RFSS: Lecture 4 Alpha Decay

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RFSS: Lecture 4 Alpha Decay Reaings Nuclear an Raiochemistry: Chapter 3 Moern Nuclear Chemistry: Chapter 7 Energetics of Alpha Decay Geiger Nuttall base theory Theory of Alpha Decay Hinrance Factors

1 RFSS: Lecture 4 Alpha Decay Reaings Nuclear an Raiochemistry: Chapter 3 Moern Nuclear Chemistry: Chapter 7 Energetics of Alpha Decay Geiger Nuttall base theory Theory of Alpha Decay Hinrance Factors Different between theory an measurement Heavy Particle Raioactivity Proton Raioactivity Ientifie at positively charge particle by Rutherfor Helium nucleus ( 4 He + ) base on observe emission bans Energetics Alpha ecay energies 4-9 MeV Originally thought to be monoenergetic, fine structure iscovere A Z (A-4) (Z-) + 4 He + Q 1

2 Fine Structure an Energetics Different alpha ecay energies for same isotope Relative intensities vary an couple with gamma ecay Over 350 alpha emitting nuclei Alpha energy use to evelop ecay schemes All nuclei with mass A > 150 are thermoynamically unstable against alpha emission Q is positive However alpha emission generally seen for heaviest nuclei, A 10 Energy ranges 1.8 MeV ( 144 N) to 11.6 MeV ( 1m Po) half-life of 144 N is 5x10 9 times longer then 1m Po Alpha ecay observe for negative bining energies

3 Q values generally increase with A variation ue to shell effects can impact tren increase Peaks at N=16 shell For isotopes ecay energy generally ecreases with increasing mass 8 neutron close shell in rare earth region increase in Q -ecay for nuclei with N=84 as it ecays to N=8 aughter short-live -emitters near oubly magic 100 Sn 107 Te, 108 Te, 111 Xe alpha emitters have been ientifie by proton ripline above A=100 Energetics 3

4 Alpha Decay Energetics Q value positive for alpha ecay Q value excees alpha ecay energy m T = m T m an T represent aughter From semiempirical mass equation emission of an -particle lowers Coulomb energy of nucleus increases stability of heavy nuclei while not affecting overall bining energy per nucleon tightly boun -particle has approximately same bining energy/nucleon as original nucleus * Emitte particle must have reasonable energy/nucleon * Energetic reason for alpha rather than proton Energies of alpha particles generally increase with atomic number of parent Q T Q Q = T = = T = T Q m (1 + m mt m + T ) mt + m m (1 + m = T ) = Q( m 4 m + m )

5 Energetics Calculation of Q value from mass excess 38 U 34 Th + + Q Isotope Δ (MeV) 38 U Th He.449 Q = ( ) = 4.70 MeV Q energy ivie between particle an heavy recoiling aughter kinetic energy of alpha particle will be slightly less than Q value Conservation of momentum in ecay, aughter an alpha are equal ρ =ρ recoil momentum an -particle momentum are equal in magnitue an opposite in irection p =mt where m= mass an T=kinetic energy 38 U alpha ecay energy m 34 T = Q( T ) MeV m + 5 = 4.70( = m )

6 Energetics Kinetic energy of emitte particle is less than Coulomb barrier -particle an aughter nucleus Equation specific of alpha Particles touching Z e Z Vc = = 1. 44MeV For 38 1/ 3 1/ 3 R 4πε A U ecay o 1.( + 4 ) (90) 59MeV fm c = 1.44MeV fm = 8MeV 1 /3 1/ 1.( ) fm 9.3 fm V 3 fm Alpha ecay energies are small compare to require energy for reverse reaction Alpha particle carries as much energy as possible from Q value, For even-even nuclei, alpha ecay leas to groun state of aughter nucleus as little angular momentum as possible groun state spins of even-even parents, aughters an alpha particle are l=0 6

7 Some ecays of o-a nuclei populate aughter excite states with spin of parent Leas to alpha fine structure Orbital angular momentum of particle can be zero 83% of alpha ecay of 49 Cf goes to 9 th excite state of 45 Cm lowest lying state with parent spin an parity Long range alpha ecay Decay from excite state of parent nucleus to groun state of aughter 1m Po.9 MeV above 1 Po groun state Decays to groun state of 08 Pb * MeV alpha particle Systematics from Coulomb potential larger mass Higher mass accelerates proucts aughter an alpha particle start further apart mass parabolas from semiempirical mass equation cut through nuclear mass surface at constant A Explains beta ecay in ecay chain Energetics Beta Decay to Energy minimum, then Alpha ecay to ifferent A Branche Decay 7

