Nuclear Reactions and Gamma Decays Exploration

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

2. 1- 1/2+ <10-14sec 130 days o 170Tm b- 77 MeV 2+ 0.57 nsec 1/2+ 0+ 0.084 MeV Lo 170Yb The electric dipole transition involves: where Yb and Yb* are both of even parity however r is odd. = 0 so this contribution vanishes The integrand is odd 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 carryingj = 1must haveP = -1 We write: E1 magnetic dipole radiation carryingj = 1must haveP = +1 We write: M1 Or in general: Ejor Mj

5. Photonj and P values are restricted by the following quantum rules: Jinitial = Jfinal + j Pinital =PfinalPg 1- 1- 1+ j=1 E1 M2 E1 M1 0+ 0+ 1+ P = 1 P = -1 Jinitial = j IfJfinal = 0 then for the specific case above right IfJfinal = Jinitial 0 then j=1 or 2

6. 3/2+ 5/2+ What g transitions are possible? M1notE1 Can proceed by either1+ 2+ 3+ 4+ dipole quadrupole octupole hexadecapole E2 M3 E4

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

8. 1- 1/2+ <10-14sec 130 days o 170Tm b- 77 MeV 2+ 0.57 nsec 1/2+ 0+ 0.084 MeV Lo 170Yb What are the dominant g transitions here?

9.   Notice ifJfinal = Jinitial= 0 then a transition byg radiation is not allowed! Why? 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 Te of the emitted electron depends on the electron binding energy, Be and the transition energy Ei-Ef Different atomic orbitals  different binding energies a given transition could produce any of several possible electron energies. Conversion electrons are thus labelled by the atomic shell from which they originated: K, L, and M. Energy level n sub-shells K-shell L-shell N-shell 1 2 4 s s,p s,p,d,f IfEi-Ef<Befor a particular shell, then electrons cannot be emitted from that shell.

13. It is possible to resolve the shell substructure, thus conversion electrons from the L shell can be labeled LI  , LII   , or LIII   , if they originated from the 2s1/2, 2p1/2 or 2p1/2atomic 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. The internal conversion coefficient, a  , is defined as the ratio of internal conversion decay probability to the g-decay probability The total decay probability is then

14. 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. 203Hg  203Tl K Internal conversion electrons Electron counting rate L Beta electrons M Electron emissions from the 203Hg to 203Tl decay, measured by A. H. Wapstra, et al., Physica 20, 169 (1954).

16. 203Hg decays to 203Tl by b emission, leaving the 203Tl in an electromagnetically excited state. Proceeding to the ground state by emitting a279.190 keVgamma 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 203Tl 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. LI 10,000 LII Electron counting rate 5,000 LIII At even higher resolution, the three L shells can be resolved. From C. J. Herrlander and R. L. Graham, Nucl. Phys. 58, 544 (1964).

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.