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

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

58 N Z 0 Mev +500 MeV MeV -500 Mev Mev 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 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

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

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

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

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

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

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

11 Nov 2004, Lecture  -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 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 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -decay and SEMF a v =15.56 MeVa c =0.697 MeV a s =17.23 MeV a a = 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)

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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: Rh,even-odd, stable A=106; Z=46; N=60: Pd,even-even, stable A=105; Z=46; N=59: Pd,odd-even, stable A=105; Z=45; N=60: Rh,odd-even, meta-stable, decays via  - to Pd in 38h yielding:

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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 Te I Xe Cs Ba La Ce Pr β- EC β+ Odd A. A=135 Single parabola even-odd and odd-even

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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 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

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

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -decay Observation: 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

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

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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

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

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

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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

11 Nov 2004, Lecture 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 ( Mo) could decay … … but does not because …

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

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 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]

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold Fission and the Rest t=0 t≈ s t> 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)

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold 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)

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

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

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

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)

0 Mev +500 MeV MeV -500 Mev Mev Mev 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

N Z ZN  stable longlived (>10 9 yrs) Even 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

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

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

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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

11 Nov 2004, Lecture 3Nuclear Physics Lectures, Dr. Armin Reichold  -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

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

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

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