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Chapter: 4 Atomic and nuclear physics
    Section: 4.2 Absorption of photons
        SubSection: 4.2.2 Attenuation of photons

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4.2.2    Attenuation of photons

The intensity I(t) of a photon beam after passing through t kg m−2 of matter is given by

  

I(t) = I(0)exp(−(μ/ρ)t)

where μ/ρ is the mass absorption coefficient. The values of μ/ρ given in the accompanying figure and table refer to the attenuation of a collimated beam of photons striking the attenuating material and an emerging beam consisting only of those photons which are undeflected and have suffered no energy loss. Inclusion of secondary products in the transmitted beam reduces this attenuation. The values given here are taken from Hubbell (1982) Int. J. Appl. Radioat. Isot., 33, 1269 and Hubbell, Gimm and Overbo (1980) J. Phys. Chem. Ref. Data, 9, 1023.
       The three main processes by which photons interact with matter are photoelectric absorption which dominates at low energies, incoherent (Compton) scattering which is most important between about 0.2 and 5 MeV, and pair production which dominates at high energies. These three components, and others, can be obtained separately from the two references above. The photonuclear interaction is excluded from the values given here.
      If the mass absorption coefficient μ/ρ is written in terms of atomic cross-sections σ as

  

 μ/ρ (NA/A) × (σphotoelectric + σCompton + σpair)

where NA is Avogadro's number and A is the atomic weight of the attenuating material, then, for purposes of rough guidance only, approximate expressions for these component cross-sections are as follows. The photoelectric cross-section is given roughly by

 

 σphotoelectric(m2) 6 ×10−37 Z4.5/Eγ3

where Z is the atomic number of the attenuating material and Eγ is the energy of the photon in MeV. The kinematics of Compton scattering are described by

  

Eγ′ = mec2/(1 − cos θ + mec2/Eγ)

where Eγ is the incident photon energy, mec2 is the electron rest energy (0.511 MeV), θ is the scattering angle and Eγ′ is the scattered photon energy. At low energies (Eγ << mec2)

  

 σCompton (8/3)πre2Z = 0.665 × 10−28Z m2,

and at high energies (Eγ >> mec2)

  

σCompton πre2Z(1 + 2 ln(2Eγ/(mec2)))/(2Eγ/(mec2)

where re = 2.82 × 10−15 m is the classical electron radius. The pair production cross-section is given roughly by

 

σpair Z2re2(ln(2Eγ/(mec2)) − 2.6)/44.

      Mass absorption coefficients for composite materials may be calculated by taking the average value of the absorption coefficients for the constituents weighted in proportion to their abundance by weight.
      Uncertainties in the mass absorption coefficients are estimated to be about ±5% up to 5 keV and about ±2% above 5 keV. Above 10 MeV the photonuclear interaction can contribute an extra ~ 1–5% to the mass absorption coefficient.

Mass obsorption coefficient as a function of element and photon energy in units of 0.01 m2 kg−1

MeV
 
 
 

Element

H

Be

C

Al

Fe

Ge

Ag

I

Pb

U

Con-
crete

Water

     0.2

2.429

1.089

1.229

1.223

1.458

1.658

2.963

3.650

7.844

9.985

12.98    

1.27

1.370

     0.3

2.112

0.946

1.066

1.042

1.098

1.130

1.557

1.768

3.238

4.026

5.191

1.08

1.187

     0.4

1.893

0.847

0.954

0.928

0.940

0.933

1.130

1.215

1.925

2.323

2.922

0.96

1.061

     0.5

1.729

0.774

0.871

0.845

0.841

0.821

0.931

0.969

1.378

1.613

1.976

0.88

0.969

     0.6

1.599

0.716

0.806

0.780

0.770

0.745

0.814

0.830

1.093

1.248

1.490

0.81

0.896

     0.8

1.405

0.629

0.708

0.684

0.670

0.643

0.676

0.674

0.806

0.887

1.016

0.71

0.787

     1.0

1.263

0.565

0.636

0.615

0.599

0.573

0.592

0.584

0.662

0.710

0.789

0.64

0.707

     1.5

1.027

0.460

0.518

0.501

0.488

0.466

0.475

0.465

0.500

0.522

0.559

0.52

0.576

     2.0

0.877

0.394

0.444

0.432

0.426

0.409

0.421

0.412

0.443

0.461

0.488

0.45

0.494

     3.0

0.692

0.314

0.356

0.354

0.362

0.352

0.375

0.372

0.408

0.423

0.445

0.37

0.397

     4.0

0.581

0.266

0.305

0.311

0.331

0.328

0.361

0.361

0.404

0.420

0.439

0.32

0.340

     5.0

0.505

0.235

0.271

0.284

0.315

0.316

0.358

0.361

0.410

0.427

0.446

0.29

0.303

     6.0

0.450

0.212

0.247

0.265

0.306

0.311

0.360

0.366

0.421

0.439

0.458

0.27

0.277

     8.0

0.375

0.182

0.215

0.244

0.299

0.310

0.372

0.382

0.447

0.468

0.488

0.24

0.243

   10.0

0.325

0.163

0.196

0.232

0.299

0.316

0.388

0.400

0.475

0.497

0.519

0.23

0.222

   15.0

0.254

0.136

0.170

0.220

0.309

0.334

0.428

0.446

0.538

0.566

0.593

0.22

0.194

   20.0

0.215

0.123

0.158

0.217

0.322

0.353

0.461

0.482

0.589

0.620

0.651

0.21

0.181

   30.0

0.175

0.110

0.147

0.220

0.347

0.385

0.513

0.540

0.665

0.702

0.739

0.21

0.171

   40.0

0.154

0.104

0.144

0.225

0.367

0.410

0.551

0.581

0.720

0.761

0.802

0.21

0.168

   50.0

0.142

0.102

0.143

0.231

0.383

0.430

0.581

0.613

0.762

0.806

0.849

0.22

0.167

   60.0

0.134

0.100

0.143

0.236

0.396

0.446

0.604

0.638

0.795

0.841

0.887

0.22

0.168

   80.0

0.124

0.099

0.144

0.245

0.417

0.471

0.640

0.676

0.844

0.893

0.943

0.23

0.170

 100.0

0.119

0.099

0.146

0.252

0.433

0.489

0.666

0.704

0.880

0.931

0.983

0.24

0.173

 150.0

0.114

0.101

0.150

0.264

0.459

0.519

0.709

0.749

0.936

0.991

1.047

0.25

0.178

 200.0

0.112

0.102

0.154

0.272

0.476

0.538

0.734

0.777

0.970

1.027

1.085

0.25

0.183

 300.0

0.112

0.105

0.159

0.282

0.495

0.559

0.765

0.809

1.010

1.069

1.131

0.26

0.189

                           

Approximate composition by weight of concrete: 50% oxygen, 31% silicon, 8% calcium, 5% aluminium, 6% other materials.


Mass absorption coefficients (m/p) as a function of element for a set of proton energies between 1 and 200 KeV

(Click the Image to View Larger Image)

Mass absorption coefficient (m/r) as a function of element for a set of photon energies between 1 and 200 keV.


D.J.S. Findlay

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