Gamma Decay

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Gamma Decay

• Energetics
• Decay Types
• Transition Probabilities
• Internal Conversion
• Angular Correlations
• Emission of photon during deexcitation of the
  nucleus
• Wide range of energies
• Isomers
• two configurations
• different total angular momenta
• Energy differences
• long-lived nuclear states are called isomeric
  states
• gamma ray decay is called isomeric transition (IT)

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? Transitions

• De-excitation of excited states are ? transitions
  
• ?- and ?-decay processes leave product nucleus in
  either ground state or, more often, an excited
  state
• Emission of electromagnetic radiation (?
  radiation), internal-conversion electrons, or
  newly created electron and positron
• internal conversion comes about by interaction
  between nucleus and extranuclear electrons
  leading to emission of electron with kinetic
  energy equal to difference between energy of
  nuclear transition involved and binding energy of
  the electron
• Characterized by a change in energy without
  change in Z and A

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Energetics

• Recoil from gamma decay
• Energy of excited state must equal
• Photon energy, and recoil
• Mc2Mc2EgTr
• Momentum same for recoil and photon
• If Eg 2 MeV, and A50
• recoil energy is about 40 eV
• Use 931.5 MeV/AMU

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Energetics
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Multipole Radiation Selection Rules

• Since ? radiation arises from electromagnetic
  effects, it can be thought of as changes in the
  charge and current distributions in nuclei
• classified as magnetic (M) or electric (E)
• E and M multipole radiations differ in parity
  properties
• Transition probabilities decrease rapidly with
  increasing angular-momentum changes
• as in ?-decay
• Ii If ? l ? ?Ii-If?, where Ii is the initial
  spin state and If is the final spin state
• if initial and final state have the same parity,
  electric multipoles of even l and magnetic
  multipoles of odd l are allowed if different
  parity, the opposite is true

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• 0 ? 0 transitions cannot take place by photon
  emission
• photon has spin and therefore must remove at
  least one unit of angular momentum
• If no change in parity in 0 ? 0 transition,
  de-excitation may occur by emission of an
  internal-conversion electron or by simultaneous
  emission of an electron-positron pair (?E ? 1.415
  MeV)
• Transitions between two I0 states of opposite
  parity cannot take place by any first-order
  process
• would require simultaneous emission of two ?
  quanta or two conversion electrons

Friedlander Kennedy, p.97
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Isomeric Transitions

• An IT is a ? decay from an isomeric state
• Transition probability or partial decay constant
  for ? emission ?? ? E2lA2l/3
• for given spin change, half lives decrease
  rapidly with increasing A and more rapidly with
  increasing E
• Use of extreme single-particle model
• assumes ? transition can be described as
  transition of a single nucleon from one
  angular-momentum state to another
• the rest of the nucleus being represented as a
  potential well
• model predicts, for given nucleus, low-lying
  states of widely differing spins in certain
  regions of neutron and proton numbers
• numbers preceding the shell closures at N or Z
  values of 50, 82, 126
• coincide with islands of isomerism

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Internal Conversion Coefficients

• Internal conversion is an alternative to ?-ray
  emission
• comes about by interaction between nucleus and
  extranuclear electrons leading to emission of
  electron with kinetic energy equal to difference
  between energy of nuclear transition involved and
  binding energy of the electron
• Internal conversion coefficient ? is ratio of
  rate of internal conversion process to rate of ?
  emission
• ranges from zero to infinity
• coefficients for any shell generally increase
  with decreasing energy, increasing ?I, and
  increasing Z

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IC and Nuclear Spectroscopy

• Internal conversion electrons show a line
  spectrum with lines corresponding to the
  ?-transition energy minus binding energies of the
  K, L, M, shells in which the conversion occurs
• difference in energy between successive lines are
  used to determine Z
• ?K/ ?L ratios can be used to characterize
  multipole order and thus ?I and ??
• this ratio, though, doesnt vary as widely as the
  individual coefficients
• If Z of x-ray-emitting species known, it can be
  determined whether it decays by EC or IT
• in former, x-rays will be of Z-1 in latter, Z

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Angular Correlations

• So far we have assumed that once removed from the
  decaying nuclei, ? rays bear no recognizable mark
  of the multipole interaction that gave birth to
  them
• usually true, but different multipole fields give
  rise to different angular distributions of
  emitted radiation with respect to nuclear-spin
  direction of the emitting nucleus
• ordinarily deal with samples of radioactive
  material that contains randomly oriented nuclei,
  so observed angular distribution of ? rays is
  isotropic

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Angular Correlations

• Schematic diagram of angular correlations
• (a) shows angular distribution of dipole
  radiation for ?m 0 and ?m ? 1
• (b) shows magnetic substrates populated in ?1?2
  cascade from J0 to J1 to J0

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• If nuclear spins can be aligned in one direction,
  angular distribution of emitted ?-ray intensity
  would depend predictably on the initial nuclear
  spin and multipole character of the radiation
• can use strong external electric or magnetic
  field at low temperatures or observe a ? ray in
  coincidence with a preceding radiation
• in coincidence experiment, where angle ? between
  the two sample-detector axes is varied, the
  coincidence rate will vary as a function of ?

