11 nov 2004, lecture 3 nuclear physics lectures, dr. armin reichold 1 lecture 3 nuclear stability,...

11 Nov 2004, Lecture 3

Nuclear Physics Lectures, Dr. Armin Reichold 1

Lecture 3

nuclear stability, decays and natural radioactivity


Nuclear Physics Lectures, Dr. Armin Reichold

2

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 -decay -decay -decay fission and the rest

3.4 Natural Radioactivity

3

A=58 (Fe58, Ni58)

A=const.

N=Z

Z=92 (U)

odd

A

even

AProtonMagic

Numbers

N

Z

• Even A stable nuclides

• Odd A stable nuclides

• Magic Proton Numbers

• Magic Neutron Numbers

• N=Z

• A=const @ 58

Neutron Magic

Numbers

• Z=92 (Uranium)

• SEMF binding energy

Z N stablelonglived (>109

yrs)

Even Even 155 11

Even Odd 53 3

Odd Even 50 3

Odd Odd 4 5

• odd-even summary

4

A=58 (Fe58, Ni58)

A=const.

N=Z

Z=92 (U)

odd

A

even

AProtonMagic

Numbers

N

Z

• Even A stable nuclides

• Odd A stable nuclides

• Magic Proton Numbers

• Magic Neutron Numbers

• N=Z

• A=const @ 58

Neutron Magic

Numbers

• Z=92 (Uranium)

• SEMF binding energy

Z N stablelonglived (>109

yrs)

Even Even 155 11

Even Odd 53 3

Odd Even 50 3

Odd Odd 4 5

• odd-even summary



5

3.2 The Valley of Stability



6

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 shell model)

But what about simple Ebind per nucleon



7

3.2 The Iron Mountain



8

3.2 The Iron Mountain Binding Energy vs. A for odd-A nuclei

Iron

Not smooth because Z not smooth function of A

9

3.3 Classification of Decays

Neutrons

Pro

ton

s

-decay: • emission of Helium nucleus• ZZ-2• NN-2• AA-4

--decay• emission of e- and • ZZ+1• NN-1• A=const

-decay• emission of • Z,N,A all const

+-decay• emission of e+ and • ZZ-1• NN+1• A=const

EC

Electron Capture (EC)• absorbtion of e- and emiss

• ZZ-1• NN+1• A=const



10

Q: How does nucleus “move” along constant A? A: Via -decay: nucleus emits e-,e=(-) or e+,e(+)

Mnucl > me for - & Mnucl > me for + Matom> me for - & Matom>2me for +

or via EC: like (+) but swallow atomic e- instead instead of emitting e+

Mnucl>-me or Matom>0 Note: Mx = Mx(mother) – Mx(daughter) Observe: e+- has continuous energy spectrum

maximum of Ekin(e+-) = Q-Erecoil(daughter) ≈ Q 1<Q/MeV<15 e carries the rest of Qsolving long standing puzzle of energy

conservation in -decay

3.3 -decay or

Into the valley of stability along the const. A direction

Z

N

valle

y of s

tabili

ty

unstable to β+ decay

(or K capture)

unstable to β- decay

valley



11

Q: How does nucleus “move” along constant A? A: Via -decay: nucleus emits e-,e=(-) or e+,e(+)

Mnucl > me for - & Mnucl > me for + Matom> me for - & Matom>2me for +

or via EC: like (+) but swallow atomic e- instead instead of emitting e+

Mnucl>-me or Matom>0 Note: Mx = Mx(mother) – Mx(daughter) Observe: e+- has continuous energy spectrum

maximum of Ekin(e+-) = Q-Erecoil(daughter) ≈ Q 1<Q/MeV<15 e carries the rest of Qsolving long standing puzzle of energy

conservation in -decay

3.3 -decay or

Into the valley of stability along the const. A direction


12

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 Ebox=n2h2/8mea2 = 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

np



13

3.3 -decay and SEMF

Aa

A

ZNa

A

ZaAaAaE pacsvBind

1)( 2

31

23

2

av=15.56 MeV ac=0.697 MeV

as=17.23 MeV aa=23.285 MeV

e=even o=odd

+ 12 MeV (e-e)

ap= 0 MeV (o-e or e-o)

- 12 MeV (o-o)

13

2 84 0bind c A

AA

dE a aa Z

dZ AA

•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. ap=0 (even-odd or odd-even)



14

3.3 -decay and SEMF

evaluate: A2/3<< 133 Z≈A/2≈N 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

45Rh ,even-odd, stable A=106; Z=46; N=60: 106

46Pd ,even-even, stable A=105; Z=46; N=59: 105

46Pd ,odd-even, stable A=105; Z=45; N=60: 105

45Rh ,odd-even, meta-stable, decays via - to 106

46Pd in 38h

11 232

3 1 12 4 2 133.63

c

a

aA A AZ A

a

This yields:



