Neutron Interactions and Dosimetry I

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Neutron Interactions and Dosimetry I

• Kinetic Energy
• Interactions
• Quality Factor
• n ? Mixed-Field Dosimetry

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Introduction

• This section is intended to provide an
  introduction to neutron dosimetry that is
  relevant to the human body, from the viewpoint of
  either radiation hazard or neutron-beam
  radiotherapy
• We will be primarily concerned about neutron
  interactions with the majority tissue elements H,
  O, C, and N, and the resulting absorbed dose

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Introduction

• Because of the short ranges of the secondary
  charged particles that are produced in such
  interactions, CPE is usually well approximated
• Since no bremsstrahlung x-rays are generated, the
  absorbed dose can be assumed to be equal to the
  kerma at any point in neutron fields at least up
  to an energy E ? 20 MeV

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Neutron Kinetic Energy

• For dosimetry purposes it is convenient to divide
  neutron fields into three energy categories
• Thermal Neutrons
• Intermediate-Energy Neutrons
• Fast Neutrons

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Thermal Neutrons

• Thermal neutrons have only the Maxwellian
  distribution of thermal motion that is
  characteristic of the temperature of the medium
  in which they exist
• Their most probable energy at 20C is E 0.025
  eV
• All neutrons with energies below 0.5 eV are
  usually referred to as thermal because of a
  simple test that can be applied to a neutron
  field to measure how completely it has been
  thermalized by passage through a moderator

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Cadmium Ratio

• A Cd filter 1 mm thick absorbs practically all
  incident neutrons below about 0.5 eV, but readily
  passes those above that energy
• A thermal-neutron detecting foil such as gold can
  be radioactivated by neutrons through the
  197Au(n,?)198Au interaction
• Exposing two such foils in the neutron field, one
  foil bare and the other enclosed in 1 mm of Cd,
  provides two activation readings
• The ratio of the bare to the Cd reading is called
  the cadmium ratio it is unity if no thermal
  neutrons are present, and rises towards infinity
  as the thermal-neutron component approaches 100

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Intermediate-Energy Neutrons

• Neutrons with energies above the thermal cutoff
  of 0.5 eV but below 10 keV are called
  intermediate-energy neutrons
• Above 10 keV, the dose in the human body is
  dominated by the contribution of recoil protons
  resulting from elastic scattering of hydrogen
  nuclei
• Below that energy the dose is mainly due to
  ?-rays resulting from thermal-neutron capture in
  hydrogen

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Fast Neutrons

• These neutrons cover the energy range from 10 keV
  upward

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Tissue Composition

• The following table gives the atomic composition,
  in percentage by weight, of human muscle tissue
  and the whole body
• The ICRU composition for muscle has been assumed
  in most cases for neutron-dose calculations,
  lumping the 1.1 of other minor elements
  together with oxygen to make a simple
  four-element (H, O, C, N) composition

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Kerma Calculations

• For a single neutron energy, type of target atom,
  and kind of interaction, the kerma that results
  from a neutron fluence ? (cm-2) at a point in a
  medium is given by
• where ? is the interaction cross section in
  cm2/(target atom), Nt is the number of target
  atoms in the irradiated sample, m is the sample
  mass in grams, and Etr is the total kinetic
  energy (MeV) given to charged particles per
  interaction

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Kerma Calculations

• K is thus given in rad (or centigrays), and its
  value is equal to the absorbed dose D at the same
  point under the usual CPE conditions
• The product of (1.602 ? 10-8?Ntm-1Etr) is equal
  to the kerma factor Fn in rad cm2/n
• Thus the equation reduces to

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Kerma Calculations

• Fn is not generally a smooth function of Z and E,
  unlike the case of photon interaction
  coefficients
• Interpolation vs. Z cannot be employed to obtain
  values of Fn for elements for which data are not
  listed, and interpolation vs. E is feasible only
  within energy regions where resonance peaks are
  absent

