## Abstract

We live in a world that abounds in radiation of all types. Many radiations, such as the neutrinos or visible light from our sun present little risk to us. Other radiations, such as medical x-rays or gamma rays emitted by radioactive materials, have the potential to cause us harm. In this entry, only the transport of *indirectly ionizing radiation* is considered. These radiations consist of chargeless particles such as neutrons or photons that, upon interacting with matter, produce energetic secondary charged particles called *directly ionizing radiation*. It is these secondary charged particles that, through ionization and excitation of ambient atoms along their paths, cause radiation damage to biological tissues or other sensitive materials.

## Keywords

Fission Neutron Monte Carlo Code Buildup Factor Point Kernel Secondary Photon## Glossary

- Albedo
A quantity describing how neutrons or photons incident on the surface of some medium (e.g., a wall) are reflected or reemitted from the surface.

- Buildup factor
A factor to account for production of secondary photons in a shield. The transmitted dose from only uncollided photons times the buildup factor equals the dose from all photons, uncollided plus secondary photons.

- Dose
A general term for the energy transferred from radiation to matter. Specifically, the absorbed dose is the amount of energy imparted to matter from ionizing radiation in a unit mass of that matter. Units are the gray (Gy) and rad, respectively, equivalent to 1 J/kg and 100 ergs/g.

- Flux
A measure of the intensity of a radiation field. Specifically, it equals the number of radiation particles entering, in a unit time, a sphere of cross-sectional area \( \Delta A \) divided by \( \Delta A \), as \( \Delta A \to 0 \). The flux, integrated over a specified time interval is called the

*fluence*.- Interaction coefficient
A quantity, denoted by \( \mu \), describing how readily a photon or neutron interacts with a given medium. Specifically, it is the probability a radiation particle of energy

*E*will interact in a specified manner per unit distance of travel, for infinitesimal distances. It thus has units of inverse length. The total interaction coefficient \( \mu = \sum\nolimits_i {\mu_i} \) where \( {\mu_i} \) is the coefficient for the*i*th type of interaction (e.g., scattering, absorption).- Neutron
A neutral subatomic particle that collectively with positively charged protons forms an atomic nucleus. Although both are composite particles composed of quarks and gluons, for the energies considered in this entry they can be viewed as fundamental unchangeable particles.

- Photon
A quantum of electromagnetic radiation with energy \( E = h\nu \), where

*h*is Planck’s constant and \( \nu \) is the frequency. Photons produced by a change in the structure of the nucleus are called*gamma photons*and those produced by atomic electron rearrangement are called*x-rays*.- Skyshine
A term for the radiation that reaches some point of interest after being scattered by the atoms in the atmosphere back to the point of interest.

- Transport equation
Also known as the linearized Boltzmann equation, it describes rigorously the spatial, energy, and angular distribution of neutrons or photons in any medium with arbitrary source distributions. From its solution, the radiation flux or dose anywhere in the medium can be determined.

