Mossbauer energy distribution

The particular dependence /r( ) is of no interest but it should be noted that the centre of gravity of this distribution is shifted by the amount r relative to the transition energy in the source. r = E HMc is the recoil energy imparted to an isolated nucleus of mass M (where c = vacuum speed of light). The energy distribution of the Mossbauer y-quanta ] E) may be considered as Lorentzian ( ) with the full half-width T such that T = Owing to the normalization conditions, /m( ) be written as... 

Hamiltonian = matrix element of the Hamiltonian H I = nuclear spin I = nuclear spin operator /r( ), /m( ) = energy distributions of Mossbauer y-rays = Boltzmann constant k = wave vector L(E) = Lorentzian line M = mass of nucleus Ml = magnetic dipole transition m = spin projection onto the quantization axes = 1 — a — i/3 = the complex index of refraction p = vector of electric dipole moment P = probability of a nuclear transition = tensor of the electric quadrupole q = eZ = nuclear charge R = reflectivity = radius-vector of the pth proton = mean-square radi-S = electronic spin T = temperature v =... 

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

Such highly ionized species have been detected for Cl-37 produced by the EC decay of Ar-37 in gaseous phase ((>). In solids, however, such anomalous states are not realized or their life time is much shorter than the half-life of the Mossbauer level (Fe-57 98 ns and Sn-119 17-8 ns) because of fast electron transfer, and usually species in ordinary valence states (2+, 3+ for Fe-57 and 2+, 4+ for Sn-119) are observed in emission Mossbauer spectra (7,8). The distribution of Fe-57 and Sn-119 between the two valence states depends on the physical and chemical environments of the decaying atom in a very complicated way, and detection of the counterparts of the redox reaction is generally very difficult. The recoil energy associated with the EC decays of Co-57 and Sb-119 is estimated to be insufficient to induce displacement of the atom in solids. 

Chemical shifts also exist in X-ray photoelectron (106), X-ray fluorescence (21), and Mossbauer (123) spectroscopy. The common theme in all these phenomena is that inner electronic or nuclear energy levels are measurably affected by chemical changes in the valence electron distribution. 

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