1. 11 Nov 2004, Lecture 3 Nuclear Physics Lectures, Dr. Armin Reichold 1 Lecture 3 Using the SEMF and realising its limitations

2. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 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  -decay  -decay  -decay (off syllabus) fission and the rest 3.4 Natural Radioactivity end of lecture 3

3. A=const @ 58 N Z 0 Mev +500 MeV +1000 MeV -500 Mev -1000 Mev -1500 Mev A=58 (Fe58, Ni58) A=const. N=Z Z=92 (U) even A Proton Magic Numbers N=Z Neutron Magic Numbers Z=92 (Uranium) ZN  stable longlived (>10 9 yrs) Even 15511 EvenOdd533 OddEven503 Odd 45 E bind /A-contours -MeV Even A stable nuclides Odd A stable nuclides SEMF total E bind odd-even summary E bind -contours SEMF E bind /A Magic Proton Numbers Magic Neutron Numbers Nuclides N=160 Z=110

4. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 4 3.2 The Valley of Stability 0 Mev +500 MeV +1000 MeV -500 Mev -1000 Mev -1500 Mev

5. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 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 Z<N) and … … wins over Asymmetry term (prefers Z=N) Rich structure in location of stable elements more stable isotopes of e-e then o-o nuclei (see  -decay) No “life” beyond Z=92 (U) and a big gap from Z=82 to 92 (the region of natural radio activity) Funny magic numbers for Z and N (see SEMF limitations) But what about simple E bind per nucleon

6. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 6 3.2 The Iron Mountain -MeV

7. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 7 3.2 The Iron Mountain Binding Energy vs. A for odd-A nuclei Iron Not smooth because Z not smooth function of A

8. 8 3.3 Classification of Decays Neutrons Protons    -decay: emission of Helium nucleus Z  Z-2 N  N-2 A  A-4  - -decay emission of e - and Z  Z+1 N  N-1 A=const  -decay emission of  Z,N,A all const  + -decay emission of e + and Z  Z-1 N  N+1 A=const  EC Electron Capture (EC) absorbtion of e - and emiss Z  Z-1 N  N+1 A=const

9. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 9 Q: How does nucleus “move” along constant A? A: Via  -decay: nucleus emits e -, e =(  -) or e +, e  (  +)  M nucl > m e for  - &  M nucl > m e for  +  M atom > 0 for  - &  M atom >2m e for  + or via EC: like (  +) but swallow atomic e - instead instead of emitting e +  M nucl >-m e or  M atom >0 Note:  M x = M x (mother) – M x (daughter) Observe: e +- has continuous energy spectrum maximum of E kin (e +- ) = Q  -E recoil (daughter) ≈ Q  1<Q  /MeV<15 e carries the rest of Q  solving long standing puzzle of energy conservation in  -decays 3.3  -decay or Into the valley of stability along the const. A direction Z N valley of stability unstable to β+ decay (or K capture) unstable to β- decay valley

10. 11 Nov 2004, Lecture 3 10 3.3  -decay Q: Where do e +- and e ( e ) come from? A: Can’t be “in” the nucleus because nucleus is to small a box for electrons of this energy E box =n 2 h 2 /8m e a 2 = 0.37 TeV @ n=1, a=1fm (i.e. n decay) e and produced during decay (particle physics) Think of  -decay as n-decay inside the nucleus n  p + e - + e Think of n-decay as quark decay inside the neutron d -1/3  u +2/3 + W - followed by W -  e - + e W - e - ( ) e d u u d u d n p

11. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 11 3.3  -decay and SEMF a v =15.56 MeVa c =0.697 MeV a s =17.23 MeV a a =23.285 MeV e=eveno=odd + 12 MeV (e-e) a p = 0 MeV (o-e or e-o) - 12 MeV (o-o) Q: How do we find SEMF predictions for  -decay A: We need the optimum Z (max binding energy) at fixed A. To make this easier lets consider A=odd i.e. a p =0 (even-odd or odd-even)

12. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 12 3.3  -decay and SEMF evaluate: for small A odd : A 2/3 << 133  Z≈A/2≈N for large A odd : A=105  Z= 3 / 4 N (Z=45; N=60): Quite close to reality. The nearest nuclei are: A=103; Z=45; N=58: 103 45 Rh,even-odd, stable A=106; Z=46; N=60: 106 46 Pd,even-even, stable A=105; Z=46; N=59: 105 46 Pd,odd-even, stable A=105; Z=45; N=60: 105 45 Rh,odd-even, meta-stable, decays via  - to 105 46 Pd in 38h yielding:

13. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 13 3.3  -decay and SEMF Odd A  -decays: single parabolic minimum only one  -stable nucleus for each odd A nearly exclusively single  - decays occur in nature double  -decay is 2 nd order weak process and very rare 58 56 54 52 Te I Xe Cs Ba La Ce Pr β- EC β+ Odd A. A=135 Single parabola even-odd and odd-even

14. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 14 3.3  -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  -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  -decay to an e-e nucleus 48 46 44 42 Mo Tc Ru Rh Pd Ag Cd β+ β- Even A. A=102 Two parabolae separated by 2δ, odd-odd and even-even odd-odd even-even

15. 11 Nov 2004, Lecture 3 15 3.3  -decay and SEMF Consequence: 2 or more even A, 1 or no odd A

16. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 16 3.3  -decay Observation: 232 90 Th emits  with E kin ≈4 MeV R Th ≈1.2*232 1/3 fm = 7.36 fm  has E pot (R Th )=24 MeV  has negative kinetic energy up to R=8*R Th Conclusion:  must tunnel out of the nucleus half lifes should have exp(E kin ) dependence (true over 24 orders, see Geiger-Nuttal plot) Geiger-Nuttal Plot

17. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 17 3.3  -decay Neutrons Protons AlphasAlphas  E bind ( 4 2  )=28.3 MeV > 4*6MeV  E sep ≈6MeV per nucleon for heavy nuclei

18. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 18 3.3  -decay (energetics) What can SEMF say about a-decay? Decay is possible if M nucl (N,Z)-M nucl (N-2,Z-2)>M(  ) SEMF as function of A only (dA=dN+dZ & dN=dZ) and ignoring pairing term (odd A only) Slope in E bind /A (A≥120) is 7.7*10 -3 MeV E bind /A [MeV] 7.7x10-3 MeV

19. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 19 3.3  -decay (energetics-but) but the world is full of isotopes with A>151 and only 7 natural  -emitters observed with A<206 because … barrier penetration has  ~exp(-E  ) energies are too low to get  << age of earth (4*10 9 years) Note: Shell effects O(1 MeV) make the life times of  emitters deviate by several orders of magnitude from SEMF predictions

20. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 20 3.3  -decay (the 3-odd ones out) SEMF says they should not exist It is a shell effect, off syllabus

21. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 21 3.3  -decay (the fine print) To compute decay rates one needs a lecture from Dr. Weidberg …

22. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 22 3.3  -decay Very similar to atomic physics transitions Q: When do nuclear  -decays happen? A: When there is not enough E to emit a strongly interacting particle (Nucleon), often after other nuclear decays E  atomic <100 keV ; E  nuclear <O(1 MeV) But: heavy nuclear rotational states can have E  nuclear, rot <O(10 keV) Note: Not on syllabus

23. 11 Nov 2004, Lecture 3 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: Z 2 /A>18 ( 98 42 Mo) could decay … … but does not because …

24. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 24 3.3 Fission and the Rest Z 2 /A log 10 (  /1 year) -5 0 5 10 15 It would take forever Fission is mainly asymmetric

25. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 25 3.3 Fission and the Rest Fission barrier changes with Z 2 /A (and via SEMF this is a change with A) Thus the huge lifetime variation observed Beyond Z 2 /A=43 (which does not exist) there would be no fission barrier E pot [MeV]

26. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 26 3.3 Fission and the Rest t=0 t≈10 -14 s t>10 -10 s Fission products: too rich in neutrons (valley is curved )  emit neutrons (needed for reactors) highly excited   -decay still away from valley of stability   -decay tunneling:  fis ~exp(-E fis )  excited nuclei (n-capture) decay much faster via fission (reactors)

27. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 27 3.3 Others Best to emit something with very large binding energy  12 C has been observed Anything else is just asymmetric fission And then there is fusion (separate chapter)

28. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 28 3.4 Natural Radioactivity Three “chains” of natural radioactivity parents: 232Th, 235U, 238U (made by last super nova,  >age of earth) 40K (odd-odd, Z=19, N=21, t=1.3*10 19 years,  - or EC) short-lived but naturally regenerated radioactive nuclei, eg 14C (radio-carbon) natural life times O(1s)<  <age-of-universe all types of decays present

29. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 29 146 144 142 140 138 136 134 132 130 128 126 93 91 89 87 85 83 81 79 238 U series αα α α α α α αα β- Neutrons 238 U 234 Th 234 U 206 Pb 210 Tl 210 Po 214 Pb 214 Po 218 Po 222 Rn 226 Ra 230 Th Protons

30. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 30 End of Lecture 3

31. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 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  -decays (off syllabus)

32. 0 Mev +500 MeV +1000 MeV -500 Mev -1000 Mev -1500 Mev A=const @ 58 N Z A=58 (Fe58, Ni58) A=const. N=Z Z=92 (U) Proton Magic Numbers N=Z Z=92 (Uranium) SEMF total E bind E bind -contours Magic Proton Numbers Magic Neutron Numbers Nuclides N=160 Z=110 Neutron Magic Numbers slide 3a

33. N Z ZN  stable longlived (>10 9 yrs) Even 15511 EvenOdd533 OddEven503 Odd 45 even A N=Z E bind /A-contours -MeV Even A stable nuclides Odd A stable nuclides odd-even summary SEMF E bind /A Nuclides slide 3b

34. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 34 Q: How does nucleus “move” along constant A? A: Via  -decay: nucleus emits e -, e =(  -) or e +, e  (  +)  M nucl > m e for  - &  M nucl > m e for  +  M atom > 0 for  - &  M atom >2m e for  + or via EC: like (  +) but swallow atomic e - instead instead of emitting e +  M nucl >-m e or  M atom >0 Note:  M x = M x (mother) – M x (daughter) Observe: e +- has continuous energy spectrum maximum of E kin (e +- ) = Q  -E recoil (daughter) ≈ Q  1<Q  /MeV<15 e carries the rest of Q  solving long standing puzzle of energy conservation in  -decays 3.3  -decay or Into the valley of stability along the const. A direction slide 9a

35. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 35 Q: How does nucleus “move” along constant A? A: Via  -decay: nucleus emits e -, e =(  -) or e +, e  (  +)  M nucl > m e for  - &  M nucl > m e for  +  M atom > 0 for  - &  M atom >2m e for  + or via EC: like (  +) but swallow atomic e - instead instead of emitting e +  M nucl >-m e or  M atom >0 Note:  M x = M x (mother) – M x (daughter) Observe: e +- has continuous energy spectrum maximum of E kin (e +- ) = Q  -E recoil (daughter) ≈ Q  1<Q  /MeV<15 e carries the rest of Q  solving long standing puzzle of energy conservation in  -decays 3.3  -decay or Into the valley of stability along the const. A direction Z N valley of stability unstable to β+ decay (or K capture) unstable to β- decay slide 9b

36. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 36 3.3  -decay (energetics) What can SEMF say about a-decay? Decay is possible if M nucl (N,Z)-M nucl (N-2,Z-2)>M(  ) SEMF as function of A only (dA=dN+dZ & dN=dZ) and ignoring pairing term (odd A only) Slope in E bind /A (A≥120) is 7.7*10 -3 MeV slide 18

37. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 37 3.3  -decay (energetics) What can SEMF say about a-decay? Decay is possible if M nucl (N,Z)-M nucl (N-2,Z-2)>M(  ) SEMF as function of A only (dA=dN+dZ & dN=dZ) and ignoring pairing term (odd A only) E bind /A [MeV] 7.7x10-3 MeV slide 18

38. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 38 3.3  -decay (the 3-odd ones out) SEMF says they should not exist It is a shell effect, off syllabus slide 20a

39. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 39 3.3  -decay (the 3-odd ones out) SEMF says they should not exist It is a shell effect, off syllabus slide 20b

40. 11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 40 if E<2m e could do internal conversion (a’la Auger in atomic) 3.3  -decay Q: What if J=0 nucleus needs to loose Energy A: It can’t loose it via  it could loose it via pair-creation if E>2m e (virtual  does not have to have S=1 and converts to pair in J=0 1 S 0 state) e + e -  nucl. e -  nucl. emitted positron absorbed atomic electron emitted electron additional information off syllabus