FACTS WHY? C. Alpha Decay Probability 1. Energetics: Q α positive for all A>140 nuclei

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1 C. Alpha Decay Probability 1. Energetics: Q α positive for all A>140 nuclei 2. Range of Measured Half-Lives (~10 44 ) y > t 1/2 > s 3. Why α? a. Proton & Neutron Emission: Q p, Q n are negative near valley of beta stability (peak of peninsula); Thermodynamically forbidden b. Other Nuclei ; e.g. 12 C, 16 O Q( 12 C), Q( 16 O) positive ; therefore possible Probability is low (i.e., t 1/2 ) is long) -- P( 14 C)/Pα ~ P Th 14 C+ 218 Po FACTS (Exotic decay mode) 11.7 MeV α particles from 212m Po are the highest energy alphas from a radioactive source 2.0 MeV alphas from Sm are the among lowest energy alphas from a radioactive source Most alpha particles from radioactive sources fall in the range of 4-8 MeV. Associated with this narrow range in energy is the enormous range in half-life noted above. WHY?

2 4. Coulomb Barrier Penetration What is the relevant potential for the nucleus? We can consider this by examining the approach of an alpha particle from infinity (microscopic reversibility). If the collision is head-on (dead center) there are two parts to consider the attractive nuclear potential and the repulsive Coulomb potential. V(r) = V nuclear + V Coulomb

3 V(r) o Q α α escapes via quantummechanical tunneling through the Coulomb barrier Q p a. Electrostatic Repulsion Energy for Two Charged Spheres: ( Z1 e)( Z2e) Z1Z2 V Coulomb = = 1.44 MeV. fm R R where Z 1 = 2 Z 2 = Z recoil R= R 1 + R 2 = r 0 (A 1 1/ /3 ) b. Example: 220 No let r = 1.4 fm V = 1.44(2)(100) Coulomb = 25. 5MeV 1 /3 1/3 1.4( ) Typical of most heavy nuclei

4 c. Q α 10 MeV ; V coul > > Q α and can't escape classically d. Relative Barriers (approximate) V coul (α): V coul ( 12 C): V coul ( 16 O) 2:6:8 (since Z & R of recoil constant) heavier fragments have much higher (and thicker) hill to punch through 5. Probability P α a. Tunneling Probability: P α P α P formation ) e ( Qα VCoulomb ) ( t 1 ( 1/ 2 α) b. P α favored by: (1) large Q α and low V coul or small Q α V c t 1/2 (α) α 1/P(α) α e (Q α V c ) or log t 1/2 α V c Q α

5 Geiger-Nuttal law D. Applications/Environment Am (458y) smoke detectors Pu (88y) remote sensing devices; power sources Rn (3.8d) natural radioactivity health effects Ra (1620y) cancer therapy 5. ( 210 Po) (138d) power sources 6. Dating tags U,Th, Sm

6 Beta-Decay: Neutron-Proton Transformations Connects nuclei that are isobars Z A = most probable NEUTRON EXCESS Negatron Decay PROTON EXCESS Positron/electron capture Decay n 1 H + β +ν 1 + H 1 n + β + ν H e n +ν

A. Beta-decay Half-lives 1. Factors that Influence Rate a. WEAK NUCLEAR FORCE: SLOW!!! t 1/2 (β ± ) 10 3 s (cf 10 21 s for α ) b. Large Q β Short half-life c.

7 A. Beta-decay Half-lives 1. Factors that Influence Rate a. WEAK NUCLEAR FORCE: SLOW!!! t 1/2 (β ± ) 10 3 s (cf s for α ) b. Large Q β Short half-life c. Structure: spin and parity changes ( I & π) retard rates 2. Example 24 Na 24 Mg + β - + ν preferred by structure (99.9%) preferred by energetics

8 B. Negatron Decay 1. Mechanism NEGATRON 1 0 β (i.e., electron of nuclear origin) A Z - -- A Z +1 0 β -1 X Y + + ν + Q [Y +1 ] is initial chemical state-cation Nuclear reactors: weird cation chemistry β CHARACTERISTIC OF NEUTRON-EXCESS NUCLEI 2. Examples β -1 H He β ν 7-1 C N + + ν 3. Energetics a. Q β = ( A X) [ ( A Y) + + e + ν ] ν 0 ;

