24. Photon and electron interactions with matter 1

24. PHOTON AND ELECTRON INTERACTIONS WITH MATTER

Revised April 1998 by D.E. Groom (LBNL).

Photon Attenuation Length

Photon energy

100

10

10–4

10–5

10–6

1

0.1

0.01

0.001

10 eV 100 eV 1 keV 10 keV 100 keV 1 MeV 10 MeV 100 MeV 1 GeV 10 GeV 100 GeV

Abs

orpt

ion

len

gth

λ (

g/cm

2)

Si

C

Fe Pb

H

Sn

Figure 24.1: The photon mass attenuation length (or mean free path) λ = 1/(µ/ρ) for various elemental absorbers as a function of photonenergy. The mass attenuation coefficient is µ/ρ, where ρ is the density. The intensity I remaining after traversal of thickness t (in mass/unitarea) is given by I = I0 exp(−t/λ). The accuracy is a few percent. For a chemical compound or mixture, 1/λeff ≈

∑elements wZ/λZ , where

wZ is the proportion by weight of the element with atomic number Z. The processes responsible for attenuation are given in Fig. 24.4. Sincecoherent processes are included, not all these processes result in energy deposition.The data for 30 eV < E < 1 keV are obtained from http://www-cxro.lbl.gov/optical constants (courtesy of Eric M. Gullikson, LBNL).The data for 1 keV < E < 100 GeV are from http://physics.nist.gov/PhysRefData, through the courtesy of John H. Hubbell (NIST).

Photon Pair Conversion Probability

Photon energy (MeV)1 2 5 10 20 50 100 200 500 1000

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

CPb

NaI

Fe

Ar

HH2O

P

Figure 24.2: Probability P that a photoninteraction will result in conversion to an e+e−

pair. Except for a few-percent contributionfrom photonuclear absorption around 10 or 20MeV, essentially all other interactions in thisenergy range result in Compton scattering offan atomic electron. For a photon attenuationlength λ (Fig. 24.1), the probability that agiven photon will produce an electron pair(without first Compton scattering) in thicknesst of absorber is P [1− exp(−t/λ)].

2 24. Photon and electron interactions with matter

Contributions to Photon Cross Section in Carbon and Lead

Photon Energy

Cro

ss s

ecti

on, b

arn

s/at

om

Cro

ss s

ecti

on, b

arn

s/at

om10 mb

1 b

1 kb

1 MbCarbon (Z = 6)

σcoherent

σincohσnuc

κN

κe

σp.e.

10 eV 1 keV 1 MeV 1 GeV 100 GeV

Photon Energy

1 Mb

1 kb

1 b

10 mb10 eV 1 keV 1 MeV 1 GeV 100 GeV

Lead (Z = 82)

σcoherent

σincoh

− experimental σtot− experimental σtotσp.e.

σnuc

κN

κe

Figure 24.3: Photon total cross sections as a function of energy in carbon and lead, showing the contributions of different processes:

σp.e. = Atomic photo-effect (electron ejection, photon absorption)σcoherent = Coherent scattering (Rayleigh scattering—atom neither ionized nor excited)

σincoherent = Incoherent scattering (Compton scattering off an electron)κn = Pair production, nuclear fieldκe = Pair production, electron field

σnuc = Photonuclear absorption (nuclear absorption, usually followed by emission of a neutron or other particle)

From Hubbell, Gimm, and Øverbø, J. Phys. Chem. Ref. Data 9, 1023 (80). Data for these and other elements, compounds, and mixturesmay be obtained from http://physics.nist.gov/PhysRefData. The photon total cross section is assumed approximately flat for at least twodecades beyond the energy range shown. Figures courtesy J.H. Hubbell (NIST).

Fractional Energy Loss for Electrons and Positrons in Lead

Bremsstrahlung

Lead (Z = 82)Positrons

Electrons

Ionization

Møller (e−)

Bhabha (e+)

Positronannihilation

1.0

0.5

0.20

0.15

0.10

0.05

(cm

2g−

1 )

E (MeV)10 10 100 1000

1 E−

dE dx

(X0−1

)

Figure 24.4: Fractional energy loss per radiationlength in lead as a function of electron or positronenergy. Electron (positron) scattering is consideredas ionization when the energy loss per collision isbelow 0.255 MeV, and as Moller (Bhabha) scatteringwhen it is above. Adapted from Fig. 3.2 from Messeland Crawford, Electron-Photon Shower DistributionFunction Tables for Lead, Copper, and Air Absorbers,Pergamon Press, 1970. Messel and Crawford useX0(Pb) = 5.82 g/cm2, but we have modified thefigures to reflect the value given in the Table of Atomicand Nuclear Properties of Materials, namely X0(Pb)= 6.4 g/cm2. The development of electron-photoncascades is approximately independent of absorberwhen the results are expressed in terms of inverseradiation lengths (i.e., scale on left of plot).