The *mass energy-transfer coefficient,* *μ*_{tr}/*ρ*, when multiplied by the photon energy fluence *ψ* (*ψ* = Φ*E*, where
Φ is the photon fluence and *E* the
photon energy), gives the dosimetric quantity *kerma.* As discussed in
depth by Carlsson (1985), kerma has been defined
(ICRU Report 33, 1980) as (and is an acronym
for) the sum of the *k*inetic *e*nergies of all those primary charged
particles *r*eleased by uncharged particles (here photons) per unit
*ma*ss. Thus *μ*_{tr}/*ρ*
takes into account the escape only of secondary photon radiations produced at
the initial photon-atom interaction site, plus, by convention, the quanta of
radiation from the annihilation of positrons (assumed to have come to rest)
originating in the initial pair- and triplet-production interactions.

Hence *μ*_{tr}/*ρ* is defined as

(eq 7) |

In (eq 7), coherent scattering has been omitted because of the negligible
energy transfer associated with it, and the factors *f* represent the
average fractions of the photon energy *E* that is transferred to kinetic
energy of charged particles in the remaining types of interactions. These
energy-transfer fractions are given by

(eq 8) |

where *X* is the average energy of fluorescence radiation
(characteristic x rays) emitted per absorbed photon;

(eq 9) |

where is the average energy of the Compton-scattered photon;

(eq 10) |

where *mc*^{2} is the rest energy of the electron; and

(eq 11) |

The fluorescence energy *X* in (eq 8),
(eq 9), and ( 11) depends on the distribution of
atomic-electron vacancies produced in the process under consideration and is in
general evaluated differently for photoelectric absorption, incoherent
scattering, and triplet production. Moreover, *X* is assumed to include
the emission of "cascade" fluorescence x rays associated with
the complete atomic relaxation process initiated by the primary vacancy, the
significance of which has been pointed out by
Carlsson (1971).

As only the characteristics of the target atom are involved in calculating
*μ*_{tr}/*ρ*, the mass
energy-transfer coefficient for homogeneous mixtures and compounds can be
obtained in a manner analogous to that for *μ*/*ρ*:

(eq 12) |

The *mass energy-absorption coefficient* involves the further emission of
radiation produced by the charged particles in traveling through the medium,
and is defined as

(eq 13) |

The factor *g* in (eq. 13) represents the average fraction of the
kinetic energy of secondary charged particles (produced in all the types of
interactions) that is subsequently lost in radiative (photon-emitting)
energy-loss processes as the particles slow to rest in the medium. The
evaluation of *g* is accomplished by integrating the cross section for the
radiative process of interest over the differential tracklength distribution
established by the particles in the course of slowing down. In the
continuous-slowing-down approximation, the tracklength distribution is replaced
by the reciprocal of the electron or positron total stopping power of the
medium. Even assuming Bragg additivity for the stopping power (that now appears
in the denominator of the integral), simple additivity for *μ*_{en}/*ρ* or - as suggested by
Attix (1984) - for *g* is formally incorrect.
When the numerical values of *g* are relatively small, the errors in
*μ*_{en}/*ρ* incurred by using
simple additivity schemes are usually small, a consequence partially mitigating
the use additivity, particularly for photon energies below 20 MeV. However,
additivity has not been used in the present work.

For the values of *μ*_{en}/*ρ*
given in Table 3 and
Table 4, the evaluation of *g* takes into
explicit account (a) the emission of bremsstrahlung, (b) positron
annihilation in flight, (c) fluorescence emission as a result of
electron- and positron-impact ionization, and (d) the effects on these
processes of energy-loss straggling and knock-on electron production as the
secondary particles slow down (i.e., of going beyond the
continuous-slowing-down approximation). This scheme thus goes beyond that of
ICRU Report 33 (1980) which, perhaps by
oversight, formally includes only (a) above, and of previous work, which
usually includes (a) and (b).

