Beta-Decay

1. Survey Beta-Decay Nuclear Beta Decay Super Kamiokande (Japan) neutrino detector 50,000 t H2O) Cerenkov counter, 11,200 PMTs

2. g a b Magnet Active sample Electron/Beta Spectrometry Iron-free “Orange” spectrometer with axially sym-metric toroidal magnetic field inside current loops Chadwick (1914): Some nuclides emit e- with continuous energy spectra “b rays” 60 Helmholtz coils every 60 arranged in a circle. Current: ~1000 A Setup used in nuclear reaction studies (counters for coincident particles & g-rays) Different energies correspond to different locations on focal detector Radioactive Ra sample in a magnetic field b= e-. Observed later in decay of neutrons and excited nuclei (internal conversion) or nuclear transmutation (bdecay). Nuclear Beta Decay Energy spectrum constructed from momentum spectrum

3. Electron and Beta Spectroscopy Nuclei can deexcite via photon, (e+, e-) , or atomic-electron emission (internal conversion) Conversion electron line spectrum for decay of 203Tl state E*=280-keV Electron binding energies in 203Tl E* Ee=E*-EB < 280keV Nuclei transmute in b decay Nuclear Beta Decay b spectrum is continuous up to Ee ≈ Q Fixed differences Q and |DI| carried by more than one decay product  additional “neutrinos”

4. The Neutrino Hypothesis Dilemma: continuous e- spectrum would violate energy/momentum balance in 2-body process.Wolfgang Pauli (1930) postulates unobserved, neutral particle (“neutron” later =“neutrino” (Fermi)) Nuclear Beta Decay

5. Evidence for Neutrino • Fixed decay energy (Q value Dmc2) • but continuous e- spectrum • e- has spin Ie=1/2 • but |Ifinal-Iin|= 0, 1 typically • Electron capture produces recoil momentum • Direct evidence by neutrino-induced reaction e- Recoil Experiment com TOF distance Nuclear Beta Decay Auger e- Detector 37Ar gas cell Recoil Detector

6. Direct Evidence for Neutrino Savannah River reactor experiment(fission fragments decay 900 hrs with reactor on 250 hrs reactor off LSc (Cd) tanks Target tanksH2O Reines Cowan Experiment: s= 7·10-19b prompt e+-delayed capture g coincidences Nuclear Beta Decay

7. Fermi Theory of b Decay Simple example: single nucleon orbiting core of paired nucleons captures atomic 1s electron. p n EC core core ne e- initial, final s.p. nuclear states Fermi’s Golden Rule (Pauli) 1st order “Perturbation Theory” for if Density of final states per unit energy ME of weak interaction H Nuclear Beta Decay GF: coupling constant, : Isospin raising operator d : delta distribution Weak Interaction Hamiltonian (point-like)

8. Weak Transition Matrix Elements Lepton wave functions vary weakly over nuclear volume  r r 104fm 104fm 5 fm 5 fm Nuclear Beta Decay =1, per def =1(allowed tr)

9. Fermi Transition ME Hydrogen-like e- wave function Plane-wave ne wave function Normalization volume, drops out in final calculations Nuclear Beta Decay Fermi transitions (“super-allowed”): No change in I, p For Pif need to evaluate density r(Ef) of final states:neutron-neutrino relative phase space

10. Neutrino Phase Space r=# final (n, n) states at energy Ef EC: Ef ≈ En neglect nuclear recoil energy Uncertainty Relation Nuclear Beta Decay Use experimental data for 7Be EC decay to determine GFGF ≈ 100 eV fm3. More exact average over many data sets:GF ≈ 88 eV fm3

11. Branching in EC b Decay n phase space depends on Q = Emax rate l increases with Emax 0.86 MeV 7Be EC 12% 0.48 MeV EC 88% Experimental value correct magnitude but disagrees quantitatively 0.0 MeV 7Li Nuclear Beta Decay Reason: yn≠ yp because of nuclear spin change 3-/2  1-/2 “forbidden” transition

12. Shape of the b± Spectrum Beta decay other than EC  3-body final stateNeglect nuclear recoil energy. Nuclear Beta Decay

13. Shape of b± Spectrum/Coulomb Correction Relativistic momentum-energy relation Should use Coulombye (r) ≠ plane wave. Electron cloud acts as barrier for e+. Nonrelativistic numerical correction factor (Fermi function) b- Z=0 b+ Nuclear Beta Decay Barrier effect