15

3.3 -decay and SEMF Odd A:

single parabolic minimum only one -stable nucleus

for each odd A nearly only single -

decays double -decay is 2nd

order weak process and very rare 58565452

Te I Xe Cs Ba La Ce Pr

β-

β-

β-

β-EC

β+

Odd A. A=135

Single parabolaeven-odd and odd-even



16

3.3 -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 48464442Mo Tc Ru Rh Pd Ag Cd

β+

β+

β+

β-

β-

β-

Even A. A=102

Two parabolae separated by 2δ,odd-odd and even-even


17

3.3 -decay and SEMF Consequence: 2 or more even A, 1 or no odd A



18

3.3 -decayObservation: 232

90Th emits with Ekin≈4 MeV

RTh≈1.2*2321/3 fm = 7.36 fm has Epot(RTh)=24 MeV has negative kinetic energy

up to R=8*RTh

Conclusion: must tunnel out of the

nucleus half lifes should have exp(Ekin)

dependence (true over 24 orders, see Geiger-Nuttal plot)



19

3.3 -decay

Neutrons

Protons

Alphas

Ebind(42)=28.3 MeV > 4*6MeV

Esep≈6MeV per nucleon for heavy nuclei



20

3.3 -decay(energetics)

What can SEMF say about a-decay? Decay is possible if Mnucl(N,Z)-Mnucl(N-2,Z-2)>M() SEMF as function of A only (dA=dN+dZ & dN=dZ) and

ignoring pairing term (odd A only)

Z=2,A=4 ( , ) ( 2, 4)bind bind bind bindE E E Z A E Z A

Slope in Ebind/A (A≥120) is 7.7*10-3 MeV

criti3 cal

328.3 MeV 4 7.7 10 MeV

7.075 MeV 7.7 10 M AeV 151

bind

bind

EA

A

EA

A

28.3 MeV 4 4 4 bindbind bind bind

binddZ dN

d E AdE dE EE A

dA dA dA A

Ebind/A[MeV]

slope:7.7x10-3 MeV



21

3.3 -decay(energetics)

What can SEMF say about a-decay? Decay is possible if Mnucl(N,Z)-Mnucl(N-2,Z-2)>M() SEMF as function of A only (dA=dN+dZ & dN=dZ) and

ignoring pairing term (odd A only)

Z=2,A=4 ( , ) ( 2, 4)bind bind bind bindE E E Z A E Z A

Slope in Ebind/A (A≥120) is 7.7*10-3 MeV

criti3 cal

328.3 MeV 4 7.7 10 MeV

7.075 MeV 7.7 10 M AeV 151

bind

bind

EA

A

EA

A

28.3 MeV 4 4 4 bindbind bind bind

binddZ dN

d E AdE dE EE A

dA dA dA A



22

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*109

years) Note: Shell effects O(1 MeV) make the life times

of –emitters deviate by several orders of magnitude from SEMF predictions



23

3.3 -decay

(the 3-odd ones out)

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



24

3.3 -decay(the fine print)

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



25

3.3 -decay Very similar to atomic physics

transitions E

atomic<100 keV ; Enuclear<O(1 MeV)

But: heavy nuclear rotational states can have E

nuclear, rot<O(10 keV) 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



26

if E<2me 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>2me (virtual does not have to have S=1 and converts to pair in J=0 1S0 state)

e+

e-

nucl.

e-

e-

nucl.

emitted positron

absorbed atomic electron

emitted electron

emitted electron


27

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/A>18 (9842Mo) could

But does not because ……



28

3.3 Fission and the Rest

Z2/A

log

10(

/1 y

ear)

-5

0

5

10

15

It would take forever

Fission is mainly asymmetric



29

3.3 Fission and the Rest Fission barrier

changes with Z2/A (and via SEMF this is a change with A)

Thus the huge lifetime variation observed

Beyond Z2/A=43 (which does not exist) there would be no fission barrier

Epot [MeV]



30

3.3 Fission and the Restt=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(-Efis)

excited nuclei (n-capture) decay much faster via fission (reactors)



31

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)



32

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*1019 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



33

146144142140138136134132130128126

93

91

89

87

85

83

81

79

238U series

αα

α

α

α

α

α

αα

β-

β-

β-

β-

β-

β-

β-

Neutrons

238U

234Th

234U

206Pb

210Tl

210Po

214Pb

214Po218Po

222Rn

226Ra

230Th

Pro

tons

11 nov 2004, lecture 3 nuclear physics lectures, dr. armin reichold 1 lecture 3 nuclear stability,...

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