Absorbed Dose in Radioactive Media II

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Absorbed Dose in Radioactive Media II

• Beta Disintegration
• Electron-Capture Transitions
• Internal Conversion

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Beta Disintegration

• Nuclei having an excess of neutrons tend to emit
  an electron (?--particle), thus leaving the
  nucleus with one less neutron and one more
  proton, i.e., the atomic number Z is increased by
  1
• Conversely, nuclei with an excess of protons
  usually emit a positron (?), effectively
  decreasing Z by 1 while increasing the neutron
  count by 1
• In either case the total number of nucleons
  (protons neutrons) remains constant, so that
  the daughter product is an isobar of the parent

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Beta Disintegration (cont.)

• The ?-rays emitted in a given mode of
  disintegration (averaged over many such
  disintegrations) have a spectrum of kinetic
  energies extending from zero to a fixed maximum
  Emax, with a skewed bell-shaped differential
  distribution exemplified by the spectrum of
  ?--rays from P-32 shown in the following diagram

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?--ray spectrum emitted from P-32.
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Beta Disintegration (cont.)

• The maximum ?- kinetic energy (Emax 1.71 MeV in
  this case) represents the net decrease in the
  rest mass of the neutral P-32 atom in becoming a
  neutral S-32 atom, since the ground state of the
  S-32 is reached directly without ?-ray emission
• The atomic mass-energy balance equation is
• where the atomic mass decrease 32P 32S
  1.71 MeV, which appears as kinetic energy shared
  between the ?- and the neutrino

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Beta Disintegration (cont.)

• The electron on the left of the equation is
  required to balance the charge and rest mass of
  the ?- on the right
• Physically, when the P-32 nucleus emits the ?-, a
  positively charged ion (32S) results, which
  promptly captures a bystanding electron to become
  a neutral S-32 atom

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Beta Disintegration (cont.)

• A neutrino, which is a nearly zero-mass,
  zero-charge particle, is emitted along with each
  ?--particle, thus conserving energy and momentum
  in the disintegration process
• The difference between the ?--ray kinetic energy
  and Emax 1.71 MeV in each disintegration is
  carried away by the associated neutrino

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Beta Disintegration (cont.)

• The average kinetic energy of the ?-- or
  ?-particles in a ?-ray spectrum is found to be
  roughly 0.3 0.4 times Emax, depending on the
  individual spectral shape, which is determined by
  the forbiddenness classification of the ?-ray
  transition
• Often, for purposes of estimating the absorbed
  dose deposited by charged particles, Eavg ? 1/3
  Emax is assumed for ?-rays, if more accurate
  information is not available

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Beta Disintegration (cont.)

• Since the neutrino is radiologically irrelevant,
  the energy spent in the material in which the
  ?-ray emitter is located is just the product of
  the number of ?-rays by their average energy, not
  their maximum energy
• It is important not to confuse Eavg with Emax

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Beta Disintegration (cont.)

• A simple example of ?-disintegration is that of
  O-15 ? N-15, for which the atomic mass-energy
  balance equation is
• where the atomic-mass decrease from O-15 to
  N-15 1.022 MeV 1.73 MeV 2.75 MeV, as
  illustrated in the following diagram, and the
  1.73 MeV kinetic energy is shared between the ?
  and the neutrino

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Beta Disintegration (cont.)

• During ?-emission a valence electron is
  simultaneously released by the O-15 atom
• Thus both the ? and the electron are lost by the
  parent atom and appear on as free particles on
  the right of the equation
• The decrease in atomic mass is equal to the sum
  of the released kinetic energy (1.73 MeV) and the
  rest masses (0.511 MeV each) of the e- and the ?
• When the ? stops, it combines in an annihilation
  interaction with a nearby electron, emitting
  1.022 MeV in the form of two 0.511-MeV oppositely
  directed ?-rays

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Absorbed Dose from Beta Disintegration

• For present purposes we will ignore any radiative
  losses (bremsstrahlung and in-flight positron
  annihilation) by the ?-rays, and simply assume
  that their kinetic energy is all spent in
  collision interactions resulting in absorbed-dose
  deposition
• Such radiative loss corrections are relatively
  unimportant in low-Z media

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Absorbed Dose from Beta Disintegration (cont.)

• Under CPE conditions the absorbed dose due to n
  ?-disintegrations per gram of medium is nEavg
  (MeV/g)
• Additional absorbed-dose contributions due to any
  ?-rays resulting from a particular radionuclide
  must be treated separately as described earlier

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Electron-Capture (EC) Transitions

• Radioactive disintegrations through electron
  capture (EC) are competitive with those by
  ?-disintegration
• In the EC process the parent nucleus, instead of
  emitting a ?-particle, captures one of its own
  atomic electrons and emits a monoenergetic
  neutrino

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Electron-Capture (EC) Transitions (cont.)

• The electrons most likely to be captured in the
  EC process are K-shell electrons (?90), with
  L-shell electrons supplying practically all of
  the remainder
• Resulting shell vacancies are promptly filled by
  an electron from a higher orbit, with the release
  of a fluorescence x-ray
• The probability that a fluorescence photon will
  escape from its native atom is called the
  fluorescence yield, YK or YL

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Fluorescence yield (YK,L) and fractional
participation in the photoelectric effect (PK,L)
by K- and L-shell electrons
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Electron-Capture (EC) Transitions (cont.)

• The parallel atomic mass-energy equations for the
  case of 22Na ? 22Ne are given below for ?-decay
  and for the EC process
• The half-life for decay by both branches together
  is 2.60 y
• The corresponding atomic energy-level diagram is
  shown after the equations

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Electron-Capture (EC) Transitions (cont.)

