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Chapter: 4 Atomic and nuclear physics
    Section: 4.5 Absorption of particles and dosimetry
        SubSection: 4.5.3 Range of electrons and beta particles

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4.5.3    Range of electrons and beta particles

The process by which electrons slow down and stop in material is characterized by variables which exhibit relatively large variations about mean values. For example, electrons spread out in transverse directions as they penetrate material, and electron energy losses and ranges are characterized by relatively large variations about the corresponding mean values of energy loss or range.

The stopping powers tabulated below (taken from L. Pages et al. (1972) Atomic Data, 4, 1) are made up of two components, the collision stopping power representing energy losses due to collisions with atomic electrons, and the radiation stopping power representing energy losses due to bremsstrahlung interactions. The radiation stopping power is more important for higher electron energies and higher atomic numbers of materials being penetrated. The ranges tabulated below (also taken from Pages) have been computed in the continuous slowing-down approximation (CSDA), i.e. the range is considered to be the distance along the path travelled by an ‘average electron’ until the electron stops. Few electrons reach a distance into the material equal to the CSDA range measured along the direction of initial incidence of the electron on the material.

Energy
(MeV)

Be

Al

 

Stopping power
(MeV m2 kg−1)

Range
(kg m−2)

Stopping power
(MeV m2 kg−1)

Range
(kg m−2)

 

collision

radiation

total

collision

radiation

total

 

 

 

 

 

 

 

 

 

0.01

1.88 100  

 2.44 10−4

1.88 100  

 2.65 10−3

1.64 100  

 8.53 10−4

1.64 100  

 3.05 10−3

0.03

8.00 10−1

2.39 10−4

8.00 10−1

2.08 10−2

7.25 10−1

8.31 10−4

7.26 10−1

2.33 10−2

0.1  

3.39 10−1

2.61 10−4

3.39 10−1

1.73 10−1

3.16 10−1

9.28 10−4

3.17 10−1

1.88 10−1

0.3  

1.93 10−1

3.80 10−4

1.93 10−1

1.02 100

1.83 10−1

1.35 10−3

1.84 10−1

1.08 100   

1     

1.49 10−1

8.75 10−4

1.50 10−1

5.37 100

1.46 10−1

2.99 103

1.49 10−1

5.55 100   

3     

1.50 10−1

2.44 10−3

1.53 10−1

1.87 101

1.51 10−1

7.43 10−3

1.58 10−1

1.86 101   

10       

1.60 10−1

9.68 10−3

1.70 10−1

6.18 101

1.64 10−1

2.82 10−2

1.92 10−1

5.85 101   

30       

1.69 10−1

3.42 10−2

2.03 10−1

1.69 102

1.75 10−1

9.83 10−2

2.73 10−1

1.46 102   

100         

1.77 10−1

1.36 10−1

3.13 10−1

4.44 102

1.85 10−1

3.82 10−1

5.67 10−1

3.20 102   

 

 

 

 

 

 

 

 

 


Energy
(MeV)

Cu

Ta

 

Stopping power
(MeV m2 kg−1)

Range
(kg m−2)

Stopping power
(MeV m2 kg−1)

Range
(kg m−2)

 

collision

radiation

total

collision

radiation

total

 

 

 

 

 

 

 

 

 

0.01

1.33 100  

1.78 10−3

1.33 100  

3.77 10−3

8.94 10−1

3.88 10−3

8.97 10−1

5.57 10−3

0.03

6.07 10−1

1.86 10−3

6.09 10−1

2.81 10−2

4.38 10−1

4.37 10−3

4.43 10−1

3.99 10−2

0.1  

2.71 10−1

2.20 10−3

2.73 10−1

2.21 10−1

2.04 10−1

5.43 10−3

2.10 10−1

2.95 10−1

0.3  

1.58 10−1

3.12 10−3

1.61 10−1

1.25 100   

1.23 10−1

7.69 10−3

1.31 10−1

1.59 100   

1     

1.26 10−1

6.48 10−3

1.33 10−1

6.29 100   

1.01 10−1

1.52 10−2

1.17 10−1

7.52 100   

3     

1.31 10−1

1.48 10−2

1.46 10−1

2.07 101   

1.07 10−1

3.15 10−2

1.39 10−1

2.32 101   

10       

1.44 10−1

5.54 10−2

2.00 10−1

6.15 101   

1.21 10−1

1.13 10−1

2.33 10−1

6.17 101   

30       

1.56 10−1

1.87 10−1

3.44 10−1

1.38 102   

1.32 10−1

3.46 10−1

4.78 10−1

1.21 102   

100         

1.67 10−1

7.24 10−1

8.91 10−1

2.60 102   

1.43 10−1

1.37 100   

1.52 100    

2.00 102   

 

 

 

 

 

 

 

 

 

D.J.S. Findlay

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