Alpha Decay Because 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 A X A 2 Y + 4 α Z Z 2 2 241 95 Decay alpha particles are monoenergetic E α = Q (1-4/A) Am 237 93 Np+ 4 2 α 1
Alpha Decay Typical alpha energies are 4 < E α < 8 MeV But half-lives vary from 10-6 s to 10 17 y! The decay probability is described by the Geiger-Nuttall law log 10 λ = 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 2
Geiger-Nuttall law Alpha Decay 3
Monoenergetic alphas 4
Common alpha sources Since de/dx is so large for alpha particles the sources are prepared in thin layers 5
Beta Decay β - decay β - decay n pe ν e β + decay p ne + ν e Electron capture (EC) pe nν e 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 6
Beta Decay 7
Beta Decay 8
Beta Decay Because beta decay is a three body decay, the electron energy spectrum is a continuum 9
Beta Decay The Q value in beta decay is effectively shared between the electron and antineutrino Q Q Q The electron endpoint energy is Q Q value for β β β β = = T = note!!: M M decay is ( A, Z ) M ( A, Z + 1) + T + T T + T ( ) since T < kev + ( A, Z + 1) e ν e ν M ( A, Z + 1) ( Te ) = ( T ) max ν max 2 Q + = M ( A, Z ) M ( A, Z 1) 2m c β Note these are atomic masses e + 10
Electron Capture Proton rich nuclei can undergo electron capture in addition to β + decay e - + p -> n + ν EC can occur for mass differences < 2m e c 2 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. 201 Tl -> 201 Hg x-rays from EC was used in myocardial perfusion imaging 11
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 α M to K transition == K β 12
Characteristic X-rays Simplified view 13
Auger Electrons Emission of Auger electrons is a competitive process to x-ray emission For Auger electrons e.g., E KLL = E K E L1 E L2 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 14
Characteristic X-rays and Auger Electrons 15
Beta Sources Most beta sources also emit gamma rays Like alpha sources, beta sources must be thin because of de/dx losses 16
Gamma Decay Gammas (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 17
Conversion Electrons A 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 18
Conversion Electrons Examples 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 E e = E ex E b Note that the conversion electrons are monenergetic 19
Conversion Electrons 20
Conversion Electrons 21
Conversion Coefficients Gamma emission and IC compete λ total = λ gamma + λ IC Conversion coefficient α == λ IC /λ gamma We can break this up according to the probabilities for ejection of K, L, and M shell electrons α = α K + α L + α M + 22
Conversion Coefficients Increase as Z 3 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/n 3 Thus we expect K shell IC to be important for low energy, high multipolarity transitions in heavy nuclei 23
Conversion Coefficients 24
Conversion Electrons Common conversion electron sources These sources are the only practical way to produce monoenergetic electrons in the kev-mev range in the laboratory 25
Gamma Sources Gamma 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 26
Gamma Sources There are also annihilation gammas In β + decay (e.g. 22 Na) the emitted positron will usually stop and annihilate producing two 0.511 MeV gammas + e e γγ 27
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 28
Neutron Sources Spontaneous fission Many of the transuranic nuclides have an appreciable spontaneous fission decay probability e.g. 252 Cf (most widely used since t 1/2 =2.6 years) Dominant decay is alpha emission Spontaneous fission x32 smaller Yield is 2.5x10 6 n/s per μg of material 29
(α,n) sources Neutron Sources Make a n source using an α beam Usually the source consists of an alloy of the alpha emitter plus target (e.g. PuBe) α + α + α + 9 9 9 Be Be Be 12 8 C Be + n + α + 3α + n n 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 30
Neutron Sources 31