Outline Quantities for Describing the Interaction of Ionizing • Kerma, components of kerma Radiation with Matter • Absorbed dose • Exposure Chapter 2 • Quantities for use in radiation protection F.A. Attix, Introduction to Radiological • Summary Physics and Radiation Dosimetry

Introduction Definitions

• Need to describe interactions of ionizing • Most of the definitions are by ICRU radiation with matter • Energy transferred by indirectly ionizing • Special interest is in the energy absorbed in radiation leads to the definition of kerma matter, absorbed dose – delivered by • Energy imparted by ionizing radiation leads directly ionizing radiation to the definition of absorbed dose • Two-step process for indirectly ionizing • Energy carried by neutrinos is ignored radiation involves kerma and absorbed dose – Very small mass, no electric charge => negligibly small cross section for interactions with matter

Energy transferred Energy transferred

•- tr energy transferred in a volume V to • The energy transferred in a volume V charged particles by indirectly ionizing nonr   R   R   Q radiation (photons and neutrons) tr in u out u  • Radiant energy R – the energy of particles uncharged nonr emitted, transferred, or received, excluding •Rout u does not include radiative losses of rest mass energy kinetic energy by charged particles • Q - energy delivered from rest mass in V (bremsstrahlung or in-flight annihilation) (positive if m  E, negative for E  m) • Energy transferred is only the kinetic energy received by charged particles Kerma Relation of Kerma to Energy •Kerma K is the energy transferred to charged fluence for photons particles per unit mass • For mono-energetic photon of energy E and medium of atomic number Z, relation is d tr d K  e  tr through the mass energy-transfer coefficient: dm dm   • Includes radiative losses by charged particles tr K     (bremsstrahlung or in-flight annihilation of   E,Z positron) • For a spectrum of energy fluence E • Excludes energy passed from one charged EE max    particle to another K  E  tr  dE     • Units: 1 Gy = 1 J/kg = 102 rad = 104 erg/g E0  E,Z

Relation of Kerma to Fluence Energy-transfer coefficient for neutrons • Neutron field is usually described in terms • Linear energy-transfer coefficient  , tr of fluence rather than energy fluence units of m-1 or cm-1  tr  • Kerma factor is tabulated instead of kerma • Mass energy-transfer coefficient   ,    (units are rad cm2/neutron, Appendix F) units of m2/kg or cm2/g E,Z    • Set of numerical values, tabulated for a F   tr   E n E,Z    range of photon energies, Appendix D.3  E,Z • For mono-energetic neutrons

K   Fn E,Z

Components of Kerma Collision Kerma • Energy received by charged particles may be spent • Subtracting radiant energy emitted by in two ways charged particles R r from energy transferred – Collision interactions – local dissipation of energy, u ionization and excitation along electron track results in net energy transferred locally – Radiative interactions, such as bremsstrahlung or  net    Rr  positron annihilation, carry energy away from the track tr tr u nonr r • Kerma may be subdivided in two components, Rin u  Rout u  Ru  Q collision and radiative: • Now collision kerma can be defined K  Kc  Kr d net K  tr • When kerma is due to neutrons, resulting charged c dm particles are much heavier, K=Kc Mass energy-absorption Mass energy-absorption coefficient coefficient • Since collision kerma represents energy • For low Z materials and low energy deposited (absorbed) locally, introduce radiative losses are small, therefore values mass energy-absorption coefficient. For of  and  are close mono-energetic photon beam tr en

 en  Kc       E,Z

• Depends on materials present along particle track before reaching point P

Kerma rate Absorbed dose • Energy imparted by ionizing radiation to • Kerma rate at point P and time t matter of mass m in volume V

dK d  d tr  K       Rin u  Rout u  Rin c  Rout c  Q dt dt  dm  due to uncharged due to charged • Units of J/(kg s), erg/(g s), or rad/s • Absorbed dose is defined as • Knowing kerma rate, kerma d D  t1 dm Kt ,t  K t dt 0 1  2 4 t0 • Units: 1 Gy = 1 J/kg = 10 rad = 10 erg/g

Example 1 R hv Absorbed dose in u  1 nonr 2 Rout u  Rout u  hv2 1

• D represents the energy per unit mass which Rin c  0, Q  0

remains in the matter at P to produce any Rout c  hv3 T r effects attributable to radiation Ru  hv3 • The most important quantity in radiological 12 Energy imparted physics   Rin u  Rout u  Rin c  Rout c  Q

