Chemical Isomer Shift ($\delta$)

The Isomer Shift arises due to the non-zero volume of the nucleus and the electron charge density due to $s$-electrons within it leading to an electric monopole (Coulomb) interaction which alters the nuclear energy levels. The volume of the nucleus in its ground and excited states are different and the $s$-electron densities are affected by the chemical environment. This relationship between $s$-electron density and nuclear radius is given by

$$\delta = \frac{2}{3}\pi{}Ze^{2} \{ \vert\psi_{s}(0)_{E}\vert^{2} ... ...(0)_{A}\vert^{2} \} \{ \langle R_{e}^{2} \rangle - \langle R_{g}^{2} \rangle \}$$ (2.6)

where $\langle R_{g}^{2} \rangle$ and $\langle R_{e}^{2} \rangle$ are the mean square radii of the ground and excited nuclear states, $\vert\psi_{s}(0)_{E}\vert^{2}$ and $\vert\psi_{s}(0)_{A}\vert^{2}$ are the electron densities at the emitting and absorbing nuclei and $Z$ is the atomic number.[5]

Any difference in the $s$-electron environment between emitter and absorber thus produces a shift in the resonance energy of the transition. This shift cannot be measured directly and so a suitable reference is necessary, such as a specific source or an absorber. In all of the results presented in this thesis isomer shifts are quoted relative to $\alpha$-Fe at room temperature (any isomer shifts quoted from other work which use a different calibration material are quoted relative to $\alpha$-Fe in this thesis for consistency).

The Isomer Shift is good for probing the valency state of the Mössbauer atom. As the wavefunctions of the $s$-electrons penetrate into outer shells changes in these shells will directly alter the $s$-electron charge density at the nucleus. For example, Fe$^{2+}$ and Fe$^{3+}$ have electron configurations of $(3d)^{6}$ and $(3d)^{5}$ respectively. The ferrous ions have less $s$-electron density at the nucleus due to the greater screening of the $d$-electrons. This produces a positive Isomer Shift greater in ferrous iron than in ferric.