## Bibliography

## Primary Literature

- 1.Shultis JK, Faw RE (2005) Radiation shielding technology. Health Phys 88:297–322CrossRefGoogle Scholar
- 2.Mutscheller A (1925) Physical standards of protection against Roentgen-ray dangers. Am J Roentgenol Radiat Ther 13:65–70Google Scholar
- 3.National Council on Radiation Protection and Measurements (1941) Safe handling of radioactive luminous compounds. NBS handbook 27. NCRP report 5. US Government Printing Office, Washington, DCGoogle Scholar
- 4.Blizard EP, Abbott LS (eds) (1962) Reactor handbook, vol III, Part B, Shielding. Wiley, New YorkGoogle Scholar
- 5.Jaeger RH (ed) (1968) Engineering compendium on radiation shielding, vol 1, Shielding fundamentals and methods. Springer, New YorkGoogle Scholar
- 6.Haffner JW (1967) Radiation and shielding in space. Academic, New YorkGoogle Scholar
- 7.Shure K (1964) P-3 multigroup calculations of neutron attenuation. Nucl Sci Eng 19:310Google Scholar
- 8.National Council on Radiation Protection and Measurements (1971) Protection against neutron radiation. NCRP report 38. National Council on Radiation Protection and Measurements, Washington, DCGoogle Scholar
- 9.National Council on Radiation Protection and Measurements (1976) Structural shielding design and evaluation for medical use of x-rays and gamma rays of energies up to 10 MeV. NCRP report 49. National Council on Radiation Protection and Measurements, Washington, DCGoogle Scholar
- 10.Kocher DC (1981) Radioactive decay tables. Technical Information Center, U.S. Department of Energy; DOE/TIC 11026, Washington, DCGoogle Scholar
- 11.Weber DA, Eckerman KE, Dillman LT, Ryman JC (1989) MIRD: radionuclide data and decay schemes. Society of Nuclear Medicine, Medical Internal Radiation Dose Committee, New YorkGoogle Scholar
- 12.ANS (American Nuclear Society) (1991) American national standard gamma-ray attenuation coefficients and buildup factors for engineering materials. ANSI/ANS-6.4.3-1991. American Nuclear Society, La Grange ParkGoogle Scholar
- 13.Caswell RS, Coyne JJ, Randolph ML (1980) Kerma factors for neutron energies below 30 MeV. Radiat Res 83:217–254CrossRefGoogle Scholar
- 14.International Commission on Radiological Protection (1987) Data for use in protection against external radiation. Publication 51. Annals of the ICRP 17(2/3). Pergamon, OxfordGoogle Scholar
- 15.International Commission on Radiological Protection (1996) Conversion coefficients for use in radiological protection against external radiation. Publication 74. Annals of the ICRP 26(3/4). Pergamon, OxfordGoogle Scholar
- 16.Adams ML, Larsen EW (2002) Fast iterative methods for discrete-ordinates particle transport calculations. Prog Nucl Energy 40(1):3–159CrossRefGoogle Scholar
- 17.Shultis JK, Faw RE (2000) Radiation shielding. American Nuclear Society, La Grange ParkGoogle Scholar
- 18.Rockwell T III (ed) (1956) Reactor shielding design manual. Van Nostrand, PrincetonGoogle Scholar
- 19.Schaeffer NM (1973) Historical background. In: Schaeffer NM (ed) Reactor shielding. TID-25951. US Atomic Energy Commission, Washington, DCGoogle Scholar
- 20.Hirayama H (1987) Exposure buildup factors of high-energy gamma rays for water, concrete, iron, and lead. Nucl Technol 77:60–67Google Scholar
- 21.Faw RE, Shultis JK (1993) Absorbed dose buildup factors in air for 10–100 MeV photons. Nucl Sci Eng 114:76–80Google Scholar
- 22.Fano U, Spencer LV, Berger MJ (1959) Penetration and diffusion of x rays. In: Encyclopedia of physics, vol 38, Part 2. Springer, BerlinGoogle Scholar
- 23.Goldstein H (1959) Fundamental aspects of reactor shielding. Addison-Wesley, ReadingGoogle Scholar
- 24.Spencer LV (1962) Structure shielding against fallout radiation from nuclear weapons. Monograph 42. National Bureau of Standards, Washington, DCGoogle Scholar
- 25.Takeuchi K, Tanaka S, Kinno M (1981) Transport calculation of gamma rays including bremsstrahlung by the discrete ordinates code PALLAS. Nucl Sci Eng 78:273–283Google Scholar
- 26.Takeuchi K, Tanaka S (1984) Buildup factors of gamma rays, including bremsstrahlung and annihilation radiation for water, concrete, iron, and lead. Nucl Sci Eng 87:478–489Google Scholar
- 27.Negin CA, Worku G (1998) Microshield v.5 user’s manual. Grove Software, LynchburgGoogle Scholar
