Neutron scattering length
A neutron may pass by a nucleus with a probability determined by the nuclear interaction distance, or be absorbed, or undergo scattering that may be either coherent or incoherent.
The scattering length may be either positive or negative. The scattering cross-section is equal to the square of the scattering length multiplied by 4π,[3] i.e. the area of a circle with radius twice the scattering length. In some cases, as with titanium and nickel, it is possible to mix isotopes of an element whose lengths are of opposite signs to give a net scattering length of zero, in which case coherent scattering will not occur at all, while for vanadium already the opposite signs of the only naturally occurring isotope's two spin configurations give a near cancellation. However, neutrons will still undergo strong incoherent scattering in these materials.[1]
There is a large difference in scattering length between
element | protons | isotope | neutron scattering length bcoh (fm) |
coherent cross-section σcoh (barn) |
incoherent cross-section σinc (barn) |
absorption cross-section σa (barn) |
---|---|---|---|---|---|---|
Hydrogen | 1 | 1[2][5] | -3.74[1][2][5][6] | 1.758[1] | 79.7,[6] 80.27[1] | 0.33,[6] 0.383[1] |
Hydrogen | 1 | 2 | 6.67[1][2][5][6] | 5.592[1] | 2.0,[6] 2.05[1] | 0.0005[1][6] |
Boron | 5 | natural | 5.30[1] | 3.54[1] | 1.70[1] | 767.0[1] |
Carbon | 6 | 12 | 6.65[1][2][5][6] | 5.550[1] | 0.0,[6] 0.001[1] | 0.0035,[6] 0.004[1] |
Nitrogen | 7 | 14 | 9.36,[1] 9.40,[2] 9.4[5][6] | 11.01[1] | 0.3,[6] 0.5[1] | 1.9[1][6] |
Oxygen | 8 | 16 | 5.80,[2] 5.8[1][5][6] | 4.232[1] | 0.0,[6] 0.000[1] | 0.00019,[6] 0.0002[1] |
Aluminum
|
13 | natural | 3.45,[1] 3.5[6] | 1.495[1] | 0.0,[6] 0.008[1] | 0.23,[6] 0.231[1] |
Silicon | 14 | natural | 4.2[6][7] | 0.0[6] | 0.17[6] | |
Phosphorus | 15 | 30 | 5.10[2] | |||
Sulfur | 16 | 32 | 2.80,[2] 2.8[5] | |||
Titanium | 22 | natural | -3.44,[1] -3.4[6][7] | 1.485[1] | 2.87,[1] 3.0[6] | 6.09,[1] 6.1[6] |
Vanadium | 23 | natural | -0.38[1] | 0.018[1] | 5.07[1] | 5.08[1] |
Chromium | 24 | natural | 3.64[1] | 1.66[1] | 1.83[1] | 3.05[1] |
Manganese | 25 | 55 (natural) | -3.73[1] | 1.75[1] | 0.4[1] | 13.3[1] |
Iron | 26 | natural | 9.45,[1] 9.5[6] | 11.22[1] | 0.4[1][6] | 2.56,[1] 2.6[6] |
Nickel | 28 | natural | 10.3[1] | 13.3[1] | 5.2[1] | 4.49[1] |
Copper | 29 | natural | 7.72[1] | 7.485[1] | 0.55[1] | 3.78[1] |
Zirconium | 40 | natural | 7.16,[1] 0.72[6] | 6.44[1] | 0.02,[1] 0.3[6] | 0.18,[6] 0.185[1] |
Niobium | 41 | 93 (natural) | 7.054[1] | 6.253[1] | 0.0024[1] | 1.15[1] |
Molybdenum | 42 | natural | 6.72[1] | 5.67[1] | 0.04[1] | 2.48[1] |
Cadmium | 48 | natural | 4.87[1] | 3.04[1] | 3.46[1] | 2520[1] |
Tin | 50 | natural | 6.23[1] | 4.87[1] | 0.022[1] | 0.626[1] |
Cerium | 58 | natural | 4.8[6] | 0.0[6] | 0.63[6] | |
Gadolinium | 64 | natural | 6.5[1] | 29.3[1] | 151[1] | 49700[1] |
Tantalum | 73 | natural | 6.91[1] | 6.00[1] | 0.01[1] | 20.6[1] |
Tungsten | 74 | natural | 4.86[1] | 2.97[1] | 1.63[1] | 18.3[1] |
Gold | 79 | 197 | 7.60[2] | |||
Lead | 82 | natural | 9.41[1] | 11.115[1] | 0.003[1] | 0.171[1] |
Thorium | 90 | 232 (natural) | 9.8[6] | 0.00[6] | 7.4[6] | |
Uranium | 92 | natural | 8.42[1][6] | 8.903[1] | 0.00,[6] 0.005[1] | 7.5,[6] 7.57[1] |
More comprehensive data is available from
References
- ^ ISBN 9780203402818.
- ^ ISBN 9780199639533.
- .
- PMID 10725379.
- ^ ISBN 9781489916150.
- ^ ISBN 9780080540320.
- ^ ISBN 9780080887371.
- ^ "Index of /resources/n-lengths/elements".
- ^ "Neutron Scattering Lengths".