1 / 26

Alpha Decay

Alpha Decay. Readings Nuclear and Radiochemistry: Chapter 3 Modern Nuclear Chemistry : Chapter 7 Energetics of Alpha Decay Theory of Alpha Decay Hindrance Factors Heavy Particle Radioactivity Proton Radioactivity Identified at positively charged particle by Rutherford

Télécharger la présentation

Alpha Decay

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.


Presentation Transcript

  1. Alpha Decay • Readings • Nuclear and Radiochemistry: Chapter 3 • Modern Nuclear Chemistry: Chapter 7 • Energetics of Alpha Decay • Theory of Alpha Decay • Hindrance Factors • Heavy Particle Radioactivity • Proton Radioactivity • Identified at positively charged particle by Rutherford • Helium nucleus (4He2+) based on observed emission bands • Energetics • Alpha decay energies 4-9 MeV • Originally thought to be monoenergetic, fine structure discovered • AZ(A-4)(Z-2) + 4He + Qa

  2. Fine Structure for 228Th decay • Different alpha decay energies for same isotope • Relative intensities vary • Coupled with gamma decay

  3. Energetics • Over 350 artificially produced alpha emitting nuclei • Alpha energy variations used to develop decay schemes • All nuclei with mass numbers greater than A of 150 are thermodynamically unstable against alpha emission (Qα is positive) • However alpha emission is dominant decay process only for heaviest nuclei, A≥210 • Energy ranges 1.8 MeV (144Nd) to 11.6 MeV (212mPo) • half-life of 144Nd is 5x1029 times longer then 212mPo Alpha decay observed for negative binding energies

  4. Energetics • Q values generally increase with A • variation due to shell effects can impact trend increase • Peaks at N=126 shell • For isotopes decay energy generally decreases with increasing mass • 82 neutron closed shell in the rare earth region • increase in Qα • α-decay for nuclei with N=84 as it decays to N=82 daughter • short-lived α-emitters near doubly magic 100Sn • 107Te, 108Te, 111Xe • alpha emitters have been identified by proton dripline above A=100

  5. Alpha Decay Energetics • Q value positive for alpha decay • Q value exceeds alpha decay energy • maTa = mdTd • md and Td represent daughter • From semiempirical mass equation • emission of an α-particle lowers Coulomb energy of nucleus • increases stability of heavy nuclei while not affecting the overall binding energy per nucleon • tightly bound α-particle has approximately same binding energy/nucleon as the original nucleus • Emitted particle must have reasonable energy/nucleon • Energetic reason for alpha rather than proton • Energies of alpha particles generally increase with atomic number of parent

  6. Energetics • Calculation of Q value from mass excess • 238U234Th + a + Q • Isotope Δ (MeV) 238U 47.3070 234Th 40.612 4He 2.4249 • Qa=47.3070 – (40.612 + 2.4249) = 4.270 MeV • Q energy divided between the α particle and the heavy recoiling daughter • kinetic energy of the alpha particle will be slightly less than Q value • Conservation of momentum in decay, daughter and alpha are equal rd=r • recoil momentum and the -particle momentum are equal in magnitude and opposite in direction • p2=2mT where m= mass and T=kinetic energy • 238Ualpha decay energy

  7. Energetics • Kinetic energy of the emitted particle is less than Coulomb barrier α-particle and daughter nucleus • Equation specific of alpha • Particles touching • For 238 U decay • Alpha decay energies are small compared to the required energy for the reverse reaction • Alpha particle carries as much energy as possible from Q value, • For even-even nuclei, alpha decay leads to the ground state of the daughter nucleus • as little angular momentum as possible • ground state spins of even-even parents, daughters and alpha particle are l=0

  8. Energetics • Some decays of odd-A heavy nuclei populate low-lying daughter excited states that match spin of parent • Leads to fine structure of alpha decay energy • Orbital angular momentum of α particle can be zero • 83% of alpha decay of 249Cf goes to 9th excited state of 245Cm • lowest lying state with same spin and parity as parent • Long range alpha decay • Decay from excited state of parent nucleus to ground state of daughter • 212mPo • 2.922 MeV above 212Po ground state • Decays to ground state of 208Pb with emission of 11.65 MeV alpha particle • Systematics result from • Coulomb potential • Higher mass accelerates products • larger mass • daughter and alpha particle start further apart • mass parabolas from semiempirical mass equation • cut through the nuclear mass surface at constant A • Explains beta decay in decay chain

  9. Mass parabolas: 235U decay series Beta Decay to Energy minimum, then Alpha decay to different A Branched decay observed (red circles)

  10. Alpha decay theory • Distance of closest approach for scattering of a 4.2 MeV alpha particle is ~62 fm • Distance at which alpha particle stops moving towards the daughter • Repulsion from Coulomb barrier • An alpha particle should not get near the nucleus • Alpha particle should be trapped behind a potential energy barrier Vc Alpha decay energy

  11. Alpha decay theory • Wave functions are only completely confined by potential energy barriers that are infinitely high • With finite size barrier wave function has different behavior • main component inside the barrier • finite piece outside barrier • Tunneling • classically trapped particle has component of wave function outside the potential barrier • Some probability to go through barrier • Closer the energy of the particle to the top of the barrier more likely the particle will penetrate barrier • Increase probability of barrier penetration • Higher alpha decay energy, higher probability to penetrate barrier • Shorter half life with higher alpha decay energy

  12. Alpha Decay Theory • Geiger Nuttall law of alpha decay • Log t1/2=A+B/(Qa)0.5 • constants A and B have a Z dependence. • simple relationship describes the data on α-decay • over 20 orders of magnitude in decay constant or half-life • 1 MeV change in -decay energy results in a change of 105 in the half-life

