-241*; Pu-241*(-X-ray)=Pu-241; Pu-241+n=Pu-242*; Pu-242*(fission 78%)
Pu-242*(-gamma)=Pu-242. Ten neutron absorptions are needed for this chain to occur and during that course fission transmutes 0.15% of the Th-232 into Pu-242.

Non-actinide decay

With elements lower on the periodic table than the actinides the predominant form of emission is gamma or beta decay. As an example, when stable O-18 absorbs a neutron it becomes O-19*, then decays to O-19*(-Beta)=F-19.

Alpha decay

A few rare isotopes undergo alpha decay, most notably Li-7+n=Li-8*; Li-8*(-1 Beta, (-2 Alpha))= 2(He-4) AND B-11+n= B-12*; B-12*(-1 Beta,(-3 Alpha))=3(He-4)OR B-12*(-Beta)=C-12. The time for these reactions to occur are under 25 milliseconds.

Within stars

Because Li-8 and B-12 form natural stopping points on the table of isotopes for hydrogen fusion it is believed that all of the higher elements are formed in very hot stars where higher orders of fusion predominate. A star like the Sun produces energy by the fusion of simple H-1 into He-4 through a series of reactions. It is believed that when the inner core exhausts its H-1 fuel the sun will contract slightly increasing its core temperature until He-4 can fuse and become the main fuel supply. Pure He-4 fusion would lead to Be-8, which decays back to 2(He-4)therefore the He-4 must fuse with isotopes either more or less massive than itself to result in an energy producing reaction. When He-4 fuses with H-2 or H-3 it forms stable isotopes Li-6 and Li-7 respectively. The higher order isotopes between Li-8 and C-12 are synthesized by similar reactions between Hydrogen, Helium and Lithium isotopes.