- 28.Malenfant RE (1967) QAD: a series of point kernel general-purpose shielding programs. LA-3573. Los Alamos National Laboratory, Los AlamosGoogle Scholar
- 29.Price JH et al (1979) Utilization instructions for QADMOD-G. RRA-N7914. Radiation Research Association, Fort Worth. Available from RSICC as CCC565/QADMOD-GPGoogle Scholar
- 30.Litwin KA et al (1994) Improvements to the point kernel code QAD-CGGP: a code validation and user’s manual. RC-1214 COG-94-65. AECL Research, Canada. Available from RSICC as CCC-645/QAD-CGGP-AGoogle Scholar
- 31.Malenfant RE (1990) \( {G^3} \): a general purpose gamma-ray scattering code. LA-5176. Los Alamos National Laboratory, Los Alamos. Available from RSICC as CCC-564/G33-GPGoogle Scholar
- 32.Archer BR (1995) History of the shielding of diagnostic x-ray facilities. Health Phys 69:750–758CrossRefGoogle Scholar
- 33.Simpkin DJ (1989) Shielding requirements for constant-potential diagnostic x-ray beams determined by a Monte Carlo calculation. Health Phys 56:151–154CrossRefGoogle Scholar
- 34.Archer BR, Conway BJ, Quinn PW (1994) Attenuation properties of diagnostic x-ray shielding materials. Med Phys 21:1499–1507CrossRefGoogle Scholar
- 35.Simpkin DJ (1995) Transmission data for shielding diagnostic x-ray facilities. Health Phys 68:704–709CrossRefGoogle Scholar
- 36.Chilton AB (1971) Effect of material composition on neutron penetration of concrete slabs. Report 10425. National Bureau of Standards, Washington, DCGoogle Scholar
- 37.Roussin RW, Schmidt FAR (1971) Adjoint Sn calculations of coupled neutron and gamma-ray transport through concrete slabs. Nucl Eng Des 15:319–343CrossRefGoogle Scholar
- 38.Roussin RW, Alsmiller RG Jr, Barish J (1973) Calculations of the transport of neutrons and secondary gamma rays through concrete for incident neutrons in the energy range 15 to 75 MeV. Nucl Eng Des 24:250–257CrossRefGoogle Scholar
- 39.Wyckoff JM, Chilton AB (1973) Dose due to practical neutron energy distributions incident on concrete shielding slabs. Proceedings of 3rd international congress IRPA, American Nuclear Society, La Grange ParkGoogle Scholar
- 40.Wang X, Faw RE (1995) Transmission of neutrons and secondary gamma rays through concrete slabs. Radiat Prot Dosim 60:212–222Google Scholar
- 41.Chilton AB, Huddleston CM (1963) A semi-empirical formula for differential dose albedo for gamma rays on concrete. Nucl Sci Eng 17:419–424Google Scholar
- 42.Chilton AB, Davisson CM, Beach LA (1965) Parameters for C-H albedo formula for gamma rays reflected from water, concrete, iron, and lead. Trans Am Nucl Soc 8:656Google Scholar
- 43.Chilton AB (1967) A modified formula for differential exposure albedo for gamma rays reflected from concrete. Nucl Sci Eng 27:481–482Google Scholar
- 44.Brockhoff RC (2003) Calculation of albedos for neutrons and photons. Ph.D. dissertation, Department of Mechanical and Nuclear Engineering, Kansas State University, ManhattanGoogle Scholar
- 45.Selph WE (1973) Albedos, ducts, and voids. In: Schaeffer NM (ed) Reactor shielding. TID-25951. US Atomic Energy Commission, Washington, DCGoogle Scholar
- 46.Simmons GL, Albert TE, Gritzner DM (1979) The SAI/EPRI information library. Report SAI-013-79-525-LJ. Science Applications Inc, La JollaGoogle Scholar
- 47.Cain VR, Emmett MV (1979) BREESE-II: auxiliary routines for implementing the albedo option in the MORSE Monte Carlo code. ORNL/TM-6807. Oak Ridge National Laboratory, Oak RidgeGoogle Scholar
- 48.Maerker RE, Muckenthaler FJ (1966) Measurements and single-velocity calculations of differential angular thermal-neutron albedos for concrete. Nucl Sci Eng 26:339Google Scholar
- 49.Coleman WA, Maerker RE, Muckenthaler FJ, Stevens PJ (1967) Calculation of doubly differential current albedos for epicadmium neutrons incident on concrete and comparison of the subcadmium component with experiment. Nucl Sci Eng 27:411–422Google Scholar
- 50.Chandrasekhar S (1960) Radiative transfer. Dover, New YorkGoogle Scholar
- 51.Wells MB (1964) Reflection of thermal neutrons and neutron capture gamma rays from concrete. USAEC report RRA-M44. Radiation Research Associates, Fort WorthGoogle Scholar
