3/2003 Rev 1 II.1.1 – slide 1 of 30 IAEA Post Graduate Educational Course Radiation Protection and Safe Use of Radiation Sources Session II.1.1 Part IIQuantities and Measurements Module 1Quantities and Units Session 1Radiometric Quantities & Interaction Coefficients

3/2003 Rev 1 II.1.1 – slide 2 of 30 Introduction  Radiometric quantities and interaction coefficients will be discussed  Students will learn about radiation fields, fluence (rate), energy fluence (rate), fluence differential in energy, cross section, mass attenuation coefficient, and mass stopping power

3/2003 Rev 1 II.1.1 – slide 3 of 30 Content  Radiation field  Fluence (rate)  Energy fluence (rate)  Fluence differential in energy  Cross section and example curves  Linear attenuation coefficient  Mass attenuation coefficient  Mass stopping power

3/2003 Rev 1 II.1.1 – slide 4 of 30 Overview  Various radiometric quantities will be introduced and defined  Associated concepts such as interaction coefficients (for example attenuation coefficients and cross section) will be discussed

3/2003 Rev 1 II.1.1 – slide 5 of 30 Radiation Field

3/2003 Rev 1 II.1.1 – slide 6 of 30 Fluence Fluence, , is the number of particles incident on a sphere of cross-sectional area dA  = Unit: m -2 dNdA

3/2003 Rev 1 II.1.1 – slide 7 of 30 Fluence Rate Fluence rate, , is the number of particles incident on a sphere of cross-sectional area dA per unit time  = Unit: m -2 s -1 dddd dt dt

3/2003 Rev 1 II.1.1 – slide 8 of 30 Energy Fluence Energy Fluence, , is total energy carried by the “rays” striking a infinitesimal sphere of area dA  =  = whereR = EN, so  = E  Unit: J m -2 dRdA

3/2003 Rev 1 II.1.1 – slide 9 of 30 Energy Fluence Rate Energy Fluence rate is the total energy carried by particles striking an infinitesimal sphere of cross-sectional area dA per unit time Energy fluence rate = Energy fluence rate = Unit: J m -2 s -1 dddd dt dt

3/2003 Rev 1 II.1.1 – slide 10 of 30 Fluence Differential In Energy The fluence differential in energy  (E), or the distribution of fluence with respect to energy:  (E) = where d  is the fluence of particles with energy between E and E + dE dddd dt dt

3/2003 Rev 1 II.1.1 – slide 11 of 30 Cross Section where  = cross section R = number of reactions per unit time per nucleus I = number of incident particles per unit time per unit area  = RI

3/2003 Rev 1 II.1.1 – slide 12 of 30 Cross Sections for Neutron Capture in Uranium

3/2003 Rev 1 II.1.1 – slide 13 of 30 Fusion Reaction Cross Sections

3/2003 Rev 1 II.1.1 – slide 14 of 30 Cross Sections for Photon Capture by Deuterons

3/2003 Rev 1 II.1.1 – slide 15 of 30 There are two types of attenuation coefficients:  Linear Attenuation Coefficient (LAC) provides a measure of the fractional attenuation per unit length of material traversed  Mass Attenuation Coefficient (MAC) provides a measure of the fractional attenuation per unit mass of material encountered Attenuation Coefficients

3/2003 Rev 1 II.1.1 – slide 16 of 30  and HVL are functions of the energy of the photon radiation and the material through which it passes I = I o e (-  x) when x = HVL, then I = (½)I o (½)I o = I o e (-  HVL) ½ = e (-  HVL) ln(½) = ln(e (-  HVL) ) ln(½) = (-  HVL) ln(2) = (  HVL) ln(2)HVL Linear Attenuation Coefficient LAC =  M,E = ln 2 HVL M,E = 

3/2003 Rev 1 II.1.1 – slide 17 of 30 LAC = MAC x density Mass Attenuation Coefficient 1 = cm 2 x g 1 = cm 2 x g cm g cm 3 The relationship between LAC and MAC is:   = x 

3/2003 Rev 1 II.1.1 – slide 18 of 30  The amount of energy deposited will be the sum of energy deposited from hard and soft collisions  The “stopping power,” S, is the sum of energy deposited for soft and hard collisions  Most of the energy deposited will be from soft collisions since it is less likely that a particle will interact with the nucleus Stopping Power

