nuclear%20stability,%20decays%20and%20natural%20radioactivity

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Lecture 3

• nuclear stability, decays and natural
  radioactivity

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3.1 Overview

• 3.2 The Valley of Stability
• interpreting the table of nuclides
• SEMF and the valley of stability
• SEMF and the iron mountain
• 3.3 Decays
• classification
• a-decay
• b-decay
• g-decay
• fission and the rest
• 3.4 Natural Radioactivity

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Z N ? stable longlived (gt109 yrs)
Even Even 155 11
Even Odd 53 3
Odd Even 50 3
Odd Odd 4 5

• Even A stable nuclides

• Odd A stable nuclides

• odd-even summary

• Magic Proton Numbers

• Magic Neutron Numbers

• NZ

• Aconst _at_ 58

• Z92 (Uranium)

• SEMF binding energy

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Z N ? stable longlived (gt109 yrs)
Even Even 155 11
Even Odd 53 3
Odd Even 50 3
Odd Odd 4 5

• Even A stable nuclides

• Odd A stable nuclides

• odd-even summary

• Magic Proton Numbers

• Magic Neutron Numbers

• NZ

• Aconst _at_ 58

• Z92 (Uranium)

• SEMF binding energy

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3.2 The Valley of Stability
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3.2 The Valley of Stability

• Observation stable nuclei not on a straight line
  in N-Z plane. The SEMF predicts this
• Coulomb term pulls them down (prefers ZltN) and
• wins over Asymmetry term (prefers ZN)
• Rich structure in location of stable elements
• more stable isotopes of e-e then o-o nuclei (see
  b-decay)
• No life beyond Z92 (U) and a big gap from Z82
  to 92 (the region of natural radio activity)
• Funny magic numbers for Z and N (see shell model)
• But what about simple Ebind per nucleon

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3.2 The Iron Mountain
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3.2 The Iron Mountain Binding Energy vs. A for
odd-A nuclei
Iron
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3.3 Classification of Decays

• a-decay
• emission of Helium nucleus
• Z?Z-2
• N?N-2
• A?A-4

• b--decay
• emission of e- and n
• Z?Z1
• N?N-1
• Aconst

• b-decay
• emission of e and n
• Z?Z-1
• N?N1
• Aconst

• Electron Capture (EC)
• absorbtion of e- and emiss n
• Z?Z-1
• N?N1
• Aconst

• g-decay
• emission of g
• Z,N,A all const

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3.3 b-decay orInto the valley of stability
along the const. A direction
valley

• Q How does nucleus move along constant A?
• A Via b-decay nucleus emits e-,ne(b-) or
  e,ne(b)
• DMnucl gt me for b- DMnucl gt me for b
• DMatomgt me for b- DMatomgt2me for b
• or via EC like (b) but swallow atomic e-
  instead instead of emitting e
• DMnuclgt-me or DMatomgt0
• Note DMx Mx(mother) Mx(daughter)
• Observe e- has continuous energy spectrum
• maximum of Ekin(e-) Qb-Erecoil(daughter) Qb
• 1ltQb/MeVlt15
• ne carries the rest of Qb solving long standing
  puzzle of energy conservation in b-decay

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3.3 b-decay orInto the valley of stability
along the const. A direction

• Q How does nucleus move along constant A?
• A Via b-decay nucleus emits e-,ne(b-) or
  e,ne(b)
• DMnucl gt me for b- DMnucl gt me for b
• DMatomgt me for b- DMatomgt2me for b
• or via EC like (b) but swallow atomic e-
  instead instead of emitting e
• DMnuclgt-me or DMatomgt0
• Note DMx Mx(mother) Mx(daughter)
• Observe e- has continuous energy spectrum
• maximum of Ekin(e-) Qb-Erecoil(daughter) Qb
• 1ltQb/MeVlt15
• ne carries the rest of Qb solving long standing
  puzzle of energy conservation in b-decay

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3.3 b-decay

• Q Where do e- and ne (ne) come from?
• A Cant be in the nucleus because nucleus is
  to small a box for electrons of this energy
• Eboxn2h2/8mea2 0.37 TeV _at_ n1, a1fm (i.e. n
  decay)
• e and n produced during decay (particle physics)
• Think of b-decay as n-decay inside the nucleus
• n ? p e- ne
• Think of n-decay as quark decay inside the
  neutron
• d-1/3 ? u2/3 W-
• followed by W-?e- ne

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3.3 b-decay and SEMF

• Q How do we find SEMF predictions for b-decay
• A We need the optimum Z (max binding energy) at
  fixed A.
• To make this easier lets consider Aodd i.e.
  ap0 (even-odd or odd-even)