- 52.Gomes IC, Stevens PN (1991) MORSE/STORM: a generalized albedo option for Monte Carlo calculations. ORNL/FEDC-91/1, TN. Oak Ridge National Laboratory, Oak RidgeGoogle Scholar
- 53.LeDoux JC, Chilton AB (1959) Gamma ray streaming through two-legged rectangular ducts. Nucl Sci Eng 11:362–368Google Scholar
- 54.National Council on Radiation Protection and Measurements (2003) Radiation protection for particle accelerator facilities. NCRP report 144. National Council on Radiation Protection and Measurements, Washington, DCGoogle Scholar
- 55.Lampley CM, Andrews MC, Wells MB (1988) The SKYSHINE-III procedure: calculation of the effects of structure design on neutron, primary gamma-ray, and secondary gamma-ray dose rates in air. RRA-T8209A. Radiation Research Associates, Fort WorthGoogle Scholar
- 56.Lampley CM (1979) The SKYSHINE-II procedure: calculation of the effects of structure design on neutron, primary gamma-ray, and secondary gamma-ray dose rates in air. RRA-T7901. Radiation Research Associates, Fort WorthGoogle Scholar
- 57.Brockhoff RC, Shultis JK, Faw RE (1996) Skyshine line-beam response functions for 20- to 100-MeV photons. Nucl Sci Eng 123:282–288Google Scholar
- 58.Gui AA, Shultis JK, Faw RE (1997) Response functions for neutron skyshine analysis. Nucl Sci Eng 125:111–127Google Scholar
- 59.Shultis JK, Faw RE, Bassett MS (1991) The integral line-beam method for gamma skyshine analysis. Nucl Sci Eng 107:228–245Google Scholar
- 60.Stedry MH (1994) A Monte Carlo line-beam calculation of gamma-ray skyshine for shielded sources. MS thesis, Kansas State University, ManhattanGoogle Scholar
- 61.Negin CA (1987) The microskyshine manual. Grove Software, LynchburgGoogle Scholar
- 62.Carlson BG, Lathrop KD (1968) Transport theory, the method of discrete ordinates. In: Greenspan H, Kelber CN, Okrent D (eds) Computing methods in reactor physics. Gordon and Breach, New YorkGoogle Scholar
- 63.Duderstadt JJ, Martin WR (1979) Transport theory. Wiley, New YorkMATHGoogle Scholar
- 64.Lewis EE, Miller WF (1984) Computational methods of neutron transport theory. Wiley, New YorkGoogle Scholar
- 65.Rhoades WA, Childs RL (1987) The TORT three-dimensional discrete ordinates neutron/photon transport code. ORNL-6268. Oak Ridge National Laboratory, Oak RidgeGoogle Scholar
- 66.Alcouffe RE, Baker RS, Dahl JA, Turner SA (2002) PARTISN user’s guide. CCS-4, LA-UR-02-5633. Los Alamos National Laboratory, Transport Methods Group, Los AlamosGoogle Scholar
- 67.Goertzel G, Kalos MH (1958) Monte Carlo methods in transport problems. In: Progress in nuclear energy, ser 1, vol 2. Pergamon, New YorkGoogle Scholar
- 68.Kalos MH (1968) Monte Carlo integration of the adjoint gamma-ray transport equation. Nucl Sci Eng 33:284–290Google Scholar
- 69.Kalos MH, Nakache NR, Celnik JC (1968) Monte Carlo methods in reactor computations. In: Greenspan H, Kelber CN, Okrent D (eds) Computing methods in reactor physics. Gordon and Breach, New YorkGoogle Scholar
- 70.Spanier J, Gelbard EM (1969) Monte Carlo principles and neutron transport problems. Addison-Wesley, ReadingMATHGoogle Scholar
- 71.Carter LL, Cashwell ED (1975) Particle-transport simulation with the Monte Carlo method. TID-26607. Los Alamos National Laboratory, Los AlamosGoogle Scholar
- 72.Lux I, Koblinger LK (1991) Monte Carlo particle transport methods: neutron and photon calculations. CRC Press, Boca RatonGoogle Scholar
- 73.Dunn WL, Shultis JK (2011) Exploring the Monte Carlo method. Elsevier, AmsterdamGoogle Scholar
- 74.Jenkins TM, Nelson TM, Rindi A (1988) Monte Carlo transport of electrons and photons. Plenum, New YorkCrossRefGoogle Scholar
- 75.Nelson WR, Hirayama H, Rogers DWO (1985) The EGS4 code system. SLAC-265. Stanford Linear Accelerator Center, Menlo ParkGoogle Scholar
- 76.Halbleib JA, Kensek RP, Mehlhorn TA, Valdez GD, Seltzer SM, Berger MJ (1992) ITS Version 3.0: the integrated TIGER series of coupled electron/photon Monte Carlo transport codes. SAND91-1634. Sandia National Laboratories, AlbuquerqueGoogle Scholar
- 77.X-5 Monte Carlo Team (2003) MCNP—a general Monte Carlo n-particle transport code, version 5. LA-UR-03-1987 (vol 1: Overview and theory), LA-UR-03-0245 (vol 2: User’s guide). Los Alamos National Laboratory, Los AlamosGoogle Scholar

