Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection

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180 Principles of Radiation Interaction in Matter and Detection

only scattering is possible. However, the two low-A nuclei (deuterium and beryl-

lium) have quite low energy thresholds for photoneutron production: 2.226 and

1.666 MeV, respectively. Deuterium is present (although in small amounts) in ma-

terial containing hydrogen, water and plastics. Thus, it can become a source of

neutrons, which has to be taken into account in radiation shielding. In addition, the

photoneutron

production on deuterium is a mechanism for photoneutron produc-

tion in heavier nuclei at energies above ≈ 30 MeV. The cross section σ

is given by

= C

− 2.226)

3/2

[mb], (2.222)

where the incoming photon energy, E

, is in MeV and C

≈ 61.0–62.4 [Ericsson

(1986)].

For photon energies above the binding energy of the least bound nucleon, the

photoneutron emission is possible. Most of the photonuclear reactions up to ≈

30 MeV occur via dipole excitations of the nucleus known as giant resonances. Non-

spherical nuclei show a double peak corresp onding to vibrations along symmetry

axes. The characteristic broad absorption of the photonuclear cross section in the

giant resonance region is centered at ≈ 24 MeV for low-A nuclei, but it decreases

up to ≈ 12 MeV for the heaviest stable nuclei. The peak width

∗

, Γ, varies between

3 and 9 MeV, depending on the target nucleus. The threshold energy, for emitting a

single neutron (γ,n), varies between ≈ 7 and 8 MeV (for high-A nuclei) and 18 MeV

(for low-

nuclei), for proton emission (

,p) between

≈

6 and 16 MeV. The emission

of other charged particles (for instance α particles) and more than one neutron is

also possible. The cross section (σ

grp

) at the energy resonance peak (E

grp

) is ≈ 6%

of the atomic electron (electronic) cross section for low-A nuclei and not larger than

≈ 2% for high-A nuclei.

For photon energies corresponding to the giant resonance maximum, the angular

distribution of emitted neutrons behaves as

F(θ) = A

+ B

sin

θ.

It shows a symmetrical behavior centered around 90

◦

. As the energy increases, the

distribution becomes less symmetric and more forward directed.

For suﬃciently massive nuclei (A > 50), the shape of the cross section reso-

nance can b e approximated by a Lorenz curve (see for instance [Fuller and Hayward

(1962)]):

crs

) ' σ

grp

g rp

− E

)

+ E

For ellipsoidal nuclei, the shape of the cross section is given by a superposition of

two Lorenz curves.

It is a neutron emitted by a nuclear target as a result of a photon interaction.

∗

This is the energy diﬀerence between points around the peak, for which the cross section de-

creases by a factor 2.

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Electromagnetic Interaction of Radiation in Matter 181

Fig. 2.65 Photon total cross section on proton and deuterium (experimental data and references are available (also via the web) from [PDB (2002)])

as a function of the photon momentum. The lines are to guide the eye.

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182 Principles of Radiation Interaction in Matter and Detection

Fig. 2.66 Ratio of the total hadronic photon cross section on nucleus to the hadronic photon cross

section on proton as a function of the mass number A (adapted and reprinted with permission

from Genzel, H., Joos, P. and Pfeil, W. (1973), Photoproduction of Elementary Particles, in

Landolt- B¨ornstein, Group I: Nuclear and Particle Physics, Vol. 8: Photoproduction of Elementary

Particles, Shopper, H. Editor, Springer, Berlin, Chapter 2, Figure 2, page 306;

° by Springer-

Verlag Berlin Heidelberg 1973; see also [Fass`o et al. (1990)]). Data were taken at photon energies

ranging from 3.3 to 16.4 GeV. The line represents σ

tot

(γA) = A σ

tot

(γp).

