Alpha Decay

1. 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 • Decay alpha particles are monoenergetic • Ea = Q (1-4/A)

2. Alpha Decay • Typical alpha energies are 4 < Ea< 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 Decay • Geiger-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

6. Beta Decay • β- 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

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 Note these are atomic masses

11. Electron Capture • Proton rich nuclei can undergo electron capture in addition to β+ decay • e- + p -> n + 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

12. 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 == Ka • M to K transition == Kb

13. Characteristic X-rays • Simplified view

14. Auger Electrons • Emission 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

16. Beta Sources • Most beta sources also emit gamma rays • Like alpha sources, beta sources must be thin because of dE/dx losses

17. 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

18. 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

19. 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 • Note that the conversion electrons are monenergetic

20. Conversion Electrons

21. Conversion Electrons

22. Conversion Coefficients • Gamma 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 electrons • α = αK + αL + αM + …

23. 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

24. Conversion Coefficients

25. 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

26. 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

27. Gamma Sources • There are also annihilation gammas • In β+ decay (e.g. 22Na) the emitted positron will usually stop and annihilate producing two 0.511 MeV gammas

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 accelerators • There are no direct neutron sources for the laboratory • Neutron sources can be produced using spontaneous fission or in nuclear reactions

29. Neutron Sources • Spontaneous 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

30. Neutron Sources • (a,n) sources • Make a n source using an a 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

31. Neutron Sources