8 Distance of closest approach for scattering of a 4. MeV alpha particle is ~6 fm Distance at which alpha particle stops moving towars aughter Repulsion from Coulomb barrier Alpha particle shoul not get near nucleus shoul be trappe behin a potential energy barrier Wave functions are only completely confine by infinitely high potential energy barriers With finite size barrier wave function has ifferent behavior main component insie barrier finite piece outsie barrier Tunneling trappe particle has component of wave function outsie potential barrier Some probability to go through barrier Relate to ecay probability Higher energy has higher tunneling probability Alpha ecay theory V c Alpha ecay energy 8

9 Alpha Decay Theory Closer particle energy to barrier maximum more likely particle will penetrate barrier More energetic alpha will encounter barrier more often Increase probability of barrier penetration ue Geiger Nuttall law of alpha ecay logt = A + 1/ 1 T = mv Q a constants A an B have Z epenence. simple relationship escribes ata on -ecay over 0 orers of magnitue in ecay constant or half-life 1 MeV change in -ecay energy results in a change of 10 5 in half-life B 9

10 Expane Alpha Half Life Calculation More accurate moels of half life are possible Example from Hatsukawa, Nakahara an Hoffman log ( t ) = A A( Z)( A Q ) [arccos X (1 ] C( Z, 1/ 10 1/ X X + N p C( Z, N) = 0 Outsie of close shells C( Z, N) = [ (8 Z) 0.070(16 N) C( Z, N) = [ ( Z 8) 0.067(16 N) 1/3 1/3 Q X = 1.49( A + 4 )( ) Z e 78 Z 8; 100 N 16 8 Z 90; 100 N 16 Theoretical escription of alpha emission base on calculating rate in terms of two factors rate at which an alpha particle appears at insie wall of nucleus probability that alpha particle tunnels through barrier λ =P*f f is frequency factor 10 P is transmission coefficient )

11 Alpha Decay Theory Now have aitional factor that escribes probability of preformation of alpha particle insie parent nucleus prior to ecay No clear way to calculate preformation probability empirical estimates have been mae theoretical estimates of emission rates are higher than observe rates uncertainties in theoretical estimates contribute to ifferences preformation factor can be estimate for each measure case Evaluation of frequency for alpha particle to reach ege of a nucleus estimate as velocity ivie by istance across nucleus twice raius, on orer of fm lower limit for velocity obtaine from kinetic energy of emitte alpha particle * Use this to etermine velocity of alpha particle in nucleus particle is moving insie a potential energy well an its velocity shoul be larger an correspon to well epth plus external energy On orer of 10 1 s -1 f = v R ( V o + Q) / µ R µ = M M M + M Reuce mass 11

12 Alpha Decay Calculations Alpha particle barrier penetration from Gamow T=e -G Determination of ecay constant from potential information R h 4π = 1/ λ exp (µ) ( U ( r) T ) µ R1 h R1 1/ r Using square-well potential, integrating an substituting Z aughter, z alpha Zze 1 T = = µ v R µ = M M M + M Zze B = R 1 λ = 1/ 1/ h 8πZze T T T exp arccos 1 µ R1 hv B B B 1/ 1

13 From Gamow t Gamow calculations 1/ = ln λ logt = A + 1/ = ln fp B Q a ln (( Vo + Q µ Calculate emission rate typically one orer of magnitue larger than observe rate observe half-lives are longer than preicte Observation suggest a route to evaluate alpha particle pre-formation factor = ) e G 13

14 Even-even nuclei unergoing l=0 ecay average preformation factor is ~ 10 - neglects effects of angular momentum Alpha Decay Theory Assumes -particle carries off no orbital angular momentum (l = 0) If ecay takes place to or from excite state some angular momentum may be carrie off by -particle Results in change in ecay constant when compare to calculate 14