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Kerma Calculations

• For a continuous neutron spectrum with a
  differential fluence distribution ??(E) (n/cm2
  MeV), the kerma contribution by j-type
  interactions with i-type target atoms is
• where Etr(E)ij is the total kinetic energy
  given to charged particles per type-j interaction
  with type-i atoms by neutrons of energy E

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Kerma Calculations

• For the same units as in the first equation, Kij
  is given in rads or centigrays
• It can be summed over all i and j to obtain the
  kerma (or dose) due to all types of interactions
  and target atoms

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Thermal-Neutron Interactions in Tissue

• There are two important interactions of thermal
  neutrons with tissue neutron capture by
  nitrogen, 14N(n,p)14C, and neutron capture by
  hydrogen, 1H(n,?)2H
• The nitrogen interaction releases a kinetic
  energy of Etr 0.62 MeV that is shared by the
  proton (0.58 MeV) and the recoiling nucleus (0.04
  MeV)

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Thermal-Neutron Interactions in Tissue

• Thermal neutrons have a larger probability of
  capture by hydrogen atoms in muscle, because
  there are 41 times more H atoms than N atoms in
  tissue
• The energy given to ?-rays per unit mass and per
  unit fluence of thermal neutrons can be obtained
  from an equation similar to Eq. (1), but
  replacing Etr by E? 2.2 MeV (the ?-ray energy
  released in each neutron capture)

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Thermal-Neutron Interactions in Tissue

• This of course does not contribute directly to
  the kerma, since the ?-rays must interact and
  transfer energy to charged particles to produce
  kerma
• If the irradiated tissue mass is small enough to
  allow the ?-rays to escape, the kerma due to
  thermal neutrons is only that resulting from the
  nitrogen (n, p) interactions
• In larger masses of tissue the ?-rays are
  increasingly absorbed before escaping, thus
  contributing to the kerma

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Thermal-Neutron Interactions in Tissue

• In the center of a 1-cm diameter sphere of tissue
  the kerma contributions from the (n, p) and (n,
  ?) processes are comparable in size
• In a large tissue mass (radius gt 5 times the
  ?-ray MFP) where radiation equilibrium is
  approximated, the kerma due indirectly to the (n,
  ?) process is 26 times that of the nitrogen (n,
  p) interaction
• The human body is intermediate in size, but large
  enough so the 1H(n, ?)2H process dominates in
  kerma (and dose) production

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Interaction by Intermediate and Fast Neutrons

• The following diagram summarizes the processes
  that contribute directly to kerma in a small mass
  of tissue in free space
• The dashed curve a is the sum of all the others
• It is dominated below 10-4 MeV by curve g, which
  represents (n,p) reactions, mostly in nitrogen
• Above 10-4 MeV elastic scattering of hydrogen
  nuclei (curve b) contributes nearly all of the
  kerma

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Interaction by Intermediate and Fast Neutrons

• The average energy transferred by elastic
  scattering to a nucleus is closely approximated
  (i.e., assuming isotropic scattering in the
  center-of-mass system) by
• where E neutron energy,
• Ma mass of target nucleus,
• Mn neutron mass

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Interaction by Intermediate and Fast Neutrons

• For hydrogen recoils?Etr ? E/2 with Etr-values
  ranging from 0 (for protons recoiling at 90) to
  Etr E for protons recoiling straight ahead
• For other tissue atoms, elastic scattering
  gives?Etr 0.142E for C atoms, 0.124E for N
  atoms, and 0.083E for O atoms

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Neutron Sources

• The most widely available neutron sources are
  nuclear fission reactors, accelerators, and
  radioactive sources
• Fissionlike spectra have average neutron energies
  around 2 MeV, and are available from nuclear
  reactors, 252Cf radioactive (spontaneous fission)
  sources, critical assemblies, and other mock
  fission sources such as that produced by 12-MeV
  cyclotron-accelerated protons on a thick Be target

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Neutron Sources

• Several types of Be(?,n) radioactive sources are
  in common use, employing 210Po, 239Pu, 241Am, or
  226Ra as the emitter
• Neutron yields are on the order of 1 neutron per
  104 ?-particles
• The following diagram exemplifies the neutron
  spectra emitted, which have average energies ? 4
  MeV