9 ( A Y) = ( A Y + ) + e Q β = ( A X) ( A Y) IF (X) > (Y) ; β emission is possible b. Observed Q-values: Q β 5 MeV (β is relativistic) c. Spectrum P(β ) Spectrum is continuous instead of discrete lines as in α (and γ) decay. First evidence for neutrinos. If 2-body, then E β Q β E β Q β (end point) For a three-body breakup, energy and momentum can be shared in an infinite number of ways;

10 C. Positron Decay: (antiparticle of electron) 1. Mechanism: A Z X β + + AY + ν 1 Z -1 CHARACTERISTIC OF PROTON-RICH NUCLEI; OCCURS INSIDE NUCLEUS [Y 1 ] is initial chemical state ; anion 2. Example: 11 C 0 β B + ν + Q β + (t 1/2 = 21 min) Used to tag biomolecules; 13 N + 15 O also, medical cyclotron 3. Energetics a. Q β + = (X) [ (Y ) + (β + ) + (ν) ] ; (e ) = (β + ) Q β + = (X) [ (Y) + (e) + β + + 0] ; (ν) 0 = (X) (Y) 2 e ; (e ) = MeV Q β + = (X) (Y) MeV

11 NOTE: Mass of antiparticle in matter world is equal to the mass of the particle. Creation requires twice the mass of the particle to raise it from antimatter state; energy is stolen from the rest of the nucleus. b. Result: For β + decay to occur: (X) (Y) MeV c. Q β + 5 MeV 4. Relative Spectrum Shape Coulomb field of nucleus attracts β-, but repels β+ ; shape is distorted

12 5. Fate of Positron a. Thermalization: collisions with other electrons reduce kinetic energy to room temperature (3 kt/2) b. Positronium Formation: (Lightest molecule) e- + e+ t 1/2 ~ s spins ortho ; J = 1 para ; J = 0 Lifetime depends on chemical environment c. Annihilation e + + e - 2γ ; E γ = MeV = M e c 2 annihilation radiation (180 deg. apart) d. Radioactive Tag Highly specific BACK-TO-BACK γs Monoenergetic MeV gamma Coincidence detection PET: positron emission tomography MeV γ e- + e MeV γ

13 C. Electron Capture Decay -- EC Alternate mechanism to positron decay for proton-rich nuclei. SAME NET RESULT for DAUGHTER H + e H n ν + QEC 0

14 a. Generic Equation A Z A Y ν + Q Z -1 X + e - + EC A X Z neutral However, the electrons are not in the ground state. b. Example: 37 Ar Cl ν (t 17 1/2 = 35.0 d) + e - + reverse reaction of solar neutrino experiment c. Q EC = (X) (Y) If (X) > (Y) EC is possible Note: Q EC = Q β MeV

15 2. Atomic Effects a. Capture Process: occurs preferentially from atomic orbitals nearest nucleus (low n) highest probability for being inside the nucleus: 1s 2s 3s K-shell L-shell M-shell Etc. RESULT: Capture Probability P EC (K) > P EC (L) > P EC (M) etc. b. For fixed principal quantum number n, capture occurs from lowest state ; i.e., s state has a higher probability of being inside nucleus. P EC (ns) > P EC (np) > P EC (nd) etc. s p d

16 3. Radiation from EC a. Primary: monoenergetic neutrino (hard to detect) heavy recoil nucleus (hard to detect) b. Secondary: Detectable Radiation x-rays emitted during electronic orbital rearrangement x-rays are characteristic of DAUGHTER nucleus. WHY? Auger electrons x-rays may interact with outer orbital electrons and eject low energy electrons instead (internal photoelectric effect) P(x ray) P(Auger) αz REASON: x-ray energy increases with Z; λ too short to interact. Gamma rays If EC populates an excited state of daughter nucleus, monoenergetic γ-ray will be emitted. c. EC most difficult to detect of all decay modes