14. Total b± Decay Rate Seek method to systematize data: Unit conversion Universal numerical function, independent of spectrum  Tables Nuclear Beta Decay

15. b± Decay ft-Values Experimental task: Emax, and t1/2 combination  nuclear matrix element Large ft: slow transitions, small|Hfi|2 6·1014 y 1s “Super allowed” b transitions: Large matrix elements, small ft observed only for light nuclei (“mirror nuclei”) and DI=0,±1 Frequency of ft Values Nuclear Beta Decay super allowed p n allowed 1st forbidden “Allowed” b transitions: DI=0,±1 Meyerhof, 1967

16. Nuclear Beta Decay

17. Kurie/Fermi Plot Kurie plot gives extrapolation to Emax of electron spectrum 64Cu b+ and b- Decays • Validity of Kurie Plot • |Hfi| ≠ f(Ee) • DI = 0 (allowed transitions) • mnc2≈ 0 eV • For DI ≠ 0  additional correction factors • Kurie plots for forbidden transitions Nuclear Beta Decay Owen et al. PR 76, 1726 (1949)

18. Neutrino Mass Effect Correct decay energy for mnc2: mn≠ 0 deviations of Kurie plot from linearity at end point. No direct evidence for mnc2≠ 0 Indirect evidence (neutrino oscillations) mnc2 > 0.1 eV Kurie Plot 3H b - Decay Nuclear Beta Decay Ee (keV)

19. Forbidden b± Decays Account for finite nuclear size: Momentum transfer off center  orbital angular momentum/parity transfer e- p R Additional effects: relativistic wave function (v/c~0.1) 36Cl Kurie Plot allowed decay 36Cl Kurie Plot 1st forbidden decay Kurie plots for forbidden transitions have additional correction factors Use to determine degree of forbiddeness Nuclear Beta Decay Ee (keV) Ee (keV)

20. Selection Rules for b± Decays Allowed transitions (=point nucleus) e- p Spin couplings of e-n pair: singlet/triplet Allowed Fermi transitions R Allowed Gamov-Teller GT (spin-flip) transitions Nuclear Beta Decay Forbidden Fermi/GT transitions

21. Fermi’s Neutrino Hypothesis Enrico Fermi (1934): Adapt Dirac’s elm field theory to weak interactions. Weak (beta-decay-type) interaction is similar to elm interaction between currents. Range of weak interaction is rWI≈ zero (relm ) Electromagnetic Current-Current Interactions Nuclear Beta Decay Fermi’s theory accepted as working hypothesis for weak interactions. Neutrino properties predicted: spin=1/2, zero charge, zero mass. Directly observed: 1956(Science)/1959(PR) by Fred Reines & Clyde Cowan

22. b- b+EC b- to K-hole Bethge, Kernphysik Elementary Modes of b Decay Fermi’s zero-range (point-like) weak interaction, coupling constant GF All neutrinos have small masses and m(only upper limits known) Nuclear bdecay and electron capture In energetics of decay, account for electrons. Mass tables apply to neutral atoms. Example: EC “recycles” e- b+ decay of p produces ion Nuclear Beta Decay

23. mc2 odd-A isobarsD = 0 b+ b- b- b+ Z  ZA Beta Decays of Odd-A and Even-A Nuclei Expand around ZA: Mass parabola bottom of valley Nuclear Beta Decay

24. 1 extra e+1 extra e- Energetics of b Decay Beta decay and EC (K)-capture Qb>0exotherm 5 1 Mass balance: Nuclear Beta Decay Decay Q-value smaller by 2mec2 for b+ decay than for b-

25. 3H Kurie Plot Solid line corresponds to mnc2=100 keV Nuclear Beta Decay

26. Allowed and Forbidden b Decays 36Cl Kurie Plot allowed decay 36Cl Kurie Plot 1st forbidden decay Nuclear Beta Decay Ee (keV)

27. Double b Decay Nuclear Beta Decay

28. Parity Violation in b Decay Light Guide • Anisotropy • a equatorial counter • b polar counter Pumping Inlet Polar NaI Counter Count Rate/Count Rate warm Anthracite Scintillator • Anisotropy average of both counters, both field polarities Sample Ce/Mg Nitrate Container Equatorial NaI Counter eg b Anisotropy Nuclear Beta Decay Count Rate/Count Rate warm t (min)