  13. Even-Even Nuclei (235U comparison)

  14. Expanded Alpha Half Life Calculation • More accurate determination of half life from Hatsukawa, Nakahara and Hoffman • Theoretical description of alpha emission based on calculating the rate in terms of two factors • rate at which an alpha particle appears at the inside wall of the nucleus • probability that the alpha particle tunnels through the barrier • a=P*f • f is frequency factor • P is transmission coefficient Outside of closed shells 78Z82; 100N126 82Z90; 100N126

  15. Alpha Decay Theory • Alternate expression includes an additional factor that describes probability of preformation of alpha particle inside parent nucleus • No clear way to calculate such a factor • empirical estimates have been made • theoretical estimates of the emission rates are higher than observed rates • preformation factor can be estimated for each measured case • uncertainties in the theoretical estimates that contribute to the differences • Frequency for an alpha particle to reach edge of a nucleus • estimated as velocity divided by the distance across the nucleus • twice the radius • lower limit for velocity could be obtained from the kinetic energy of emitted alpha particle • However particle is moving inside a potential energy well and its velocity should be larger and correspond to the well depth plus the external energy • On the order of 1021 s-1

  16. Alpha Decay Calculations • Alpha particle barrier penetration from Gamow • T=e-2G • Determination of decay constant from potential information • Using the square-well potential, integrating and substituting • Z daughter, z alpha

  17. Gamow calculations • From Gamow • Log t1/2=A+B/(Qa)0.5 • Calculated emission rate typically one order of magnitude larger than observed rate • observed half-lives are longer than predicted • Observation suggest probability to find a ‘preformed’ alpha particle on order of 10-1

  18. Alpha Decay Theory • Even-even nuclei undergoing l=0 decay • average preformation factor is ~ 10-2 • neglects effects of angular momentum • Assumes α-particle carries off no orbital angular momentum (ℓ = 0) • If α decay takes place to or from excited state some angular momentum may be carried off by the α-particle • Results in change in the decay constant when compared to calculated

  19. Hindered -Decay • Previous derivation only holds for even-even nuclei • odd-odd, even-odd, and odd-even nuclei have longer half-lives than predicted due to hindrance factors • Assumes the existence of pre-formed -particles • a ground-state transition from a nucleus containing an odd nucleon in highest filled state can take place only if that nucleon becomes part of the -particle and therefore if another nucleon pair is broken • less favorable situation than formation of an -particle from already existing pairs in an even-even nucleus and may give rise to the observed hindrance. • if -particle is assembled from existing pairs in such a nucleus, the product nucleus will be in an excited state, and this may explain the “favored” transitions to excited states • Hindrance from difference between calculation and measured half-life • Hindrance factors between 1 and 3E4 • Determine by ratio of measured alpha decay half life over calculated alpha decay half life

  20. Hindrance Factors • Transition of 241Am (5/2-) to 237Np • states of 237Np (5/2+) ground state and (7/2+) 1st excited state have hindrance factors of about 500 (red circle) • Main transition to 60 keV above ground state is 5/2-, almost unhindered

  21. Hindrance Factors • 5 classes of hindrance factors based on hindrance values • Between 1 and 4, the transition is called a “favored” • emitted alpha particle is assembled from two low lying pairs of nucleons in the parent nucleus, leaving the odd nucleon in its initial orbital • Hindrance factor of 4-10 indicates a mixing or favorable overlap between the initial and final nuclear states involved in the transition • Factors of 10-100 indicate that spin projections of the initial and final states are parallel, but the wave function overlap is not favorable • Factors of 100-1000 indicate transitions with a change in parity but with projections of initial and final states being parallel • Hindrance factors of >1000 indicate that the transition involves a parity change and a spin flip

  22. Heavy Particle Decay • Possible to calculate Q values for the emission of heavier nuclei • Is energetically possible for a large range of heavy nuclei to emit other light nuclei. • Q-values for carbon ion emission by a large range of nuclei • calculated with the smooth liquid drop mass equation without shell corrections • Decay to doubly magic 208Pb from 220Ra for 12C emission • Actually found 14C from 223Ra • large neutron excess favors the emission of neutron-rich light products • emission probability is much smaller than the alpha decay • simple barrier penetration estimate can be attributed to the very small probability to preform 14C residue inside the heavy nucleus

  23. Proton Decay • For proton-rich nuclei, the Q value for proton emission can be positive • Line where Qp is positive, proton drip line • Describes forces holding nuclei together • Similar theory to alpha decay • no preformation factor for the proton • proton energies, even for the heavier nuclei, are low (Ep~1 to 2 MeV) • barriers are large (80 fm) • Long half life

  24. Topic Review • Understand and utilize systematics and energetics involved in alpha decay • Calculate Q values for alpha decay • Relate to alpha energy and fine structure • Correlate Q value and half-life • Models for alpha decay constant • Tunneling and potentials • Hindered of alpha decay • Understand proton and other charged particle emission

  25. Homework Questions • Calculate the alpha decay Q value and Coulomb barrier potential for the following, compare the values • 212Bi, 210Po, 238Pu, 239Pu, 240Am, 241Am • What is the basis for daughter recoil during alpha decay? • What is the relationship between Qa and the alpha decay energy (Ta) • What are some general trends observed in alpha decay? • Compare the calculated and experimental alpha decay half life for the following isotopes • 238Pu, 239Pu, 241Pu, 245Pu • Determine the hindrance values for the odd A Pu isotopes above • What are the hindrance factor trends? • How would one predict the half-life of an alpha decay from experimental data?

  26. Pop Quiz • Calculate the alpha decay energy for 252Cf and 254Cf from the mass excess data below. • Which is expected to have the shorter alpha decay half-life and why? • Calculate the alpha decay half-life for 252Cf and 254Cf from the data below. (use % alpha decay)

More Related