## Books and Reviews

- Blizard EP, Abbott LS (eds) Reactor handbook, vol 3, Part B, Shielding. Wiley, New YorkGoogle Scholar
- Faw RE, Shultis JK (1999) Radiological assessment: sources and doses. American Nuclear Society, La Grange ParkGoogle Scholar
- Goldstein H (1959) Fundamental aspects of reactor shielding. Addison-Wesley, ReadingGoogle Scholar
- Haffner JW (1967) Radiation and shielding in space. Academic, New YorkGoogle Scholar
- ICRP (2007) The 2007 recommendations of the international commission on radiological protection. Report 103. Annals of the ICRP 37:2–4Google Scholar
- ICRP (2008) Nuclear decay data for dosimetric calculations. Report 107. Annals of the ICRP 38(3):1–96Google Scholar
- ICRU (1993) Quantities and units in radiation protection dosimetry. Report 51. International Commission on Radiation Units and Measurements, BethesdaGoogle Scholar
- ICRU (1998) Fundamental quantities and units for ionizing radiation. Report 60. International Commission on Radiation Units and Measurements, BethesdaGoogle Scholar
- Jaeger RG (ed) (1968–1975) Engineering compendium on radiation shielding. Shielding materials and design, vol 1; Shielding materials and designs, vol 2; Shield design and engineering, vol 3. Springer, New YorkGoogle Scholar
- NCRP (2003) Radiation protection for particle accelerator facilities. Report 144. National Council on Radiation Protection and Measurements, BethesdaGoogle Scholar
- NCRP (2005) Structural shielding design for medical x-ray imaging facilities. Report 147. National Council on Radiation Protection and Measurements, BethesdaGoogle Scholar
- NCRP (2005) Structural shielding design and evaluation for megavoltage x- and gamma-ray radiotherapy facilities. Report 151. National Council on Radiation Protection and Measurements, BethesdaGoogle Scholar
- Rockwell T III (ed) (1956) Reactor shielding design manual. Van Nostrand, PrincetonGoogle Scholar
- Schaeffer NM (ed) (1973) Reactor shielding. TID-25951, U.S. Atomic Energy Commission, Washington, DCGoogle Scholar
- Shultis JK, Faw RE (2000) Radiation shielding. American Nuclear Society, La Grange ParkGoogle Scholar
- UN (1977, 1982, 1988, 1993, 2000) Reports of the United Nations Scientific Committee on the Effects of Atomic Radiation, New York. http://www.unscear.org/unscear/en/publications.html