Using the SEMF and realising its limitations

1
Lecture 3

• Using the SEMF and realising its limitations

2
3.1 Overview

• 3.2 Stability of Nuclides
• interpreting the table of nuclides
• SEMF and the valley of stability
• SEMF and the iron mountain
• 3.3 Decays
• classification of decays
• b-decay
• a-decay
• g-decay (off syllabus)
• fission and the rest
• 3.4 Natural Radioactivity

3
Z110
Z N ? stable longlived (gt109 yrs)
Even Even 155 11
Even Odd 53 3
Odd Even 50 3
Odd Odd 4 5
N160

• Even A stable nuclides

• Odd A stable nuclides

• odd-even summary

• Aconst _at_ 58

• SEMF total Ebind

• SEMF Ebind/A

• Magic Proton Numbers

• Nuclides

• Z92 (Uranium)

• Ebind/A-contours

• Ebind-contours

• Magic Neutron Numbers

• NZ

4
3.2 The Valley of Stability
1000 MeV
500 MeV
0 Mev
-500 Mev
-1000 Mev
-1500 Mev
5
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 with increasing Z 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 SEMF
  limitations)
• But what about simple Ebind per nucleon

6
3.2 The Iron Mountain
-MeV
7
3.2 The Iron Mountain Binding Energy vs. A for
odd-A nuclei
Iron
8
3.3 Classification of Decays

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

EC

• 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

9
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 0 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-decays

10
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

11
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)

12
3.3 b-decay and SEMF

• yielding

• evaluate
• for small Aodd A2/3ltlt 133 ? ZA/2N
• for large Aodd 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 10546Pd in 38h

13
3.3 b-decay and SEMF

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

14
3.3 b-decay and SEMF

• Even A
• two parabolae
• one for o-o one for e-e
• lowest o-o nucleus often has two decay modes
• since double b-decay is extremely weak most e-e
  nuclei have two stable isotopes
• there are nearly no stable o-o nuclei in nature
  because these can nearly all b-decay to an e-e
  nucleus

odd-odd
even-even
15
3.3 b-decay and SEMF

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

16
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)

Geiger-Nuttal Plot
17
3.3 a-decay
Protons
Alphas
Neutrons
18
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

19
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 a-emitters deviate by several orders of
  magnitude from SEMF predictions

20
3.3 a-decay(the 3-odd ones out)

• SEMF says they should not exist
• It is a shell effect, off syllabus

21
3.3 a-decay(the fine print)

• To compute decay rates one needs
• a lecture composed Dr. Weidberg
• and presented by me (lecture 8)

22
3.3 g-decay

• Very similar to atomic physics transitions
• 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
• Egatomiclt100 keV EgnuclearltO(1 MeV)
• But heavy nuclear rotational states can have
  Egnuclear, rotltO(10 keV)
• Note Not on syllabus

23
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 decay
• but does not because

24
3.3 Fission and the Rest

• It would take forever

• Fission is mainly asymmetric

25
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

26
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)

27
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)

28
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

29
Protons
30
End of Lecture 3
31
Notes

• In the following I reproduce some slides that
  have animated overlays and can not be read
  completely with the overlays turned on. The
  number of the slide they refer to is indicated in
  the top right corner.
• There is one additional slide on g-decays (off
  syllabus)

32
Z110
slide 3a
N160

• Aconst _at_ 58

• SEMF total Ebind

• Magic Proton Numbers

• Nuclides

• NZ

• Z92 (Uranium)

• Ebind-contours

• Magic Neutron Numbers

33
Z N ? stable longlived (gt109 yrs)
Even Even 155 11
Even Odd 53 3
Odd Even 50 3
Odd Odd 4 5
slide 3b

• Even A stable nuclides

• Odd A stable nuclides

• odd-even summary

• SEMF Ebind/A

• Nuclides

• NZ

• Ebind/A-contours

34
3.3 b-decay orInto the valley of stability
along the const. A direction
slide 9a

• 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 0 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-decays

35
3.3 b-decay orInto the valley of stability
along the const. A direction
slide 9b

• 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 0 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-decays

36
3.3 a-decay(energetics)
slide 18

• 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

37
3.3 a-decay(energetics)
slide 18

• 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)

38
3.3 a-decay(the 3-odd ones out)
slide 20a

• SEMF says they should not exist
• It is a shell effect, off syllabus

39
3.3 a-decay(the 3-odd ones out)
slide 20b

• SEMF says they should not exist
• It is a shell effect, off syllabus

40
3.3 g-decay
additional information off syllabus

• 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