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 monoenergetic E = Q (1-4/A)

42

23793

24195

42

22

NpAm

YX AZ

AZ

2

Alpha DecayTypical alpha energies are 4 < E <

8 MeV But half-lives vary from 10-6s to 1017y!

The decay probability is described by the Geiger-Nuttall law log10λ = C – D/√E

λ is the transition probability C, D weakly depend on Z E 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

Monoenergetic alphas

5

Common alpha sources

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

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Beta Decayβ- decay

β- 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 enep

enpe

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

ZAMZAMQ

Q

e

e

ZAMeeZAM

Note these areatomic masses

11

Electron CaptureProton rich nuclei can undergo

electron capture in addition to β+

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

Most often a K or L electron is captured EC will leave the atom in the excited state Thus 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

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Characteristic X-rays

Nuclear de-excitation Gamma ray emission Internal conversion (IC)

Atomic de-excitation x-ray emission Auger electron emission

Assume the K shell electron was ejected L to K transition == K

M to K transition == K

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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 bound

The 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

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Beta SourcesMost beta sources also emit gamma raysLike alpha sources, beta sources must be

thin because of dE/dx losses

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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 state

Nuclei in highly excited states most often de-excite by the emission of a neutron or proton

If emission of a nucleon is not energetically possible, gamma emission or internal conversion occurs

Typical gamma ray energies range from 0.1 to 10 MeV

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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 ejected

The electrons are called conversion electrons

IC is more important for heavy nuclei where the EM fields are large and the orbits of inner shell electrons are close to the nucleus

Internal conversion is a competing process to gamma emission

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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

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Conversion CoefficientsGamma emission and IC compete

λtotal = λgamma + λIC

Conversion coefficient α == λIC/λgamma We can break this up according to the

probabilities for ejection of K, L, and M shell electronsα = αK + αL + αM + …

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Conversion Coefficients Increase as Z3

Decrease with increasing transition energy Opposite to gamma emission

Increase with the multipole order May 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

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Conversion Coefficients

25

Conversion ElectronsCommon conversion electron sources

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

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Gamma SourcesGamma sources usually begin with beta

decay to put the nucleus in an excited state Encapsulation of the source absorbs the

electron Typical gamma energies are ~1 MeV

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Gamma SourcesThere are also annihilation gammas In β+ decay (e.g. 22Na) the emitted

positron will usually stop and annihilate producing two 0.511 MeV gammas

ee

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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 accelerators

There are no direct neutron sources for the laboratory

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

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Neutron SourcesSpontaneous fission

Many of the transuranic nuclides have an appreciable spontaneous fission decay probability

e.g. 252Cf (most widely used since t1/2=2.6 years)

Dominant decay is alpha emission

Spontaneous fission x32 smaller Yield is 2.5x106 n/s per μg of

material

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Neutron Sources (,n) sources

Make a n source using an beam Usually 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 troublesome

Even though the emitted alpha is monoenergetic, the alpha beam is not due to dE/dx losses Hence the neutrons are not monoenergetic

nBe

nBeBe

nCBe

39

89

129

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Neutron Sources