.
Multiple scattering for particles in matter.
In addition to inelastic
collisions with the atomic electrons,
particles passing through matter suffer
repeated elastic Coulomb scattering from
nuclei although with a smaller probability.
Considering that usually nuclei have mass greater than the incoming particle, the energy transfer is negligible but each scattering centre adds a small deviation to the incoming particle’s trajectory also. Even if this deflection is small the sum of all the contribution adds a random component to the particle’s path which proceeds with a zigzag path (see Figure 1.). As result, incoming beam after a thickness of material shown a divergence greater than the initial.
�
Fig 1.
Effect of Multiple Coulomb Scattering.
Three situations can
be considered:
1. Single scattering. When the thickness is extremely small and the probability to have more than one interaction is negligible. This situation is well described by the Rutherford formula:
2.
Plural
scattering. When the number of Coulomb
scattering increases but remains under few
tens of interactions. This is the most
difficult case to deal with, several works
have been done by different authors (see [1]
for further information).
3.
MMultiple scattering. When the thickness
increases and the number of interactions
become high the angular dispersion can be
modelled as Gaussian.
Referring to multiple scattering, that is the most common situation, naming Θ the solid angle into which is concentrated the 98% of the beam after a thickness X of material, if we define Θ_{0}= Θ/√2 as the projection of Θ on a plane, the angular dispersion can be calculated by the relation:
where p is the momentum and Xo is the
radiation length. This last quantity is
characteristic of the material and can be
found tabulated by Y.S. Tsai [2] or can be
used the approximated formula
References

E. Keil, E.Zeitler, and W. Zinn, Zeitschrift f�r Naturforschung A, vol. 15A, no. 1031, 1960.

YungSu Tsai, Pair production and bremsstrahlung of charged leptons, Reviews of Modern Physics, vol. 46, no. 815, 1974
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