Gamma Decay

1. Gamma Decay • Readings • Modern Nuclear Chemistry, Chap. 9; • Nuclear and Radiochemistry, Chapter 3 • Energetics • Decay Types • Transition Probabilities • Internal Conversion • Angular Correlations • Moessbauer spectroscopy • Emission of photon during deexcitation of the nucleus • Wide range of energies • Isomers • two configurations • different total angular momenta • Energy differences • long-lived nuclear states are called isomeric states • gamma ray decay is called isomeric transition (IT) • Few keV to many MeV

2.  Transitions • De-excitation of excited states are  transitions • - and -decay processes leave product nucleus in either ground state or, more often, an excited state • Emission of electromagnetic radiation ( radiation), internal-conversion electrons, or newly created electron and positron • Internal conversion from interaction between nucleus and extranuclear electrons leading to emission of electron • kinetic energy equal to difference between energy of nuclear transition involved and binding energy of the electron

3.  Transitions • Pair production • Exceeds 1.02 MeV • Emitted with kinetic energies that total excitation energy minus 1.02 MeV • Uncommon mode • Characterized by a change in energy without change in Z and A • E = hv • Majority of g transitions have very short lifetimes, 1E-12 seconds • g transitions important for determining decay schemes

4. Energetics • Recoil from gamma decay • Energy of excited state must equal • Photon energy, and recoil • M*c2=Mc2+Eg+Tr • Momentum same for recoil and photon • If Eg = 2 MeV, and A=50 • recoil energy is about 40 eV • Use 931.5 MeV/AMU • Calculate recoil energy from 15.1 MeV photon from 12C

5. Multipole Radiation & Selection Rules • Since  radiation arises from electromagnetic effects, it can be thought of as changes in the charge and current distributions in nuclei • Charge distributions resulting electric moments • Current distributions yield magnetic moments • Gamma decay can be classified as magnetic (M) or electric (E) • E and M multipole radiations differ in parity properties • Transition probabilities decrease rapidly with increasing angular-momentum changes • as in -decay

6. Multipole Radiation & Selection Rules • Carries of angular momentum • l=1,2,3,4 • 2l –pole (dipole, quadrupole, octupole…) • Shorthand notation for electric (or magnetic) 2l –pole radiation • El or Ml • E2 is electric quadrupole • Ii+ If l  Ii-If, where Ii is the initial spin state and If is the final spin state • If initial and final state have the same parity electric multipoles of even l and magnetic multipoles of odd l are allowed • If different parity, the opposite is true • Example: • Transition is between a 4+ and a 2+ state • l between 6 and 2 • E even, M odd • E2, M3, E4, M5, E6 transitions are allowed • Generally lowest multipole observed

7. 0  0 transitions cannot take place by photon emission • Photon has spin and therefore must remove at least one unit of angular momentum • If no change in parity in 0  0 transition, de-excitation may occur by emission of an internal-conversion electron or by simultaneous emission of an electron-positron pair (E  1.02 MeV) • 72Ge, 214Po, 18O, 42Ca • Transitions between two I=0 states of opposite parity cannot take place by any first-order process • would require simultaneous emission of two  quanta or two conversion electrons

9. Isomeric Transitions • An IT is a  decay from an isomeric state • Transition probability or partial decay constant for  emission •   E2lA2l/3 (l not 1) • For given spin change, half lives decrease rapidly with increasing A and more rapidly with increasing E • Use of extreme single-particle model as basis of charge and current distribution • Single particle model assumes nuclear properties dictated by unpaired nucleon • Assumes  transition can be described as transition of a single nucleon from one angular-momentum state to another • Remainder of the nucleus being represented as a potential well • Model predicts, for given nucleus, low-lying states of widely differing spins in certain regions of neutron and proton numbers • numbers preceding the shell closures at N or Z values of 50, 82, 126 • coincide with “islands of isomerism” • Predictions strong for M4 isomers, E2 isomers 100 faster than predicted • Variations in nuclear shape from model

11. Weisskopf single particle estimates of the transition rates for electric multipoles (left) and magnetic multipoles (right)

12. Internal Conversion Coefficients • Internal conversion is an alternative to -ray emission • Interaction between nucleus and extranuclear electrons leading to emission of electron with kinetic energy equal to difference between energy of nuclear transition involved and binding energy of the electron • Internal conversion coefficient  is ratio of rate of internal conversion process to rate of  emission • ranges from zero to infinity • coefficients for any shell generally increase with decreasing energy, increasing I, and increasing Z

14. IC and Nuclear Spectroscopy • Internal conversion electrons show a line spectrum corresponding to the -transition energy minus binding energies of the K, L, M, … shells in which the conversion occurs • difference in energy between successive lines are used to determine Z • K/ L ratios can be used to characterize multipole order and thus I and  • this ratio doesn’t vary as widely as the individual coefficients • If Z of x-ray-emitting species known, it can be determined whether it decays by EC or IT • For EC, x-rays will be of Z-1 • For IT, x-rays from Z

16. Angular Correlations • Assumes  rays have no track of the multipole interaction that gave birth to them • Usually true but different multipole fields give rise to different angular distributions of emitted radiation with respect to nuclear-spin direction of the emitting nucleus • ordinarily deal with samples of radioactive material that contains randomly oriented nuclei • Observed angular distribution of  rays is isotropic

