1

Alpha DecayBecause the binding energy of the alpha particle is so large (28.3 MeV), it is often energetically favorable for a heavy nucleus to emit an alpha particle

Nuclides with A>150 are unstable against alpha decay

Decay alpha particles are monoenergeticEα = Q (1-4/A)

α

α42

23793

24195

42

22

+→

+→ −−

NpAm

YX AZ

AZ

2

Alpha DecayTypical alpha energies are 4 < Eα < 8 MeV

But half-lives vary from 10-6s to 1017y!The decay probability is described by the Geiger-Nuttall law

log10λ = C – D/√Eλ is the transition probabilityC, D weakly depend on ZE is the alpha kinetic energy

The Geiger-Nuttall law can be derived using QM to calculate the tunneling probability

3

Alpha DecayGeiger-Nuttall law

4

Monoenergeticalphas

5

Common alpha sourcesSince dE/dx is so large for alpha particles the sources are prepared in thin layers

6

Beta Decayβ- decayβ- decay β+ decay Electron capture (EC)

β- decay is the most common type of radioactive decay

All nuclides not lying in the valley of stability can β-

decay β- decay is a weak interaction

The quark level Feynman diagram for β- decay is shown on a following slide We call this a semileptonic decay

epen ν−→enep ν+→

enpe ν→−

7

Beta Decay

8

Beta Decay

9

Beta Decay

Because beta decay is a three body decay, the electron energy spectrum is a continuum

10

Beta Decay

The Q value in beta decay is effectively shared between the electron and antineutrino

The electron endpoint energy is Q

( ) ( )

( ) ( )( )( ) ( )

( ) ( ) 2

maxmax

1,1,

21,,:!!

since

1,, isdecay for value

cmZAMZAMQnote

TTQ

keVTTTTTTQ

ZAMZAMQQ

e

e

ZAMeeZAM

−−−=

==

<+≈++=

+−=

+

−

++−

−

++

−

β

νβ

ννβ

β

β Note these areatomic masses

11

Electron Capture

Proton rich nuclei can undergo electron capture in addition to β+ decay

e- + p -> n + νEC can occur for mass differences < 2mec2

Most often a K or L electron is capturedEC will leave the atom in the excited stateThus EC can be accompanied by the emission of characteristic fluorescent x-rays or Auger electrons

e.g. 201Tl ->201Hg x-rays from EC was used in myocardial perfusion imaging

12

Characteristic X-rays

Nuclear de-excitationGamma ray emission Internal conversion (IC)

Atomic de-excitationx-ray emission Auger electron emission

Assume the K shell electron was ejectedL to K transition == Kα

M to K transition == Kβ

13

Characteristic X-rays

Simplified view

14

Auger ElectronsEmission of Auger electrons is a competitive process to x-ray emission

For Auger electrons e.g., EKLL = EK – EL1 –EL2

The Auger effect is more important in low Z (Z < 15) elements because the electrons are more loosely boundThe fluorescent yield is defined as the fraction of characteristic x-rays emitted from a given shell after vacancy

15

Characteristic X-rays and Auger Electrons

16

Beta SourcesMost beta sources also emit gamma raysLike alpha sources, beta sources must be thin because of dE/dx losses

17

Gamma DecayGammas (photons) are emitted when a higher energy nuclear state decays to a lower energy one

Alpha and beta decays, fission, and nuclear reactions often leave the nucleus in an excited stateNuclei in highly excited states most often de-excite by the emission of a neutron or protonIf emission of a nucleon is not energetically possible, gamma emission or internal conversion occursTypical gamma ray energies range from 0.1 to 10 MeV

18

Conversion ElectronsA competing process to gamma decay is internal conversion (IC)

In IC, the excitation energy of a nucleus is transferred to one of the electrons in the K, L, or M shells that are subsequently ejectedThe electrons are called conversion electronsIC is more important for heavy nuclei where the EM fields are large and the orbits of inner shell electrons are close to the nucleusInternal conversion is a competing process to gamma emission

19

Conversion ElectronsExamples are seen in the electron spectra shown in the two figures

The first figure is particularly simple and shows three conversion lines arising from the transfer of 1.4 MeV to electrons in the K, L, and M shells

Note that the conversion electrons are monenergetic

bexe EEE −=

20

Conversion Electrons

21

Conversion Electrons

22

Conversion CoefficientsGamma emission and IC competeλtotal = λgamma + λIC

Conversion coefficient α == λIC/λgammaWe can break this up according to the probabilities for ejection of K, L, and M shell electronsα = αK + αL + αM + …

23

Conversion CoefficientsIncrease as Z3

Decrease with increasing transition energyOpposite to gamma emission

Increase with the multipole orderMay compete with gamma emission at high L

Decrease with atomic shell number as 1/n3

Thus we expect K shell IC to be important for low energy, high multipolarity transitions in heavy nuclei

24

Conversion Coefficients

25

Conversion ElectronsCommon conversion electron sources

These sources are the only practical way to produce monoenergetic electrons in the keV-MeVrange in the laboratory

26

Gamma SourcesGamma sources usually begin with beta decay to put the nucleus in an excited state

Encapsulation of the source absorbs the electronTypical gamma energies are ~1 MeV

27

Gamma SourcesThere are also annihilation gammasIn β+ decay (e.g. 22Na) the emitted positron will usually stop and annihilate producing two 0.511 MeV gammas

γγ→−+ee

28

Neutron Sources

Nuclei that decay by neutron decay are rarely found in nature

Exotic nuclei can be produced in high energy processes in stars or at heavy ion acceleratorsThere are no direct neutron sources for the laboratory

Neutron sources can be produced using spontaneous fission or in nuclear reactions

29

Neutron SourcesSpontaneous fission

Many of the transuranic nuclides have an appreciable spontaneous fission decay probabilitye.g. 252Cf (most widely used since t1/2=2.6 years)Dominant decay is alpha emissionSpontaneous fission x32 smallerYield is 2.5x106 n/s per μg of material

30

Neutron Sources(α,n) sources

Make a n source using an α beamUsually the source consists of an alloy of the alpha emitter plus target (e.g. PuBe)

There is an accompanying large gamma decay component associated with these sources that make them troublesomeEven though the emitted alpha is monoenergetic, the alpha beam is not due to dE/dx losses

Hence the neutrons are not monoenergetic

nBenBeBe

nCBe

+→+

++→+

+→+

αα

αα

α

39

89

129

31

Neutron Sources