15 Hinere -Decay Previous erivation only hols for even-even nuclei o-o, even-o, an o-even nuclei have longer half-lives than preicte ue to hinrance factors Assumes existence of pre-forme -particles Groun-state transition from nucleus containing o nucleon in highest fille state can take place only if that nucleon becomes part of -particle therefore another nucleon pair is broken less favorable situation than formation of an -particle from alreay existing pairs in an even-even nucleus * may give rise to observe hinrance -particle is assemble from existing pairs in such a nucleus, prouct nucleus will be in an excite state this may explain higher probability transitions to excite states Hinrance from ifference between calculation an measure half-life Hinrance factors between 1 an 3E4 Hinrance factors etermine by ratio of measure alpha ecay half life over calculate alpha ecay half life ratio of calculate alpha ecay constant over measure alpha ecay constant t t 1/ 1/ measure calculate = calculate λ = λ measure Hinrance factor 15

16 Hinrance Factors Transition of 41 Am (5/-) to 37 Np states of 37 Np (5/+) groun state an (7/+) 1 st excite state have hinrance factors of about 500 (re circle) Main transition to 60 kev above groun state is 5/-, almost unhinere 16

17 Hinrance Factors 5 classes of hinrance factors base on hinrance values hinrance factors increase with increasing change in spin Parity change also increases hinrance factor Between 1 an 4, transition is calle a favore emitte alpha particle is assemble from two low lying pairs of nucleons in parent nucleus, leaving o nucleon in its initial orbital Hinrance factor of 4-10 inicates a mixing or favorable overlap between initial an final nuclear states involve in transition Factors of inicate that spin projections of initial an final states are parallel, but wave function overlap is not favorable Factors of inicate transitions with a change in parity but with projections of initial an final states being parallel Hinrance factors of >1000 inicate that transition involves a parity change an a spin flip 17

Heavy Particle Decay Possible to calculate Q values for emission of heavier nuclei Is energetically possible for a large range of heavy nuclei to emit other

Q-values for carbon ion emission by a large range of nuclei calculate with smooth liqui rop mass equation without shell corrections Decay to oubly magic 08

18 Heavy Particle Decay Possible to calculate Q values for 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 calculate with smooth liqui rop mass equation without shell corrections Decay to oubly magic 08 Pb from 0 Ra for 1 C emission Actually foun 14 C from,3 Ra large neutron excess favors emission of neutron-rich light proucts emission probability is much smaller than alpha ecay simple barrier penetration estimate can be attribute to very small probability to preform 14 C resiue insie heavy nucleus 18

19 For proton-rich nuclei, Q value for proton emission can be positive Line where Q p is positive, proton rip line Describes forces holing nuclei together Similar theory to alpha ecay no preformation factor for proton proton energies, even for heavier nuclei, are low (Ep~1 to MeV) barriers are large (80 fm) Long half life Proton Decay 19

20 Topic Review Unerstan an utilize systematics an energetics involve in alpha ecay Calculate Q values for alpha ecay Relate to alpha energy an fine structure Correlate Q value an half-life Moels for alpha ecay constant Tunneling an potentials Hinere of alpha ecay Unerstan proton an other charge particle emission 0

21 Homework Questions Calculate alpha ecay Q value an Coulomb barrier potential for following, compare values 1 Bi, 10 Po, 38 Pu, 39 Pu, 40 Am, 41 Am What is basis for aughter recoil uring alpha ecay? What is relationship between Q a an alpha ecay energy (T a ) What are some general trens observe in alpha ecay? Compare calculate an experimental alpha ecay half life for following isotopes 38 Pu, 39 Pu, 41 Pu, 45 Pu Determine hinrance values for o A Pu isotopes above What are hinrance factor trens? How woul one preict half-life of an alpha ecay from experimental ata? 1

22 Question Respon to the PDF quiz for lecture 4 Sen in when complete Comment on the blog

Theoretical Studies on the α-decay Half-Lives of Even-Even Lv Isotopes

Theoretical Studies on the α-decay Half-Lives of Even-Even Lv Isotopes International Journal of Energy an Power Engineering 17; 6(1: 1-5 http://www.sciencepublishinggroup.com/j/ijepe oi: 1.11648/j.ijepe.1761.11 ISSN: 36-957X (Print; ISSN: 36-96X (Online Theoretical Stuies