Correlation function
where Aa2a4
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Mössbauer Spectroscopy

• Principles
• Conditions
• Spectra
• Principles
• Nuclear transitions
• emission and absorption of gamma rays
• sometimes called nuclear gamma resonance
  spectroscopy
• Only suitable source are isotopes
• Emission from isotope is essentially
  monochromatic
• Energy tuning done by Doppler effect
• Vibration of source and absorber
• spectra recorded in mm/s (1E-12 of emission)

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Recoil

• Gaseous atom or molecule emits radiation (energy
  E)
• momentum of E/c
• Recoil (P) -E/c Mv
• M mass of emitter, v is recoil velocity
• Associated recoil energy of emitter
• ER Mv2 /2 E2/2Mc2
• ER (in eV) 537 E2/M (E in MeV)
• For radiation near UV or below with normal atoms
  or molecules v is very small
• With gamma decay E is large enough to have a
  measurable effect
• ETE ER for emission

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Recoil

• If E is to excite a nucleus
• E ET ER
• Molecules in gas or liquid cannot reabsorbed
  photon
• In practice lattice vibrational modes may be
  excited during absorption
• Emitting nuclei in chemical system
• Thermal equilibrium, moving source
• Doppler shift of emitted photon
• J is angle between direction of motion of the
  nucleus and emitted photon

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Recoil Free Fraction

• J can vary from -1 to 1,so distribution is ET -ER
• distribution around 0.1 eV at room temp
• Some chemical energy goes into photon, and some
  recoil energy goes into lattice phonon
• Heisenberg uncertainly implies distribution of
  energy from finite half-life
• G (in eV) 4.55E-16/t1/2 (sec)
• What Mössbauer did
• Total recoil in two parts, kinetic and
  vibrational
• If emitter and absorber are part of lattice,
  vibrations are quantized
• Recoil energy transfer only in correct quanta

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Recoil Free Fraction

• If recoil energy is smaller than quantized
  vibration of lattice the whole lattice vibrates
• Mass is now mass of lattice, v is small, and so
  is kinetic part of recoil energy
• E ET and recoil energy goes into lattice
  phonon system
• lattice system is quantized, so it is possible to
  find a state of the system unchanged after
  emission
• 0.9 for metallic, 0.2 for metal-organic
• related to stiffness of crystal

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Recoil free fraction

• E gt 150 keV nearly all events vibrate lattice
• E ET for a small amount of decays
• Where E ET gives rise to Mössbauer spectra
• Portion of radiation which is recoil free is
  recoil-free fraction
• Vibration of lattice reduced with reduced T
• Recoil-free fraction increases with decreasing T
• T range from 100 to 1000 K
• Half-lives greater than 1E-11 seconds, natural
  width around 1E-5 eV
• For gamma decay of 100 keV, Doppler shift of
• 1E-5 eV is at a velocity of 3 cm/s

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Isomeric or Chemical Shift

• Volume of nucleus in excited state is different
  from ground state
• Probability of electron orbitals found in the
  nucleus is different
• Difference appears as a difference in the total
  electron binding state and contributes to
  transition energy
• ET ²E(nucl) ²E(elect) binding energies
• Consider an emitting nucleus (excited) and
  absorber (ground) in different chemical states
• Difference in ²E(elect) and therefore ET
• Change is chemical shift

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Magnetic Dipole Splitting

• magnetic moment will add to transition energy
• ET ²E(nucl) ²E(elect) ²E(mag)
• Change in magnetic moment will effect shift
• Split also occurs (2I1) values
• around 1cm/s
• Electric Quadrapole Splitting
• inhomogeneous magnetic field
• ET ²E(nucl) ²E(elect) ²E(mag)²E(quad)
• around 1cm/2

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Technique

• Intensity of photon from emitter is detected
• Velocity of emitter and absorber recorded
• important to know these values
• May be cooled and place in magnetic field
• Used in
• amorphous materials
• catalysts
• soil
• coal
• sediments
• electron exchange

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Decay Scheme
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Mössbauer Devise