• Absorbed dose rate: nonr Energy transferred  tr  Rin u  Rout u  Q dD d  d  D     Net energy net nonr r dt dt  dm   tr  Rin u  Rout u  Ru  Q transferred Example 1 Example 2

Rin u  hv1 nonr 2 Rout u  Rout u  hv2 1 Positron has no excess

Rin c  0, Q  0 3 kinetic energy to transfer R  hv T 12 to photons after out c 3 annihilation r Ru  hv3 12 12 3

  hv  hv  hv T  0 r 1 2 3 Rin u  Rin c  Rout c  Ru  0 R  R nonr  2hv 1.022MeV  tr  hv1  hv2  0  T out u out u 2 2 net Q  hv1  2m0c  2m0c  hv1 pair annihilation  tr  hv1  hv2  hv3  0 production net  T  hv3    tr   tr  hv1 1.022 MeV  T1 T2

Example 3 Exposure • Positron transfers excess • Historically, was introduced before kerma and kinetic energy T3 to photons after annihilation. dose, measured in roentgen (R) T3 3 • It generates radiative loss • Defined as a quotient 12 from charged-particle dQ kinetic energy X  n • Affects  and  tr by dm 12 3 subtraction of T3 • dQ is absolute value of the total charge of the ions R  R  R  0 in u in c out c of one sign produced in air when all electrons Rout u  2hv T3 1.022MeV T3 liberated by photons in air of mass dm are nonr completely stopped in air Rout u  2hv 1.022MeV Rr  T • Ionization from the absorption of radiative loss of u 3 kinetic energy by electrons is not included 2 2 Q  hv1  2m0c  2m0c  hv1

Exposure Relation of exposure to energy fluence • Exposure is the ionization equivalent of the collision kerma in air for x and -rays • Exposure at a point due to energy fluence of mono-energetic photons • Introduce mean energy expended in a gas per    e ion pair formed, W , constant for each gas, en   X       independent of incoming photon energy   E,airW air • For dry air  e  Kc air   Kc air /33.97 W 33.97 eV/i.p. W air air  1.602 1019 J/eV e 1.602 1019C/electron • Units of [X]=C/kg in SI  33.97 J/C Units of exposure Exposure rate • The roentgen R is the customary unit • Exposure rate at a point P and time t: • The roentgen is defined as exposure dX producing in air one unit of esu of charge X  per 0.001293 g of air irradiated by the dt photons. Conversion • Units are C/(kg-sec) or R/sec 1esu 1C 103 g • Exposure t 1R   9  1 0.001293g 2.99810 esu 1kg X  X (t)dt 4   2.58010 C/kg t0 1C/kg  3876 R

Significance of exposure Significance of exposure

• Energy fluence is proportional to exposure for any given photon energy or spectrum • Due to similarity in effective atomic number – Air can be made a tissue equivalent medium with respect to energy absorption – convenient in measurements – Collision kerma in muscle per unit of exposure is nearly independent of photon energy Ratio of mass energy-absorption coefficients for muscle/air and water/air are nearly constant (within <5%) for energies from 4keV to 10 MeV

Significance of exposure Significance of exposure

• X-ray field at a point can be characterized by means of exposure regardless of whether there is air actually located at this point • It implies that photon energy fluence at that point is such that it would produce exposure of a stated value • Same is applicable to kerma or collision kerma, except that reference medium (not Ratio of mass energy-absorption coefficients for bone/air and necessarily air) has to be specified acrylic/air are nearly constant for energies above 100keV Radiation protection quantities Radiation protection quantities

• Quality factor Q – weighting factor to be applied to absorbed dose to provide an estimate of the relative human hazard of ionizing radiation • It is based on relative biological effectiveness (RBE) of a particular radiation source • Q is dimensionless • Higher-density charged particle tracks (higher collision stopping power) are more damaging per unit dose

Radiation protection quantities Summary • Quantities describing the interaction of • Dose equivalent H, is defined as ionizing radiation with matter – Kerma, components of kerma H  DQN – Absorbed dose • Here D – dose, Q- quality factor, N-product – Exposure of modifying factors (currently=1) • Relationship with fluence and energy fluence • Units of H: • Quantities for use in radiation protection – severs, Sv, if dose is expressed in J/kg – Quality factor Q – rem, if dose is in rad (10-2 J/kg) – Dose equivalent H