6-1

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§ Different % yields

• 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)• Gamma decay energy range from few

keV to many MeV

6-2

Gamma decay example: 152Eu• Many gamma transitions from decay of 152Eu

§ Different decay modes of isotope• What gamma data provides % yield

§ From chart of the nuclides, gamma energies at 121. 8 keV, 1408 keV, and 344.3 keV

6-3

Gamma Data• % yield transitions

available• Search for % yield for

specific isotope§ http://nucleardata.

nuclear.lu.se/NuclearData/toi/nucSearch.aspà Lbl site has

some issues• Can also select by

energy§ http://

nucleardata.nuclear.lu.se/NuclearData/toi/radSearch.asp

6-4

Gamma Data• Table of the isotope data

§ % yields and transitions

6-5

Gamma Data

6-6

Transitions

• De-excitation of excited states are transitions § - and -decay processes leave product nucleus in either

ground state or excited stateà Excited state de-excitation

• De-excitation§ Emission of electromagnetic radiation ( radiation)§ internal-conversion electrons§ newly created electron and positron (higher energy)§ Internal conversion from interaction between nucleus and

extranuclear electrons leading to emission of atomic electron à kinetic energy equal to difference between energy of

nuclear transition involved and binding energy of electron

6-7

Transitions• Pair production

§ Exceeds 1.02 MeV§ Emitted with kinetic energies that total excitation

energy minus 1.02 MeV§ Uncommon mode

• Gamma decay characterized by a change in energy without change in Z and A§ E = hv§ Majority of g transitions have very short lifetimes, 1E-12

secondsà Table of the Isotopes provide dataà Longer lived states are metastable

• g transitions important for determining decay schemes

6-8

Energetics• Recoil from gamma decay

§ Energy of excited state must equalà 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 eVà Use 931.5 MeV/AMU

M2

E

M2T

22

r

r

6-9

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

6-10

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

à E2 is electric quadrupole• Ii+ If l Ii-If, where Ii is initial spin state and If

is final spin state§ Initial and final state have same parity

allowed transitions are:à electric multipoles of even l à magnetic multipoles of odd l

§ If initial and final state different parityà electric multipoles of odd l à magnetic multipoles of even l

• Example:§ Transition is between a 4+ and a 2+ state§ l between 6 and 2

à 4+2 to 4-2§ Same parity, both +

à E even, M odd* E2, M3, E4, M5, E6

transitions are allowedØ Generally lowest

multipole observedØ Expect E2 as the

main transition

6-11

Non-photon emission for de-excitation

• 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 deexcitation

occurs by other means§ emission of an internal-conversion electron § simultaneous emission of an electron-positron pair

(E 1.02 MeV)à Examples: 72Ge, 214Po, 18O, 42Ca

• Transitions between two I=0 states of opposite parity cannot take place by any first-order process§ requires simultaneous emission of two quanta or

two conversion electrons

6-12

Isomeric Transitions• Isomeric transition (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• Single-particle model basis of charge and current distribution

§ nuclear properties dictated by unpaired nucleon§ transition can be described as transition of single nucleon

from one angular-momentum state to anotheràRemainder of nucleus being represented as a potential

well•Shell model application to gamma decay

§ Weisskopf single particle model

6-13

Isomeric Transitions•Model predicts low-lying states of widely differing spins in certain regions of neutron and proton numbers

§ numbers preceding shell closures at N or Z values of 50, 82, 126§ coincide with “islands of isomerism”

à Large number of isomeric states near magic numbers•Predictions strong for M4 isomers

§ E2 isomers 100 faster than predictedà Variations in nuclear shape from model lead to differences

6-14

Internal Conversion Coefficients

• Internal conversion is an alternative to -ray emission§ Excited nucleus ejects atomic electron

à Discrete energy emission, only one particleà Generally k shell electrons

•Interaction between nucleus and extranuclear electrons § emission of electron with kinetic energy equal to

difference between energy of nuclear transition and electron binding energy

• Internal conversion favored when:§ energy gap between nuclear levels is small§ 0+→0+ transitions

6-15

Internal Conversion Coefficients

• Internal conversion coefficient § 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

• Internal conversion electrons show a line spectrum § correspond to -

transition energy minus binding energies of electron shells in which conversion occurs

§ difference in energy between successive lines are used to determine Z

6-16

Internal conversion spectrum• K/ L ratios can be used to characterize multipole order

§ Determine I and • If Z of x-ray-emitting species known, it can be determined whether it decays by EC or IT

§ X-rays generated from daughter isotopeà For EC, x-rays will be of Z-1à IT x-rays from Z

• Specific lines generated from nuclear transition§ Overlain on beta spectrum§ Can determine specific peaks and electron binding energies

198HgBinding energiesfor 203Tl (keV)

K 85.529

LI 15.347

LII 14.698

LIII 12.657

M 3.704

6-17

Angular Correlations of Gamma Decay

• Assumes rays have no track of multipole interaction from production§ In some cases different multipole fields give rise to

angular distributions of emitted radiation with respect to nuclear-spin direction of emitting nucleus

•General;y not observed during gamma decay§ordinarily samples contain randomly oriented nuclei§ Observed angular distribution of rays is isotropic

due to random orientationà Would be remove if nuclei aligned

6-18

Angular correlation• If nuclear spins can be aligned in one direction, angular

distribution of emitted -ray intensity would depend predictably on initial nuclear spin and multipole character of radiation§ Align nuclei in magnetic or electric field at near 0 K§ observe a ray in coincidence with a preceding radiation

à Alpha, beta, or gamma•coincidence experiment

§ angle between two sample-detector axes is varied, 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 (fits)

6-19

Angular Correlations

• Correlate gamma emission with preceding radiation§ Need very short gamma lifetime§ Measure coincidence as function of q

• Schematic diagram of angular correlations § 12 cascade, Z axis defined by 1

§ Requires time and spatial correlated detectors

6-20

Mössbauer Spectroscopy• Principles• Conditions• Spectra

Principles• Nuclear transitions

§ emission and absorption of gamma rayssometimes called nuclear gamma resonance spectroscopy

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

6-21

Recoil• Recoil converted to vibrational energy• 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

6-22

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 nucleus and emitted photon

E vcEcos

6-23

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

6-24

Recoil Free Fraction

•If recoil energy is smaller than quantized vibration of lattice whole lattice vibrates•Mass is now mass of lattice

§ v is small as is recoil kinetic energy•E ET and recoil energy goes into lattice phonon system§ lattice system is quantized, so it is possible to

find a state of system unchanged after emission

6-25

Recoil free fraction• E > 150 keV nearly all events vibrate lattice

§ E = ET for a small amount of decays

§ 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

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

6-26

Isomeric or Chemical Shift• Volume of nucleus in excited state is different from

ground state• Probability of electron orbitals found in nucleus is

different• Difference appears as a difference in 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

E(elect) 25Ze2 (rex

2 rgr2 )[ ex (0)

2 gr (0)2]

6-27

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)

6-28

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

6-29

Mössbauer Devise

6-30

6-31

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 nucleus

• Moessbauer spectroscopy

6-32

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

6-33

Pop Quiz• 60Co decays into 60Ni with two strong gamma lines at

1332.5 keV and 1173.2 keV. The decay scheme is below. § Fill in the gamma transitions that yield the energies

provided above.§ What is the energy and multipolarity of the gamma

ray that deexcites each excited state?

60Co5+

60 Ni

0+

2+

2+4+

0

1332.5

2158.62505.7

Spin and parity Energy above ground (keV)