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Lesson11b - Lesson 11b Interactions of Charged Particles...

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Lesson 11b Interactions of Charged Particles with Mat- ter MP200 Radiation Physics - 2010 Duke Medical Physics Graduate Program 1
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Dependence on the medium dT ρdx c = 0 . 3071 Zz 2 2 13 . 8373 + ln β 2 1 - β 2 - β 2 - ln I MeV.cm 2 .g - 1 When Z (medium) is increased, the number of electrons per unit mass Z A decreases. When Z is increased, ln( I ) increases; Therefore, dT ρdx c decreases. Dependence on particle velocity When v increases, β increases. Because of 1 β 2 is outside of the bracket dT ρdx c decreases. When particle charge z increases, dT ρdx c increases. Dependence on particle mass The particle’s mass does not appear in dT ρdx c formula. So, dT ρdx c does not depend on particle mass. Relation between kinetic energy T and β (Relativistic scaling) The kinetic energy T of a particle of rest mass M 0 is connected to the parameter β . T = M 0 c 2 ( γ - 1) = M 0 c 2 1 1 - β 2 - 1 2
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β = 1 - 1 1 + T M 0 c 2 2 1 2 The following table gives rest masses for heavy particles Particle Mc 2 ( MeV ) Z muon 105.66 1 pion 139.60 1 proton 938.28 1 neutron 939.57 0 deuteron 1875.63 1 α 3727.41 2 For any two particles A and B , for a given value β ( same velocity) , the kinetic energies, T A = M A c 2 ( γ - 1) T B = M B c 2 ( γ - 1) T A T B = M A M B i.e. If two particles travel at the same speed, their ratio of kinetic en- ergies are proportional to the ratios of their rest masses. Minimum ionizing particles The variation of dT ρdx c with T , for some particles is shown in the figure. The value of dT ρdx c with T , for many different particles approaches a constant broad minimum value at higher energies. 3
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Figure 1: minimum ionizing particles For light materials thus dT ρdx c with T , the value corresponds to 2 MeV cm 2 .g - 1 . Because of their similar energy loss behavior, these relative particles are called ”Minimum Ionizing Particles” .
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