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)

 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

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

Energetics

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

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  1.415 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

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”

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

Decay Scheme

Mössbauer Devise