Ionizing stopping power

The stopping power of a material for a particular radiation is commonly expressed as the rate of energy loss (R.E.L.) or the linear energy transfer (L.E.T.) of the radiation in the material. These quantities are assumed to be proportional to the linear ion density and the specific ionization. Stopping powers range from approximately 106 e.v./cm. for fast electrons (1 Mev.) in water to 1011 e.v./cm. for fission recoils. The ranges of particles are frequently expressed in mg./cm.2, which when multiplied by the density of the material yields the range. 

One can get an estimate (Bichsel et al. 2002) of the stopping power of various particles in various substances using Fig. 8.2. In Fig. 8.3 the ionization stopping power is plotted for various charged particles as measured in copper as a function of kinetic energy one can see the scaling with particle mass. 

In the region 104-109 eV, where the energy loss is via electronic excitation and ionization, Bethe s formula with corrections (Eq. 2.11) describes the stopping power quite accurately. In the interval 104-106 eV, the decrease of stopping power with energy is attributable to the v-2 term. It reaches a minimum of —0.02 eV/A at -1.5 MeV then it shows a relativistic rise before the restricted part rides to the Fermi plateau at -40 MeV. 

Another procedure for calculating the W value has been developed by La Verne and Mozumder (1992) and applied to electron and proton irradiation of gaseous water. Considering a small section Ax of an electron track, the energy loss of the primary electron is S(E) Ax, where S(E) is the stopping power at electron energy E. The average number of primary ionizations produced over Ax is No. Ax where o. is the total ionization cross section and N is the number density of molecules. Thus, the W value for primary ionization is 0)p = S(E)/No.(E). If the differential ionization cross section for the production... 

Note that Eq. (8.1) is remarkably independent of electron velocity. The stopping power -dE Idx = v-1(-dE /dt) does depend on velocity, but Frohlich and Platzman preferred not to use the stopping power due to a lack of knowledge of the actual tortuous path. Taking s = 80, ir = 5, d = 3.3A, and x = 10-11 s for water at 20°, they computed -dE /dt 1013 s-1, which is about three orders of magnitude less than that for excitation and ionization at higher energies. 

EXPLAIN the relationship between stopping power and specific ionization. 

Specific ionization times the energy per ion pair yields the stopping power (LET), as shown in Equation 6-3. 

Stopping power is proportional to specific ionization. Radiation detection terms discussed in this chapter are summarized below. 

Figure 15 Total ionization cross sections due to dressed ion impact on water vapor. Cross sections for and He were adjusted to reproduce stopping powers for the lower energy protons and alpha particles. (Experimental data from Refs. 200, 213, and 217.)...

Thus, a more energetic ion will tend to lose energy at a lower rate than a less energetic ion. Be careful to note that we have ignored the relativistic terms, y2 and (32, in the parentheses, which produce a minimum in the complete function near (3 0.96 and a small rise at higher velocities. (Particles with (3 0.96 are called minimum ionizing particles.) The proportionality of the stopping power... 

The principal parameter characterizing the molecular stopping power in Bethe s theory is the average ionization potential Im, which depends only on the properties of the molecule. There are different ways of... 

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