17 4. Chemical Effects EC is only decay mode affected by the chemical environment a. Ligand dependence: t 1/2 (Be) < t 1/2 (BeF 2 ): F Be F b. Pressure dependence: High pressure shortens half-life c. Stars: 7 Be cannot decay, no e - s ; Q β+ = MeV 4 5. EC/β + Competition a. If Q EC < MeV, EC ONLY If Q EC MeV, EC & β + b. If both EC and β+ are possible: P(EC) P( β + ) αz For A > 180, EC predominates ; Factors: Coulomb barrier inhibits β+ Probability that 1s electron is inside the nucleus increases with increasing Z and A.

18 IV. Gamma Decay Analogous process to photon emission from atoms and molecules (uv, x-rays, IR ) A ZX Am Z 0 γ 0 A Z X + X where m * = excited state E γ Q γ (recoil energy negligible) i.e. Nucleus changes its energy state E 2 E 1 E I 2, π I 1, π I 0, π E γ 1 = E 2 E 0 E γ 2 = E 2 E1 E γ 3 = E 1 E 0 Q γ = E γ + E R ; E R ~ ev

19 A. Occurrence 1. De-excitation after nuclear reactions or radioactive decay. t 1/2 (γ) s ELECTROMAGNETIC INTERACTION 2. t 1/2 (γ) = f (E γ, I, π) Short t 1/2 (γ): Large E γ, I = 0, π = NO Long t 1/2 (γ): Small E γ, I = large, π = YES 3. Isomers: t 1/ s (arbitrary definition) Unusually long-lived γ-ray emitters NOTE: For radioactive labeling of compounds, would like t 1/2 ~ hours days stable product

20 B. Competing Mechanisms for γ-decay 1. Photon Emission: Two-body decay DISCRETE ENERGIES Eγ 2. Internal Conversion: IC a. Excess nuclear energy transferred to an atomic electron Am Z A Z X X + + e - 2s γ 1s e E e = E γ BE(e ) BE(e ) = electron binding energy b. Distinguishing Electrons observed in Nuclear Decay IC: E e is monoenergetic ; Discrete spectra: E e ~ E γ (MeV) EC Auger: E e is monoenergetic ; Discrete peak: E e ~ E xray (ev) Negatron Decay: ; Spectrum continuous: E max ~ Q β

21 c. Atomic Rearrangement Vacancy in inner shell (same as EC) IC is followed by x-rays and Auger electrons IC x-rays characteristic of parent ( Z = 0) EC x-rays characteristic of daughter ( Z = 1) d. Competition between γ and IC: Large Z Favors IC; more compact orbitals; higher probability that e is inside nucleus Large I Low E γ favors IC; since e has mass, it can carry away angular momentum easier. favors IC; wavelength of γ close to that of atomic electrons; high E γ short wavelength

23 3. Pair Production Am Z A β - Z + β - + Qpp REVERSE OF ANNIHILATION X X +

24 Q pp A + [ ( X ) + ( β ) + ( )] Am = ( X ) β (β +) = (β ) = (e ) Am A ( X ) ( X ) = Q γ Q pp Q MeV = γ Pair Production cannot occur unless Q γ MeV b. Momentum Conservation: p(β + ) E β + = E β E β ± = E γ 1.022MeV 2 NOTE: eventually the β + annihilates and gives MeV back

25 4. All Three Modes Compete mode relevant energy observe observed energy Low E γ IC ( 0.2 MeV) ELECTRON Q γ E BE Medium E γ γ (~ 1 MeV) PHOTON Q γ High E γ β ± pair ( 2 MeV) β β + pair Q γ 1.022

Composite Nucleus (Activated Complex)

Composite Nucleus (Activated Complex) Lecture 10: Nuclear Potentials and Radioactive Decay I. Nuclear Stability and Basic Decay Modes A. Schematic Representation: Synthesis Equilibration Decay X + Y + Energy A Z * Z ( 10 20 s) ( ~ 10 16 10