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Neutron Sources

• Low-energy neutron generators accelerate
  deuterium to 0.1 0.4 MeV and impinge them on
  targets containing either deuterium or tritium
• The output neutrons are in the range of 1.9 3.4
  MeV for the D(d,n)3He reaction, and 12.9 15.6
  MeV for T(d,n)4He
• Outputs on the order of 1011 and 1013 n/s,
  respectively, can be achieved in this way

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Neutron Sources

• Cyclotrons can be used to produce neutron beams
  by accelerating protons or deuterons into various
  targets, most commonly Be
• The following diagram shows the typical
  bell-shaped neutron spectra that result from
  deuteron bombardment
• The neutron energies extend from zero to somewhat
  above the deuteron energy, and have an average of
  about 0.4 times that energy

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Neutron Quality Factor

• For purposes of neutron radiation protection the
  dose equivalent H is equal to DQ, where Q is the
  quality factor, which depends on neutron energy
  according to the following curve
• The quality factor for all ?-rays is taken to be
  unity for purposes of combining neutron and ?-ray
  dose equivalents

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n ? Mixed-Field Dosimetry

• Neutrons and ?-rays are both indirectly ionizing
  radiations that are attenuated more or less
  exponentially in passing through matter
• Each is capable of generating secondary fields of
  the other radiation, by (n, ?) and (?, n)
  reactions, respectively

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n ? Mixed-Field Dosimetry

• (?, n) reactions are only significant for
  high-energy ?-rays (?10 MeV), but (n, ?)
  reactions can proceed at all neutron energies and
  are especially important in the case of
  thermal-neutron capture, as discussed for 1H(n,
  ?)2H
• As a result neutron fields are normally found to
  be contaminated by secondary ?-rays
• Since neutrons generally have more biological
  effectiveness per unit of absorbed dose than
  ?-rays, it is usually desirable to perform
  dosimetry in a way that provides separate dose
  accounting for ? and n components

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n ? Mixed-Field Dosimetry

• It will be convenient to discuss three general
  categories of dosimeters for n ? applications
• Neutron dosimeters that are relatively
  insensitive to ? rays
• ?-ray dosimeters that are relatively insensitive
  to neutrons
• Dosimeters that are comparably sensitive to both
  radiations

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n ? Mixed-Field Dosimetry

• It is especially important in the case of neutron
  dosimeters to specify the reference material to
  which the dose reading is supposed to refer
• Usually, because of the universal interest in
  radiation effects on the human body, kerma or
  absorbed dose in muscle tissue provides the
  reference basis for specifying dosimeter
  performance

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n ? Mixed-Field Dosimetry

• It should be noted that water is not as close a
  substitute for muscle tissue for neutrons as it
  is for photons
• Water is 1/9 hydrogen by weight muscle is 1/10
  hydrogen
• Water contains no nitrogen, and hence can have no
  14N(n,p)14C reactions by thermal neutrons

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Equation for n ? Dosimeter Response

• The general equation for the response of a
  dosimeter to a mixed field of neutrons and ?-rays
  can be most simply written in the form
• or alternatively as

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Equation for n ? Dosimeter Response

• where Qn,? total response due to the combined
• effects of the ?-rays and
  neutrons,
• A response per unit of absorbed
  dose in
• tissue for ?-rays,
• B response per unit of absorbed
  dose in
• tissue for neutrons,
• D? ?-ray absorbed dose in tissue,
  and
• Dn neutron absorbed dose in tissue

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Equation for n ? Dosimeter Response

• By convention the absorbed dose referred to in
  these terms is assumed to be that under CPE
  conditions in a small imaginary sphere of muscle
  tissue, centered at the dosimeter midpoint with
  the dosimeter absent
• Most commonly this tissue sphere is taken to be
  just large enough (0.52-g/cm2 radius) to produce
  CPE at its center in a 60Co beam