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  1. Kinetics of Nuclear Decay Decay

  2. Nuclear Decay Types There are many unstable nuclei - in natureNuclear Science began with Henri Becquerel’s discovery (1896) of uranium radioactivityand man-made: N neutron numberZ proton number A=N+Z Types of decay: Nuclear Decay “weak” interactions

  3. 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

  4. Observing a Finite Lifetime of the 198Au g.s. E. Norman et al., Spectrum of b delayed 198Au g-rays 411.8 keV # 1 Nuclear Decay Spectrum of b delayed 198Au g-rays • decay of 198Hg exc. state is prompt: tg  tb 11 measurementsEach spectrum ran for 12 hours real time#11 taken 5 days after #1 # 11 411.8 keV

  5. Produce analog signal  Radiation Source Energy Slow Binary data to computer Amp PreAmp Data Acquisition System Detector Fast EnergyDiscriminator DE-Tag External Time reference signal t0 electron. Clock(TAC) Start Stop Produce timing signal  Time Trigger Activity DA(Dt)/DA(t0) Dt (Channel #) 1 i 0.1 . 0.01 0 100 200 300 400 Dt Measuring “Decay Curves”:Fast-Slow Signal Processing Principles Meas Measured: Energy and time of arrival Dt=t-t0 (relative to an external time-zero t0) for radiation (e.g., g-rays), energy discriminator to identify events (DA) in a certain energy interval DE by setting an identifier “tag.” Calibrate Dt axis channel #  time units (s, y,..)Watch that Dt-channel  t.

  6. Disintegration of Radioactive Sample 1 0.8 0.6 i 0.4 0.2 0 0 100 200 300 400 t i Sample Activity A(t)/A(0) time t time t 1 i 0.1 2 . 1 10 0 100 200 300 400 t Kinetics of Nuclear Decay: Logarithmic Decay Law

  7. Sum Radioactivity Genetically independent species: Sample with 2 components (N1, N2)  same type of radiation (g-rays) (N1)(N2) (l1)(l2) Nuclear Decay Decompose total decay curve l1, l2. Simultaneous fit or deduce constant l2 for“shallow” decay first

  8. Branching Decay Genetically dependent species: Sample depopulated by 2 decay paths (l1, l2) G l1l2 Nuclear Decay Partial decay rates/half lives: Identify radiation type i to measure partial decay rates/half lives.

  9. 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% Nuclear Beta Decay Experimental value correct order of magnitude but disagrees quantitatively 0.0 MeV 7Li Reason: yn≠ yp because of nuclear spin change 3-/2  1-/2 weaker magnetictransition

  10. Activation and Decay Competition production/decay for a species with N(t) members,Example of genetically related decay chain. N Irradiation of sample produces unstable species N.Constant rate of production P=const. Constant decay rate l Gain- Loss Equation P lN Generation of Sample Nuclear Decay Generation inefficient for t  3 t

  11. Genetically Related Decay Chain Gain and loss for i-th daughter N1 N2 l1 Coupled DEq. For populations Niof nuclei in chain l2 N3 Nuclear Decay Check by differentiation

  12. Activities and Equilibrium in Decay Chains Transitory/secular Equilibrium Nuclear Decay 200Pb: t1/2=21h  200Tl: t1/2=26h  200Hg teq

  13. Secular Equilibrium in a Decay Chain Gain and loss for i-th daughter Ni-1 Population Niof daughter i in chain Ni li-1 li Ni+1 Chain survives for long time, if l1 «li, for all i > 2. Only term survives. Nuclear Decay Secular Equilibrium

  14. Example: Determination of 238U Lifetime Extremely long lifetime of 238U  direct measurement difficult One of the decay products is 226Ra with t1/2 = 1620 a Relative abundance NU/NRa = 2.8 ·106 238U lU 226Ra lRa Secular Equilibrium Nuclear Decay

  15. Recoil Distance Doppler Shift Method Mean Lifetime Determination of the 106Cd Iπ= 2+1state, =d d Forward Backward Stopped Stopped Nuclear Decay

  16. Crystal Blocking Technique Principle of the crystal blocking technique. Heavy ions bombard a single-crystal target, form CN.CN fissions with lifetime ~10-18s. FF emitted in the plane of the target atoms (ψ=0) are blocked from reaching the detector. FF emitted from recoiling nuclei that survive long enough to move into a channel between the crystal planes (distance d) are detected with little energy loss. Thermal vibrations in the crystal determine the lower time limit for blocking. Nuclear Decay 238U+Ge @ E/A= 6.09 MeV Blocking dip observed for Z=124, FF 67<ZFF<85. The width of the dip depends on atomic number and kinetic energy of the fission fragment M. Morjean et al., Phys. Rev. Lett. 101, 072701 (2008)

  17. Applications of Nuclear Instruments and Methods Age Determination ( Dating ) Applications

  18. Age of Earth Nucl. Synth. years Halflives of Radio-Isotopes for Dating Applications a, b, b- : particles measured to identify fractional abundance of radioactive isotope, K: K electron capture R : measure series of several decay products

  19. Rb/Sr Dating of Rocks/Age of the Earth All rocky objects (planets, asteroids, meteorites) of solar system crystallized ≈ simultaneously (t=0) out of interstellar dust/nebula (supernova remnants). Undisturbed by erosion/transmutation R Applications Different minerals in meteorite containing different amounts of NP  different x Construct isochron Age of rock (since formation)

  20. Age of the Earth Age of Earth = 4.5·109 aMoon has similar age Applications Terrestrial volcanic activity dated: produces younger rocks

  21. (a) CE  Calibration of 14C Dating Methods Variation in 14C Production t-dependent flux of cosmic rays (solar cycles) t-dependent 14C production and intake Calibration: 14C-analyze yearly rings in trees of different ages (number and widths of rings), connect to fossils Errors in very old samples lead to underestimation of age (few hundred years). Applications

  22. Conventional method: b counting Direct 14C counting method: Accelerator Mass Spectroscopy  R10 -16 (10 5 a) Carbon Dating of Organic Objects n Measure 14C/12C ratio of sample at t Applications

  23. Activation and Decay Irradiate 51V with thermal neutrons, daughter b-decays to 52Cr* 52Cr* de-excites by g emission A(t)/P vs. t Nuclear Decay Fit Curve g intensity  activity