17. Angular Correlations • Schematic diagram of angular correlations • (a) shows angular distribution of dipole radiation for m =0 and m =  1 • (b) shows magnetic substrates populated in 12 cascade from J=0 to J=1 to J=0

18. Angular correlation • If nuclear spins can be aligned in one direction, angular distribution of emitted -ray intensity would depend predictably on the initial nuclear spin and multipole character of the radiation • Can use strong external electric or magnetic field at low temperatures or observe a  ray in coincidence with a preceding radiation • In coincidence experiment, where angle  between the two sample-detector axes is varied, the coincidence rate will vary as a function of  Correlation function: where A=a2+a4 (fits)

19. Mössbauer Spectroscopy • Principles • Conditions • Spectra Principles • Nuclear transitions • emission and absorption of gamma rays sometimes called nuclear gamma resonance spectroscopy • Only suitable source are isotopes • Emission from isotope is essentially monochromatic • Energy tuning done by Doppler effect Vibration of source and absorber spectra recorded in mm/s (1E-12 of emission)

20. Recoil • Gaseous atom or molecule emits radiation (energy E) • momentum of E/c • Recoil (P) = -E/c =Mv M = mass of emitter, v is recoil velocity • Associated recoil energy of emitter • ER =Mv2 /2= E2/2Mc2 • ER (in eV)= 537 E2/M (E in MeV) • For radiation near UV or below with normal atoms or molecules v is very small • With gamma decay E is large enough to have a measurable effect • ET=E+ ER for emission

21. Recoil • If E is to excite a nucleus • E= ET + ER • Molecules in gas or liquid cannot reabsorbed photon • In practice lattice vibrational modes may be excited during absorption • Emitting nuclei in chemical system • Thermal equilibrium, moving source • Doppler shift of emitted photon J is angle between direction of motion of the nucleus and emitted photon

22. Recoil Free Fraction J can vary from -1 to 1,so distribution is ET -ER distribution around 0.1 eV at room temp Some chemical energy goes into photon, and some recoil energy goes into lattice phonon • Heisenberg uncertainly implies distribution of energy from finite half-life • G (in eV) =4.55E-16/t1/2 (sec) • What Mössbauer did • Total recoil in two parts, kinetic and vibrational • If emitter and absorber are part of lattice, vibrations are quantized • Recoil energy transfer only in correct quanta

23. Recoil Free Fraction • If recoil energy is smaller than quantized vibration of lattice the whole lattice vibrates • Mass is now mass of lattice, v is small, and so is kinetic part of recoil energy • E ­ ET and recoil energy goes into lattice phonon system • lattice system is quantized, so it is possible to find a state of the system unchanged after emission • ­0.9 for metallic, 0.2 for metal-organic • related to stiffness of crystal

24. Recoil free fraction • E > 150 keV nearly all events vibrate lattice • E = ET for a small amount of decays • Where E = ET gives rise to Mössbauer spectra • Portion of radiation which is recoil free is “recoil-free fraction” • Vibration of lattice reduced with reduced T • Recoil-free fraction increases with decreasing T • T range from 100 to 1000 K • Half-lives greater than 1E-11 seconds, natural width around 1E-5 eV • For gamma decay of 100 keV, Doppler shift of 1E-5 eV is at a velocity of 3 cm/s

25. Isomeric or Chemical Shift • Volume of nucleus in excited state is different from ground state • Probability of electron orbitals found in the nucleus is different • Difference appears as a difference in the total electron binding state and contributes to transition energy • ET = ²E(nucl) + ²E(elect) [binding energies] • Consider an emitting nucleus (excited) and absorber (ground) in different chemical states • Difference in ²E(elect) and therefore ET • Change is chemical shift

26. Magnetic Dipole Splitting • magnetic moment will add to transition energy • ET = ²E(nucl) + ²E(elect)+ ²E(mag) • Change in magnetic moment will effect shift • Split also occurs (2I+1) values • around 1cm/s Electric Quadrapole Splitting • inhomogeneous magnetic field • ET = ²E(nucl) + ²E(elect)+ ²E(mag)+²E(quad) • around 1cm/2

27. Technique • Intensity of photon from emitter is detected • Velocity of emitter and absorber recorded • important to know these values • May be cooled and place in magnetic field • Used in • amorphous materials • catalysts • soil • coal • sediments • electron exchange

28. Decay Scheme

29. Mössbauer Devise

30. Topic Review • Trends in gamma decay • How does it come about, how is it different from alpha and beta • Energetics of gamma decay • Decay Types • Photon emission, IC, pair production • E and M transitions • Probabilities, modes, and how to define • Angular Correlations • How are they measured and what do they inform about the nucleus • Moessbauer spectroscopy

31. Questions • 195Pt has a ground state spin and parity of ½-, with excited states at 0.029 MeV (3/2-) and 0.130 MeV (5/2-). Does the 5/2 level decay primarily to the 3/2- level or to the ½- level? Why? What is the transition multipolarity? • What is the spin of a photon? • What type of gamma decay is expected from a 0+ to 0+ transition? • Classify the most likely multipolarity for the -ray decay of 60mCo. • Describe Moessbauer spectroscopy • Why do angular correlations arise in the nucleus? How are they measured

32. Pop Quiz • 51V has a ground state spin and parity of 7/2- with excited states at 0.3198 MeV (5/2-) and at 0.930 MeV (3/2-). • Sketch the decay scheme • What is the energy and multipolarity of the gamma ray that deexcites each excited state?