1. Week 11 Lecture 27 Monday, Oct 30, 2006 NO CLASS : DPF06 conference Lecture 28 Wednesday, Nov 1, 2006 GammaDecaysGammaDecays Lecture 29 Friday, Nov 3, 2006 MossbauerEffectMossbauerEffect Week 12 Lecture 30 Monday, Nov 6, 2006 MossbauerEffect Nuclear Reactions Lecture 31 Wednesday, Nov 8, 2006 Nuclear Reactions Lecture 32 Friday, Nov 10, 2006 Nuclear Reactions Cross SectionsMossbauerEffectNuclear Reactions Cross Sections Week 13 Lecture 33 Monday, Nov 13, 2006 Nuclear Fission Lecture 34 Wednesday, Nov 15, 2006 Nuclear Fission Lecture 35 Friday, Nov 17, 2006 Fission Reactors Nuclear Fission Fission Reactors Week 14 Lecture 36 Monday, Nov 20, 2006 EXAM 3 Thanksgiving Break Wed, Nov 22-Fri, Nov 24

2. 11 170 Tm 130 days 0+ 170 Yb 2+ 0.57 nsec  0.084 MeV 77 MeV 1/2+ <10  14 sec oo oo The electric dipole transition involves: where  Yb and  Yb* are both of even parity however r is odd. The integrand is odd = 0 so this contribution vanishes forces us to look at the contribution of magnetic poles or higher order electric poles

3. Emitted radiation is characterized by its angular momentum quantum number j and parity P. a photon can carry away even or odd parity! electric radiation: P = (  1) j magnetic radiation: P =  (  1) j Reflecting the pseudovector nature of B-field sources.

4. Note: electric dipole radiation carrying j = 1 must have P =  1 We write: E1 magnetic dipole radiation carrying j = 1 must have P =  1 We write: M1 Or in general: Ej or Mj

5. Photon j and P values are restricted by the following quantum rules: J initial = J final + j P inital = P final P  1+ 0+ 11 11 1+ If J final = 0 then J initial = j j=1j=1 P = 1 P =  1 M1 E1 If J final = J initial  0 then j =1 or 2 E1 M2 for the specific case above right

6. 3/2+ 5/2+ What   transitions are possible? Can proceed by either 1+ 2+ 3+ 4+ dipole quadrupole octupole hexadecapole M1 not E1 E2 M3 E4

7. Dipole Quadrupole Octupole Relative Transition Rate W sp (sec -1 )

8. 11 170 Tm 130 days 0+ 170 Yb 2+ 0.57 nsec  0.084 MeV 77 MeV 1/2+ <10  14 sec oo oo What are the dominant   transitions here?

9. Notice if J final = J initial = 0 then a transition by  radiation is not allowed! Why? 00 0+ But what if that’s the last step to the ground state? Will the nucleus sit in that excited state forever? 

10. Radial probability distributions for a particle in a Coulomb potential (hydrogenic atom). Note the probability vanishes at r=0.

11. Internal Conversion competes with gamma emission. the multipole electric fields of the nucleus may interact with orbital electrons with enough energy to eject them from the atom. not a gamma ray knocking out an atomic electron not beta decay (this electron already existed) (the electron in beta decay is produced by the decay of a neutron)

12. The T e of the emitted electron depends on the electron binding energy, B e and the transition energy E i -E f Different atomic orbitals  different binding energies a given transition could produce any of several possible electron energies. (3.30)(3.30) (3.31)(3.31) (3.32)(3.32) If E i -E f < B e for a particular shell, then electrons cannot be emitted from that shell. Energy level n sub-shells Conversion electrons are thus labelled by the atomic shell from which they originated: K, L, and M. 124124 K-shell L-shell N-shell s s,p s,p,d,f

13. The internal conversion coefficient, , is defined as the ratio of internal conversion decay probability to the  -decay probability (3.30)(3.30) The total decay probability is then (3.31)(3.31) (3.32)(3.32) It is possible to resolve the shell substructure, thus conversion electrons from the L shell can be labeled L I, L II, or L III, if they originated from the 2s 1/2, 2p 1/2 or 2p 1/2 atomic orbitals, respectively. The vacancy left in the atomic shell is filled by one from a higher shell and the difference in energy is released as an X-ray.

14. (3.30)(3.30) (3.31)(3.31) The internal conversion coefficient depends on the energy of the transition, the atomic number of the nucleus and the principal atomic quantum number in approximately the following way: Internal conversion coefficients are larger for magnetic transitions than electric transitions, and increase with increasing multipolarity.

15. Electron emissions from the 203 Hg to 203 Tl decay, measured by A. H. Wapstra, et al., Physica 20, 169 (1954). Beta electrons K L M Internal conversion electrons Electron counting rate 203 Hg  203 Tl

16. 203 Hg decays to 203 T l by  emission, leaving the 203 Tl in an electromagnetically excited state. Proceeding to the ground state by emitting a 279.190 keV gamma ray, is forbidden. The internal conversion process can interact with any of the orbital electrons. This results in a spectrum of internal conversion electrons superimposed upon the electron energy spectrum of the beta emission. The energy yield of this electromagnetic transition is 279.190 keV, so the ejected electrons will have that energy minus their binding energy in the 203 Tl daughter atom.

17. At higher resolution, the internal conversion electrons from the L, M and N shells can be resolved. Z. Sujkowski, Ark. Fys. 20, 243 (1961).

18. At even higher resolution, the three L shells can be resolved. From C. J. Herrlander and R. L. Graham, Nucl. Phys. 58, 544 (1964). Electron counting rate 10,000 5,000 LILI L II L III

19. The resolution in electron detection is good enough that internal conversion electron spectra can be used to study the binding energies of the electrons in heavy atoms. In this case, the measured electron energies can be subtracted from the transition energy as indicated by the gamma emission, 279.190 keV. Binding energies for 203 Tl K85.529 keV LILI 15.347 keV L II 14.698 keV L III 12.657 keV M3.704 keV