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 ( 4 He 2+ ) based on observed emission bands §Energetics àAlpha decay energies 4-9 MeV àOriginally thought to be monoenergetic, fine structure discovered A Z  (A-4) (Z-2) + 4 He + Q 

2 Fine Structure and Energetics Different alpha decay energies for same isotope §Relative intensities vary §Coupled with gamma decay 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 (Q α is positive) §However alpha emission is dominant decay process only for heaviest nuclei, A≥210 §Energy ranges 1.8 MeV ( 144 Nd) to 11.6 MeV ( 212m Po) àhalf-life of 144 Nd is 5x10 29 times longer then 212m Po

3 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 Q α §α-decay for nuclei with N=84 as it decays to N=82 daughter short-lived α-emitters near doubly magic 100 Sn § 107 Te, 108 Te, 111 Xe alpha emitters have been identified by proton dripline above A=100

4 Alpha Decay Energetics Q value positive for alpha decay §Q value exceeds alpha decay energy  m  T  = m d T d §m d and T d 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 àtightly 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

5 Energetics Calculation of Q value from mass excess  238 U  234 Th +  + Q àIsotope Δ (MeV) 238 U Th He  Q  = – ( ) = MeV §Q energy divided between the α particle and the heavy recoiling daughter àkinetic energy of the alpha particle will be slightly less than Q value Conservation of momentum in decay, daughter and alpha are equal  d =   §recoil momentum and the  -particle momentum are equal in magnitude and opposite in direction §p 2 =2mT where m= mass and T=kinetic energy 238 U alpha decay energy

6 Energetics Kinetic energy of emitted particle is less than Coulomb barrier α-particle and daughter nucleus §Equation specific of alpha §For 238 U decay Alpha decay energies are small compared to the required energy for 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

7 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 249 Cf goes to 9 th excited state of 245 Cm §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 the daughter § 212m Po à2.922 MeV above 212 Po ground state àDecays to ground state of 208 Pb with emission of MeV alpha particle Systematics result from §Coulomb potential àHigher mass accelerates products §larger mass àdaughter 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 Beta Decay to Energy minimum, then Alpha decay to different A

8 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 daughter §Repulsion from Coulomb barrier §Alpha particle should not get near the nucleus from outside Alpha particle should be trapped behind a potential energy barrier 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 àRelated to decay probability Alpha decay energy VcVc

9 Alpha Decay Theory Closer the energy of the particle to the top of the barrier more likely the particle will penetrate barrier More energetic the particle is relative to a given barrier height, more frequently the particle will encounter barrier §Increase probability of barrier penetration Geiger Nuttall law of alpha decay  Log t 1/2 =A+B/(Q  ) 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 10 5 in the half-life

10 Expanded Alpha Half Life Calculation More accurate determination of half life from Hatsukawa, Nakahara and Hoffman Theoretical description of alpha emission based on calculating 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  =P*f àf is frequency factor àP is transmission coefficient Outside of closed shells 78  Z  82; 100  N   Z  90; 100  N  126

11 Alpha Decay Theory Alternate expression includes 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 àuncertainties in the theoretical estimates that contribute to the differences Frequency for alpha particle to reach edge of a nucleus §estimated as velocity divided by the distance across the nucleus àtwice the radius àlower limit for velocity could be obtained from the kinetic energy of emitted alpha particle àHowever 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 s -1

12 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

13 Gamow calculations From Gamow  Log t 1/2 =A+B/(Q  ) 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

14 Alpha Decay Theory Even-even nuclei undergoing l=0 decay §average preformation factor is ~ §neglects effects of angular momentum àAssumes 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

15 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 existence of pre-formed  -particles §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 àanother nucleon pair is broken àless favorable situation than formation of an  -particle from existing pairs in an even-even nucleus *observed hindrance. àif  -particle is assembled from existing pairs in such a nucleus, the product nucleus will be in an excited state, *explain the “favored” transitions to excited states Hindrance factor determine by ratio of measured alpha decay half life over calculated alpha decay half life §Calculations underpredict half life §Hindrance factors between 1 and 3E4

16 Hindrance Factors Transition of 241 Am (5/2-) to 237 Np §states of 237 Np (5/2+) ground state and (7/2+) 1 st excited state have hindrance factors of about 500 §Main transition to 60 keV above ground state is 5/2-, almost unhindered 5 classes of hindrance factors (half live measure/half life calculated) §Between 1 and 4, the transition is called a “favored” àemitted 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 indicate that spin projections of the initial and final states are parallel, but the wave function overlap is not favorable §Factors of 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

17 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 208 Pb from 220 Ra for 12 C emission §Actually found 14 C from 223 Ra §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 14 C residue inside the heavy nucleus

18 Proton Decay For proton-rich nuclei, the Q value for proton emission can be positive §Line where Q p 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

19 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

20 Homework Questions Calculate the alpha decay Q value and Coulomb barrier potential for the following, compare the values § 212 Bi, 210 Po, 238 Pu, 239 Pu, 240 Am, 241 Am What is the basis for daughter recoil during alpha decay? What is the relationship between Q a and the alpha decay energy (T a ) What are some general trends observed in alpha decay? Compare the calculated and experimental alpha decay half life for the following isotopes § 238 Pu, 239 Pu, 241 Pu, 245 Pu §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?

21 Pop Quiz Calculate the alpha decay energy for 252 Cf and 254 Cf 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 252 Cf and 254 Cf from the data below.