For the calculation of *g*, the radiative (bremsstrahlung) stopping powers
used are based on the results by Seltzer and Berger
(1985, 1986) and Kim *et al.* (1986), and are
very slightly different from the values used in ICRU
Report 37 (1984). The collision stopping powers, evaluated according
to the prescriptions in ICRU Report 37 (1984),
include departures from simple Bragg additivity due to chemical-binding, phase,
and density effects, as reflected in the choice of the mean excitation energy
*I* and density *ρ* for the
medium. These departures from Bragg additivity for the stopping power of the
matrix can result in discernable differences in the mass energy-absorption
coefficient, such as between those for water vapor and liquid.

Further details of the calculations are given in
Seltzer (1993) and will not be repeated
here. Instead, a summary of expressions used for the calculation of *g*
is given below. The formulas include the integration over the initial particle
spectra, and have been generalized to include mixtures and compounds.

* Photoelectric Absorption.* The radiative losses for the
photoelectrons have been evaluated according to

(eq 14) |

where *μ*_{pe}/*ρ* is the total
photoeffect mass attenuation coefficient for an incident photon of energy
*E* in the medium, *μ*_{pe}/*ρ*)_{n,i}^{th} atomic electron subshell of the i^{th} elemental
constituent, *B*_{n,i} is the binding energy of that subshell, and

(eq 15) |

is the total radiative yield. The total radiative yield has been evaluated as
the sum of two components. The *bremsstrahlung yield,*
*Y*_{b}(*T*), is the mean fraction of the initial kinetic
energy *T* of an electron (or positron) that is converted to
bremsstrahlung energy as the particle slows down to rest; and the *x-ray
energy yield,* *Y*_{x}(*T*), usually very much smaller
than *Y*_{b}(*T*), is the mean fraction of the initial
kinetic energy converted to fluorescence emission due to ionization by the
electron (or positron) in the course of slowing down. The very small radiative
losses for the associated Auger electrons have been neglected.

* Incoherent (Compton) Scattering.* For incoherent scattering

(eq 16) |

where *S(q,Z*_{i}) is the incoherent scattering factor, taken from
the compilation of Hubbell *et al.* (1975),
d*σ*_{KN}/d*E*′
is the Klein-Nishina cross section differential in the Compton-scattered photon
energy *E*′,
*E*_{min} = *E*/(1 + 2*E*/*mc*^{2}) is the minimum
energy of the scattered photon (corresponding to 180° scattering), and
*Y*(*T*) is the total radiative yield.

*Pair and Triplet production.* The radiative losses from electrons and
positrons created in the pair and triplet processes, including the effects of
positron annihilation in flight, have been evaluated according to:

(eq 17) |

where *P*_{pair,i}(*T*_{+})d*T*_{+} is
the probability that the positron from a pair-production interaction with the
i^{th} constituent atom will have a kinetic energy between
*T*_{+} and T_{+} + d*T*_{+},
*Y*_{-}(*T*_{-}) and
*Y*_{+}(*T*_{+}) are the total radiation yields for
the electrons and positrons, respectively, and *η*(T_{+}) is the correction for positron annihilation in flight.
Pair spectra have been evaluated using Bethe-Heitler theory in conjunction with
screening and Coulomb corrections. The annihilation-in-flight correction has
been derived on the basis outlined in Berger (1961),
and has been evaluated using the two-quanta annihilation-in-flight cross
section of Bethe (1935) plus estimates for the
one-quantum annihilation-in-flight cross section.

Computation of *g*_{trip} proceeds similarly, but using the
threshold for triplet production of 4 *mc*^{2} instead of
2 *mc*^{2} in (eq 17), and using the
Wheeler-Lamb (1939) expressions for the screening
corrections to the triplet spectra.

Abstract **|**
Introduction **|**
Mass Atten. Coef. **|**
**Mass Energy-Absorp. Coef. |**
Summary **|**
References