3/2003 Rev 1 II.1.1 – slide 19 of 30  The stopping power is a function of the charge of the particle, the energy of the particle, and the material in which the charged particle interacts Stopping Power

3/2003 Rev 1 II.1.1 – slide 20 of 30  Stopping power has units of MeV/cm – the amount of energy deposited per centimeter of material as a charged particle traverses the material  It is the sum of energy deposited for both hard and soft collisions. S = = + S = = + Stopping Power dEdx Tot dE s dx dE h dx

3/2003 Rev 1 II.1.1 – slide 21 of 30 Mass Stopping Power  Often the stopping power is divided by the density of the material,   This is called the “mass stopping power”  The dimensions for mass stopping power are MeV – cm 2 g

3/2003 Rev 1 II.1.1 – slide 22 of 30 Mass Stopping Power m 0 c 2 is the rest mass of the charged particle in MeV 3727 MeV for an alpha particle and MeV for an electron or beta particle MeV for an electron or beta particle S  = (0.3071) Zz 2 A2A2A2A ln -  2 – ln I 2222 (1-  ) 2 moc2moc2moc2moc2 E ½  = = = =

3/2003 Rev 1 II.1.1 – slide 23 of 30 Stopping Power  Z = atomic number  z = charge of the particle (  = 2,  = 1)  m 0 = rest mass of the particulate radiation  c = speed of light (3 x cm/s)  I = the mean excitation potential of an atom of the absorbing material (2.16 x ) (Z)

3/2003 Rev 1 II.1.1 – slide 24 of 30 Stopping Power Stopping power is used to determine dose from charged particles by the relationship: D =  in units of MeV/g, where  =the particle fluence, the number of particles striking an object over a specified time interval dE  dx

3/2003 Rev 1 II.1.1 – slide 25 of 30 Stopping Power Converting this to units of dose results in the relationship: D =  (1.6 x ) Gy dE  dx

3/2003 Rev 1 II.1.1 – slide 26 of 30 Summary  Radiometric quantities and interaction coefficients were discussed  Students learned about a radiation field, fluence (rate), energy fluence (rate), fluence differential in energy, cross section, mass attenuation coefficient, and mass stopping power

3/2003 Rev 1 II.1.1 – slide 27 of 30 Where to Get More Information  Cember, H., Introduction to Health Physics, 3 rd Edition, McGraw-Hill, New York (2000)  Firestone, R.B., Baglin, C.M., Frank-Chu, S.Y., Eds., Table of Isotopes (8 th Edition, 1999 update), Wiley, New York (1999)  International Atomic Energy Agency, The Safe Use of Radiation Sources, Training Course Series No. 6, IAEA, Vienna (1995)

3/2003 Rev 1 II.1.1 – slide 28 of 30  Knoll, G.T., Radiation Detection and Measurement, 3 rd Edition, Wiley, New York (2000)  Attix, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986)  International Atomic Energy Agency, Determination of Absorbed Dose in Photon and Electron Beams, 2 nd Edition, Technical Reports Series No. 277, IAEA, Vienna (1997) Where to Get More Information

3/2003 Rev 1 II.1.1 – slide 29 of 30  International Commission on Radiation Units and Measurements, Quantities and Units in Radiation Protection Dosimetry, Report No. 51, ICRU, Bethesda (1993)  International Commission on Radiation Units and Measurements, Fundamental Quantities and Units for Ionizing Radiation, Report No. 60, ICRU, Bethesda (1998)  Hine, G. J. and Brownell, G. L., (Ed. ), Radiation Dosimetry, Academic Press (New York, 1956) Where to Get More Information

3/2003 Rev 1 II.1.1 – slide 30 of 30  Bevelacqua, Joseph J., Contemporary Health Physics, John Wiley & Sons, Inc. (New York, 1995)  International Commission on Radiological Protection, Data for Protection Against Ionizing Radiation from External Sources: Supplement to ICRP Publication 15. A Report of ICRP Committee 3, ICRP Publication 21, Pergamon Press (Oxford, 1973) Where to Get More Information