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3.3 b-decay and SEMF

• This yields

• evaluate
• A2/3ltlt 133 ? ZA/2N
• A105 ? Z3/4 N (Z45 N60)
• Quite close to reality. The nearest nuclei are
• A103 Z45 N58 10345Rh ,even-odd, stable
• A106 Z46 N60 10646Pd ,even-even, stable
• A105 Z46 N59 10546Pd ,odd-even, stable
• A105 Z45 N60 10545Rh ,odd-even,
  meta-stable, decays via b- to 10646Pd in 38h

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3.3 b-decay and SEMF

• Odd A
• single parabolic minimum
• only one b-stable nucleus for each odd A
• nearly only single b-decays
• double b-decay is 2nd order weak process and very
  rare

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3.3 b-decay and SEMF

• Even A
• two parabolae for o-o e-e
• lowest o-o nucleus often has two options for
  decay
• since double b-decay extremely weak most e-e
  nuclei have two stable isotopes
• nearly no stable o-o nuclei

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3.3 b-decay and SEMF

• Consequence 2 or more even A, 1 or no odd A

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3.3 a-decay

• Observation
• 23290Th emits a with Ekin4 MeV
• RTh1.22321/3 fm 7.36 fm
• a has Epot(RTh)24 MeV
• a has negative kinetic energy up to R8RTh
• Conclusion
• a must tunnel out of the nucleus
• half lifes should have exp(Ekin) dependence (true
  over 24 orders, see Geiger-Nuttal plot)

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3.3 a-decay
Protons
Alphas
Neutrons
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3.3 a-decay(energetics)

• What can SEMF say about a-decay?
• Decay is possible if Mnucl(N,Z)-Mnucl(N-2,Z-2)gtM(a
  )
• SEMF as function of A only (dAdNdZ dNdZ) and
  ignoring pairing term (odd A only)

• Slope in Ebind/A (A120) is 7.710-3 MeV

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3.3 a-decay(energetics)

• What can SEMF say about a-decay?
• Decay is possible if Mnucl(N,Z)-Mnucl(N-2,Z-2)gtM(a
  )
• SEMF as function of A only (dAdNdZ dNdZ) and
  ignoring pairing term (odd A only)

• Slope in Ebind/A (A120) is 7.710-3 MeV

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3.3 a-decay(energetics-but)

• but the world is full of isotopes with Agt151
• and only 7 natural a-emitters observed with Alt206
  because
• barrier penetration has texp(-Ea)
• energies are too low to get t ltlt age of earth
  (4109 years)
• Note Shell effects O(1 MeV) make the life times
  of emitters deviate by several orders of
  magnitude from SEMF predictions

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3.3 a-decay(the 3-odd ones out)

• SEMF says they should not exist
• It is a shell effect, see next lecture

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3.3 a-decay(the fine print)

• To compute decay rates one needs
• a lecture from Dr. Weidberg

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3.3 g-decay

• Very similar to atomic physics transitions
• Egatomiclt100 keV EgnuclearltO(1 MeV)
• But heavy nuclear rotational states can have
  Egnuclear, rotltO(10 keV)
• Q When do nuclear g-decays happen?
• A When there is not enough E to emit a strongly
  interacting particle (Nucleon), often after other
  nuclear decays

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3.3 g-decay

• Q What if J0 nucleus needs to loose Energy
• A It cant loose it via g
• it could loose it via pair-creation if Egt2me
  (virtual g does not have to have S1 and converts
  to pair in J0 1S0 state)

emitted electron
emitted positron

• if Elt2me could do internal conversion (ala Auger
  in atomic)

emitted electron
absorbed atomic electron
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3.3 Fission and the Rest

• Fission in the liquid drop model

• Yet another tunneling process
• Complicated dynamics
• Coulomb repulsion fights surface term
• Call it surface barrier
• Theoretical limit
• Z2/Agt18 (9842Mo) could
• But does not because

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3.3 Fission and the Rest

• It would take forever

• Fission is mainly asymmetric

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3.3 Fission and the Rest
Epot MeV

• Fission barrier changes with Z2/A (and via SEMF
  this is a change with A)
• Thus the huge lifetime variation observed
• Beyond Z2/A43 (which does not exist) there would
  be no fission barrier

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3.3 Fission and the Rest

• Fission products
• too rich in neutrons (valley is curved )? emit
  neutrons (needed for reactors)
• highly excited ? g-decay
• still away from valley of stability ? b-decay
• tunneling tfisexp(-Efis)? excited nuclei
  (n-capture) decay much faster via fission
  (reactors)

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3.3 Others

• Best to emit something with very large binding
  energy ? 12C has been observed
• Anything else is just asymmetric fission
• And then there is fusion (separate chapter)

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3.4 Natural Radioactivity

• Three chains of natural radioactivity parents
  232Th, 235U, 238U (made by last super nova, tgtage
  of earth)
• 40K (odd-odd, Z19, N21, t1.31019 years, b- or
  EC)
• short-lived but naturally regenerated radioactive
  nuclei, eg 14C (radio-carbon)
• natural life times O(1s)lttltage-of-universe
• all types of decays present

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Protons