The photon wavelength for energies above 30 MeV becomes smaller than the

average inter-nucleon distance. Thus, the interaction can occur on a single or on a

few nucleons. Most of the reactions happen on a nucleon pair (proton–neutron pair),

the so-called quasi-deuteron. The cross section σ

q d

for the quasi-deuteron interaction

theory proposed by Levinger (1951) is given by

= Le

(A − D)D

, (2.223)

where σ

is the cross section on free deuterium, given by Eq. (2.222) up to

≈ 140 MeV; Le is the so-called Levinger parameter ' 6.4; and, ﬁnally, D is the num-

ber of quasi-deuteron pairs inside the nucleus. The A-dependence of the Levinger

parameter seems to be well represented by [Giannini (1986)]

Le =

13.82 A

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Electromagnetic Interaction of Radiation in Matter 183

where R

is the experimental root mean square charge radius in units of fermi [Gi-

annini (1986)]. The angular and energy distributions of emitted nucleons are in

principle similar to those on free deuteron, but they are broadened due to the in-

ternal motion and re-interactions, before emerging from the nucleus.

As the photon energy increases above the pion production threshold ('

140 MeV), the photon cross section shows peaks corresponding to the excitation

of baryonic resonances, as shown in Fig. 2.65 [PDB (2002)] for γ–p and γ–d cross

sections. During the photon interaction and the de-excitation of such states, spal-

lation nucleons, nuclear fragments and mesons can be produced.

At high energies, the photon–proton (σ

γ,p

) and photon–neutron (σ

γ,n

) cross

sections [Bauer, Spital and Yennie (1978)] approach similar values.

High-energy photon–nucleus collisions were studied experimentally and theoret-

ically (see for instance [Lohrmann (1969); Genzel, Joos and Pfeil (1973); Bauer, Spi-

tal and Yennie (1978); Engel, Ranft and Roesler (1997)] and references therein). It

was pointed out that there are similarities between photon–nucleus and hadron–

nucleus features, like for instance the so-called shadowing eﬀect, i.e., the decrease of

the cross section per nucleon as the mass numb er increases (see Fig. 2.66 and [Gen-

zel, Joos and Pfeil (1973)]). The photon hadronic-feature was included within the

framework of the Vector Dominance Model (VDM, see for instance [Bauer, Spi-

tal and Yennie (1978); Engel, Ranft and Roesler (1997)] and references therein)

or others, like the Generalized Vector Dominance Model (GDVDM, see for in-

stance [Engel, Ranft and Roesler (1997)] and references therein). The VDM predicts

that, at high energies, a photon behaves like a hadron in strong interactions. In fact,

from the quantum-mechanical point of view because of the uncertainty principle, a

photon

∗∗

may convert virtually into a vector meson.

††

The lifetime ∆t, for such a

ﬂuctuation in the laboratory system, is ∆t ∼ ~/(q

c), where q

is the diﬀerence

between the longitudinal momenta of the photon and of the produced vector me-

son. In the high-energy limit for which q

→ 0, ∆t might become large enough so

that the impinging photon is already in the virtual state of a vector meson. Hence,

a strong interaction with the nucleus can occur and can be theoretically treated

within the framework of the Gribov–Glauber formalism [Glauber (1955)]. As a con-

sequence, shadowing eﬀects, typical of hadron–nucleus interactions, are expected to

be also found in the photon–nucleus interaction.

2.3.5 Attenuation Coeﬃcients, Dosimetric and Radiobiological

Quantities

In Sects. 2.3, 2.3.1, 2.3.2.4, the mass attenuation coeﬃcients were introduced to de-

scribe the absortion and/or scatttering of photons in matter. In the present section,

the notations are the same of those used in the previous sections.

∗∗

The spin-parity of a photon is J

= 1

−

††

The vector mesons are strongly interacting mesonic particles with J

= 1

−

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184 Principles of Radiation Interaction in Matter and Detection

The mass attenuation and mass energy-absorption coeﬃcients are extensively

used in calculations for γ-ray transport in matter and for photon energy deposi-

tions in biological and other materials, e.g., for dosimetric applications [Hubbell

(1977)] in the medical and biological context [Hubbell (1999)]. These coeﬃcients

were tabulated and discussed in details in literature and, at present, are also avail-

able on the web (see [Hubbell (1969); Henke, Gullikson and Davis (1993); Hubbell

and Seltzer (2004); Berger, Hubbell, Seltzer, Chang, Coursey, Sukumar and Zucker

(2005)] and references therein).

