9-1

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)

9-2

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 positroninternal 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

9-3

Energetics

• Recoil from gamma decay Energy of excited state must equal

Photon energy, and recoil

* M*c2=Mc2+E+Tr

Momentum same for recoil and photon

• If E = 2 MeV, and A=50 recoil energy is about 40 eV

Use 931.5 MeV/AMU

2

22

r

r

M2

E

M2T

9-4

Energetics

9-5

Multipole Radiation & Selection Rules• Since radiation arises from electromagnetic effects, it can

be thought of as changes in the charge and current distributions in nucleiclassified as magnetic (M) or electric (E)

E and M multipole radiations differ in parity properties

• Transition probabilities decrease rapidly with increasing angular-momentum changesas in -decay

• Ii+ If l Ii-If, where Ii is the initial spin state and If is the final spin stateif 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

9-6

• 0 0 transitions cannot take place by photon emissionphoton 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 1.415 MeV)

• Transitions between two I=0 states of opposite parity cannot take place by any first-order processwould require simultaneous emission of two quanta

or two conversion electrons

Friedlander & Kennedy, p.97

9-7

9-8

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 anotherthe 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 numbersnumbers preceding the shell closures at N or Z values of 50, 82,

126coincide with “islands of isomerism”

9-9

Internal Conversion Coefficients

• Internal conversion is an alternative to -ray emissioncomes 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 emissionranges from zero to infinitycoefficients for any shell generally increase with

decreasing energy, increasing I, and increasing Z

9-10

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 occursdifference 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 ITin former, x-rays will be of Z-1; in latter, Z

9-11

9-12

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 themusually true, but different multipole fields give rise to

different angular distributions of emitted radiation with respect to nuclear-spin direction of the emitting nucleusordinarily deal with samples of radioactive

material that contains randomly oriented nuclei, so observed angular distribution of

rays is isotropic

9-13

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 12 cascade from J=0 to J=1 to J=0

9-14

• 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 radiationcan use strong external electric or magnetic field at

low temperatures or observe a ray in coincidence with a preceding radiationin coincidence experiment, where angle

between the two sample-detector axes is varied, the coincidence rate will vary as a function of

44

22 coscos1)( aaW

)90(

)90()180(o

oo

W

WWA

Correlation function:

where A=a2+a4

9-15

Mössbauer Spectroscopy• Principles• Conditions• Spectra

Principles• Nuclear transitions

emission and absorption of gamma rayssometimes called nuclear gamma resonance spectroscopy

• Only suitable source are isotopesEmission from isotope is essentially monochromaticEnergy tuning done by Doppler effectVibration of source and absorber spectra recorded in mm/s (1E-12 of emission)

9-16

Recoil• Gaseous atom or molecule emits radiation (energy E)

momentum of E/cRecoil (P) = -E/c =Mv

M = mass of emitter, v is recoil velocity

• Associated recoil energy of emitterER =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

9-17

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 systemThermal equilibrium, moving sourceDoppler shift of emitted photon

is angle between direction of motion of the nucleus and emitted photon

E vcEcos

9-18

Recoil Free Fraction can vary from -1 to 1,so distribution is ET -ER

distribution around 0.1 eV at room tempSome chemical energy goes into photon, and some recoil

energy goes into lattice phonon• Heisenberg uncertainly implies distribution of energy

from finite half-life• (in eV) =4.55E-16/t1/2 (sec)• What Mössbauer did

Total recoil in two parts, kinetic and vibrationalIf emitter and absorber are part of lattice,

vibrations are quantizedRecoil energy transfer only in correct quanta

9-19

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

9-20

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 TRecoil-free fraction increases with decreasing TT range from 100 to 1000 KHalf-lives greater than 1E-11 seconds, natural width

around 1E-5 eVFor gamma decay of 100 keV, Doppler shift of

1E-5 eV is at a velocity of 3 cm/s

9-21

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 energyET = ²E(nucl) + ²E(elect) [binding energies]Consider an emitting nucleus (excited) and absorber

(ground) in different chemical statesDifference in ²E(elect) and therefore ET Change is chemical shift

E(elect) 25Ze2 (rex

2 rgr2 )[ ex (0)

2 gr (0)2]

9-22

Magnetic Dipole Splitting

• magnetic moment will add to transition energyET = 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

9-23

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 materialscatalystssoilcoalsedimentselectron exchange

9-24

Decay Scheme

9-25

Mössbauer Devise