Radiometric Quantities & Interaction Coefficients Quantities and Measurements -1 Radiometric Quantities & Interaction Coefficients Day 2 – Lecture 7

Objective To discuss about various radiometric quantities and associated concepts such as interaction coefficients (for example attenuation coefficients and cross section)

Content Radiation field Fluence (rate) Energy fluence (rate) Cross section and example curves Linear attenuation coefficient Mass attenuation coefficient Mass stopping power

Radiation Field A complete description of a radiation field requires the fluence (defined in the next slide) distribution as a function of: 1. particle type e.g. electrons, photons, neutrons (including any relevant quantum state e.g. spin) 2. spatial position, 3. direction, 4. energy and 5. time.

Fluence Fluence, , is the number of particles incident on a sphere of cross-sectional area dA  = Unit: m-2 dN dA Particles could be photons or actual particles such as protons, neutrons, etc.

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 dt

Energy Fluence Energy Fluence, , is total energy carried by the “rays” striking a infinitesimal sphere of area dA  = where R = EN, so  = E Unit: J m-2 dR dA Rays could be photons or particles such as neutrons, etc. N is the number of incident rays, each of energy E. If the incident beam is not monoenergetic, E could be the average energy of the beam.

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 = Unit: J m-2 s-1 d dt

Cross Section R  = where  = cross section  = R I where  = cross section R = number of reactions per unit time per nucleus I = number of incident particles per unit time per unit area To characterize the probability that a certain nuclear reaction will take place, it is customary to define an effective size of the nucleus for that reaction, called a cross section. The cross section has the units of area and is on the order of the square of the nuclear radius. A commonly used unit is the barn, which is equal to 10-24 cm2. A standard old story was that in the early days of the field, a particular cross section turned out to be much bigger than expected. An experimenter exclaimed "Why, that's as big as a barn!" and a unit name was born.

Cross Sections for Neutron Capture in Uranium The next few slide shows some examples of cross sections and how they are dependent on incident particle energy, as well as the isotope which captures the particle. There are many, many different reactions for which cross sections have been measured and these slides show only a selected few. This slide shows an example of how cross sections vary with incident particle energy. The graphs shows neutron cross sections as a function of neutron energy for the isotopes U-235 and U-238. The cross section is expressed in units of barns and the neutron energy is in eV. Note how the cross section peaks at certain specific neutron energies.

Attenuation Coefficients 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

Mass Attenuation Coefficient The relationship between LAC and MAC is: LAC = MAC x density 1 = cm2 x g cm g cm3  is the linear attenuation coefficient, dimension of 1/cm (or cm-1). In most tables you will find the mass attenuation coefficient which is  / and has dimensions of (1/cm)/(g/cm3) which dimensionally equals cm2/g

Stopping Power 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 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

Summary Radiometric quantities and interaction coefficients were discussed participants learned about a radiation field, fluence (rate), energy fluence (rate), fluence differential in energy, cross section, mass attenuation coefficient, and mass stopping power

Where to Get More Information Cember, H., Johnson, T. E, Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2009) International Atomic Energy Agency, Postgraduate Educational Course in Radiation Protection and the Safety of Radiation Sources (PGEC), Training Course Series 18, IAEA, Vienna (2002)