As discussed along this section, the energy and Z-dependence of the mass atte-

nuation coeﬃcients are mainly determined by the total cross sections for photoelec-

tric eﬀect, Compton scattering and pair production. They depend on the incoming

photon energy and atomic number. The photonuclear absorption by nuclei mostly

results in ejecting nucleons. This interaction contributes by less than (5–10)% to

the total photon cross section in a fairly narrow energy region between a few MeV

and a few tens of MeV. This cross section is usually omitted in tabulations due to

a) the lack of theoretical models comparable to those available for the description

of other photo-interaction processes, b) some incomplete experimental information

and, ﬁnally, c) its irregular dependence on A (i.e., the relative atomic mass or

atomic weight, Sect. 1.4.1) and Z (i.e., the atomic number, Sect. 3.1). The Comp-

ton eﬀect dominates at medium reduced-energies, E, and low-Z. At high E and

high-Z, the pair production mechanism is the dominant process of (primary) pho-

ton interaction in matter. At low-Z and low E, the photoelectric process b ecomes

the dominant process of photon interaction.

A web database (XCOM) is currently available in [Berger, Hubbell, Seltzer,

Chang, Coursey, Sukumar and Zucker (2005)]. The version available on the web

gives detailed and updated references to the literature from which numerical ap-

proximations were derived. While in previous sections, the emphasis was mainly put

on the discussion of principles, on which theoretical models are based; the XCOM

database provides photon cross sections for scattering, photoelectric absorption and

pair production, as well as total attenuation coeﬃcients, for any element, compound

or mixture (Z ≤ 100), at energies from 1 keV to 100 GeV. At lower energies bet-

ween 30 eV and 30 keV, mass attenuation coeﬃcients and indeces of refraction were

tabulated, based on both measurements and theoretical calculations, and are also

available on the web in [Henke, Gullikson and Davis (1993)].

As mentioned above, from the XCOM database we can obtain total cross sec-

tions, attenuation coeﬃcients and partial cross sections for the individual following

processes: incoherent Compton scattering, coherent Rayleigh scattering, photoelec-

tric absorption, pair production in the ﬁeld of nuclei and in the ﬁeld of atomic

electrons. The incoherent Compton scattering takes into account the incoherent

scattering function S(q, Z), the radiative corrections and the double Compton ef-

fect. The values for the coherent Rayleigh scattering were evaluated introducing

the atomic form factor F(q, Z). For compounds, the quantities tabulated are par-

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Electromagnetic Interaction of Radiation in Matter 185

Fig. 2.67 Mass attenuation coeﬃcients for dry air at sea level as a function of the incoming photon energy (data from [Berger, Hubbell, Seltzer,

Chang, Coursey, Sukumar and Zucker (2005)]). The air density and Z/A are 1.205×10

−3

and 0.499, respectively.

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186 Principles of Radiation Interaction in Matter and Detection

Fig. 2.68 Mass attenuation coeﬃcients for water as a function of the incoming photon energy (data from [Berger, Hubbell, Seltzer, Chang, Coursey,

Sukumar and Zucker (2005)]).

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Electromagnetic Interaction of Radiation in Matter 187

Fig. 2.69 Mass attenuation coeﬃcients for brain as a function of the incoming photon energy (data from [Berger, Hubbell, Seltzer, Chang, Coursey,

Sukumar and Zucker (2005)], composition of grey/white matter as from [ICRUM (1989)]). The brain density and Z/A are 1.04 g/cm

and 0.552,

respectively.

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188 Principles of Radiation Interaction in Matter and Detection

Fig. 2.70 Mass attenuation coeﬃcients for Al as a function of the incoming photon energy (data from [Berger, Hubbell, Seltzer, Chang, Coursey,

Sukumar and Zucker (2005)]).

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Electromagnetic Interaction of Radiation in Matter 189

Fig. 2.71 Mass attenuation coeﬃcients for Si as a function of the incoming photon energy (data from [Berger, Hubbell, Seltzer, Chang, Coursey,

Sukumar and Zucker (2005)]).