• ?-Branch
• where the atomic mass decrease is equal to

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Electron-Capture (EC) Transitions (cont.)

• EC Branch
• where the atomic mass decrease is equal to

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Electron-Capture (EC) Transitions (cont.)

• It will be seen from the diagram that for
  ?-disintegration to take place in any
  radionuclide requires a minimum mass difference
  between the parent neutral atom and its daughter
  atom of 2m0 ( 1.022 MeV)
• Otherwise only EC can occur, since no kinetic
  energy would be available for a ?-particle, and
  in that case the dose deposited in EC events
  becomes relatively important

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Electron-Capture (EC) Transitions (cont.)

• In the EC branch equation the Eb-term indicates
  the electron binding energy in the K- or L-shell
• The kinetic energy of the emitted neutrino equals
  the difference in atomic rest mass between the
  Na-22 and the excited state of Ne-22 ( 1.568
  MeV), less the electron binding energy Eb (? 1
  keV for the K shell)

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Absorbed Dose for the EC Process

• When a ? is emitted, it contributes its average
  kinetic energy to the production of absorbed
  dose, and then its annihilation ?-rays may
  contribute more dose, depending upon the size and
  shape of the radioactive mass of material
• If an EC event occurs instead of ?emission,
  neither of these dose components is present, and
  virtually all of the energy available for
  absorbed dose in an EC event (if there is no
  subsequent ?-ray emission from an excited state)
  is contained in the electron-binding term Eb,
  which is very small compared to the energy that
  is removed by the neutrino

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Absorbed Dose for the EC Process (cont.)

• EC contributes a more significant fraction of the
  dose when ?-emission is prohibited and only EC
  can occur
• An example is 55Fe ? 55Mn, which emits Mn
  fluorescence x-rays of 5.9 keV and no other
  radiation (besides monoenergetic neutrinos)
• These photons are so easily attenuated that
  radiation equilibrium exists at the center of a
  1-cm-radius water sphere

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Absorbed Dose for the EC Process (cont.)

• Thus the energy contributing to the dose there
  per EC event is equal to the electron binding
  energy Eb in each case, whether a fluorescence
  x-ray is emitted or not
• Since approximately 88 of these EC events
  involve the K-shell, and the other 12 can be
  assumed to be with the L, the energy spent on the
  dose per EC event is
• where the binding energies are those for the
  daughter product, Mn

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Internal Conversion vs. ?-Ray Emission

• An excited nucleus, instead of emitting a ?-ray
  of energy h?, can impart the same amount of
  energy directly to one of its own atomic
  electrons, which then escapes the atom with a net
  kinetic energy of h? - Eb, where Eb is the
  binding energy of the electrons original shell
• This process, called internal conversion (IC),
  has nothing to do with the photoelectric effect,
  since the nucleus emits no photons in this case
• The ratio of the number Ne of conversion
  electrons emitted to the number N? of ?-rays
  emitted by a given species of excited nucleus is
  called the internal-conversion coefficient

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Internal Conversion vs. ?-Ray Emission

• An example of internal conversion is shown in the
  following diagram for
• It will be seen that 94.6 of the 137Cs atoms
  decay to an excited state of 137Ba, indicated as
  137mBa, where the m indicates a metastable or
  long-lived isomeric state with a half-life of
  2.55 minutes

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Internal Conversion vs. ?-Ray Emission

• Isomers are nuclei having the same Z and the same
  number A of nucleons, but differing energy states
• These excited 137mBa nuclei then decay in the
  following proportions
• 89.9 ?-ray emission (0.662 MeV)
• 8.2 conversion of K-shell electrons
• 1.9 other-shell conversions

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Internal Conversion vs. ?-Ray Emission

• Normally IC branching is not shown on
  energy-level diagrams, but the figure here
  includes it for clarity
• Note that the percentages shown there have been
  normalized to a total of 96.4, so that, for
  example, there are 85.0 ?-rays emitted per 100
  disintegrations of 137Cs
• Internal conversion is always possible in place
  of ?-ray emission by an excited nucleus
• However, in many cases the probability of IC is
  negligibly small and can be ignored

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Absorbed Dose for Internal Conversion

• When IC occurs in competition with ?-ray
  emission, it generally results in a net increase
  in absorbed dose in small objects, since the
  penetrating ?-radiation is thus replaced by a
  relatively short-range electron of nearly the
  same energy
• That is, the energy of the conversion electron is
• which will all be spent on absorbed dose
  under CPE conditions, neglecting radiative losses

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Absorbed Dose for IC (cont.)

• In addition, the binding energy Eb also will be
  entirely contributed to the dose, provided that
  no part of it escapes from the radioactive body
  in the form of fluorescence x-rays
• If the fraction p 1 AF of these x-rays can
  escape from the radioactive body, then the energy
  contributed per IC event to dose under CPE
  conditions becomes
• where
• with ?en and r defined as before

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Tables for Dose Estimation in Appendix C

• For each source the table gives the types of
  radiations emitted, the number of particles (or
  photons) of each type emitted per parent
  disintegration, the mean energy per particles,
  and the corresponding equilibrium dose constant
  in g rad/?Ci h
• The latter quantity can be converted into J/Bq h
  by multiplying by 2.703 ? 10-10
• It represents the energy contributed to the
  absorbed dose, per unit activity and time, under
  RE conditions (or CPE conditions for ?-rays)