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Thermal neutron capture cross-sections of elements[1]
Barns Element Z
0.00019 Oxygen O 8
0.0035 Carbon C 6
0.007 Helium He 2
0.0092 Beryllium Be 4
0.0096 Fluorine F 9
0.03 Polonium Po 84
0.034 Bismuth Bi 83
0.04 Neon Ne 10
0.063 Magnesium Mg 12
0.171 Lead Pb 82
0.171 Silicon Si 14
0.172 Phosphorus P 15
0.184 Zirconium Zr 40
0.232 Aluminum Al 13
0.3326 Hydrogen H 1
0.38 Rubidium Rb 37
0.43 Calcium Ca 20
0.53 Sulfur S 16
0.53 Sodium Na 11
0.6 Cerium Ce 58
0.626 Tin Sn 50
0.675 Argon Ar 18
0.72 Radon Rn 86
0.96 Platinum Pt 78
1.11 Zinc Zn 30
1.15 Niobium Nb 41
1.28 Yttrium Y 39
1.28 Strontium Sr 38
1.3 Barium Ba 56
1.91 Nitrogen N 7
2.1 Potassium K 19
2.2 Germanium Ge 32
2.56 Ruthenium Ru 44
2.56 Iron Fe 26
2.6 Molybdenum Mo 42
2.9 Gallium Ga 31
3.1 Chromium Cr 24
3.43 Thallium Tl 81
3.78 Copper Cu 29
4.3 Arsenic As 33
4.49 Nickel Ni 28
4.7 Tellurium Te 52
4.91 Antimony Sb 51
5.08 Vanadium V 23
6.09 Titanium Ti 22
6.2 Iodine I 53
6.8 Bromine Br 35
6.9 Palladium Pd 46
7.37 Thorium Th 90
7.57 Uranium U 92
8.98 Lanthanum La 57
11.5 Praseodymium Pr 59
11.7 Selenium Se 34
12.8 Radium Ra 88
13.3 Manganese Mn 25
15 Osmium Os 76
18.3 Tungsten W 74
20 Technetium Tc 43
20.6 Tantalum Ta 73
23.4 Terbium Tb 65
23.9 Xenon Xe 54
25 Krypton Kr 36
27.2 Scandium Sc 21
29 Cesium Cs 55
34.8 Ytterbium Yb 70
35.5 Chlorine Cl 17
37.2 Cobalt Co 27
49 Neodymium Nd 60
63.6 Silver Ag 47
65 Holmium Ho 67
70.5 Lithium Li 3
75.3 Americium Am 95
79 Curium Cm 96
84 Lutetium Lu 71
89.7 Rhenium Re 75
98.7 Gold Au 79
100 Thulium Tm 69
104 Hafnium Hf 72
144.8 Rhodium Rh 45
160 Einsteinium Es 99
160 Erbium Er 68
168.4 Promethium Pm 61
180 Neptunium Np 93
194 Indium In 49
200.6 Protactinium Pa 91
374 Mercury Hg 80
425 Iridium Ir 77
515 Actinium Ac 89
710 Berkelium Bk 97
767 Boron B 5
920 Dysprosium Dy 66
1017.3 Plutonium Pu 94
2450 Cadmium Cd 48
2900 Californium Cf 98
4600 Europium Eu 63
5800 Fermium Fm 100
5922 Samarium Sm 62
49000 Gadolinium Gd 64

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.


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.

  1. 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.
  2. The nucleus may emit gamma or X-ray radiation.
  3. The nucleus may β− decay, where a neutron is converted into a proton, an electron and an electron-type antineutrino (the antiparticle of the neutrino)
  4. 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. E.g. 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 neither in element nor isotope.

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


U-235 decay

U-235 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.

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