1. Gamma Decay Energetics Decay Types Transition Probabilities
Internal Conversion
Angular Correlations
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)

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 comes about by 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
Characterized by a change in energy without change in Z and A

3. 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 MeV/AMU

4. Energetics

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
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
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

6. 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  MeV)
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
Friedlander & Kennedy, p.97

8. Isomeric Transitions
An IT is a  decay from an isomeric state
Transition probability or partial decay constant for  emission:   E2lA2l/3
for given spin change, half lives decrease rapidly with increasing A and more rapidly with increasing E
Use of extreme single-particle model
assumes  transition can be described as transition of a single nucleon from one angular-momentum state to another
the rest 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”

9. Internal Conversion Coefficients
Internal conversion is an alternative to -ray emission
comes about by 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

10. IC and Nuclear Spectroscopy
Internal conversion electrons show a line spectrum with lines 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, though, 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
in former, x-rays will be of Z-1; in latter, Z

12. Angular Correlations
So far we have assumed that once removed from the decaying nuclei,  rays bear no recognizable mark 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, so observed angular distribution of  rays is isotropic

13. 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

14. 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

15. Mössbauer Spectroscopy
Principles
Conditions
Spectra
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)

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. Decay Scheme

25. Mössbauer Devise