Introduction to the Mössbauer Effect
The Mössbauer Effect, also known as recoilless nuclear absorption of γ-radiation, was discovered by Rudolf Mössbauer in 1958. In general, emission of a γ-photon does not induce excitation of a corresponding nucleus by the emitted photon, because the energy of the emitted photon is usually less than that required to excite a corresponding nucleus. The energy deficit has gone into the recoil energy of the emitting nucleus, in accordance to conservation of momentum.
Occasionally, the emitted photon has sufficient energy to excite a corresponding nucleus. This may happen in the event of recoilless emission of the photon, or by the Doppler effect to increase the energy of the emitted photon, to make up for the energy deficit. Overlap of the emission and absorption lines by cooling/heating may also be employed. Figure 1 below shows the emission and absorption lines of resonant γ-radiation. The recoil energy on the emitter nucleus is represented by ER. When the nucleus is bound in a crystal, instead of a smooth continuum of recoil energies, one gets peaks corresponding to zero, one and multi-phonon emissions. In the lower graphs, we can see that the zero phonon emission peaks coincide, permitting resonant emission and absorption.
Figure 1: Emission and absorption lines of resonant γ-radiation 
Recoilless nuclear emission was explained by Rudolf Mössbauer in the following manner: “This situation might be explained likely by a person throwing a stone from a boat. The majority of the energy is submitted to the stone, but a small amount goes into the kinetic energy of the recoiling boat. During summer time, the boat will simply pick up this recoil energy. If, however, the person throws the stone during winter time, with the boat frozen into the lake, then practically all energy is going into the stone thrown and only a negligible amount is submitted to the boat. The entire lake will, thus, take up the recoil and this procedure thus occurs as recoilless process.” (sic) 
Mathematically, the recoil energy of the nucleus is given by ER = p2/2M, where p is the momentum of the emitted gamma photon, and M is the mass of the recoiling nucleus. As we can see, the greater the mass of the recoiling nucleus, the lower the recoiling energy. In crystal lattices, the apparent mass of the nucleus is much larger than its actual mass, resulting in near negligible recoil energies.
Introduction to Mössbauer Spectroscopy
One of the earliest practical realisations of the Mössbauer effect is arguably the original experiment by Mössbauer, depicted in Figure 2 below. In this setup, a γ-source is rotated on a centrifuge. When resonance with the absorber sample occurs, there will be a drop in the transmitted photons to the detector, and an increase in the number of scattered photons.
Figure 2: Actual realisation of the Mössbauer Effect, using Doppler shifts of the emitting nuclei relative to the absorbing nuclei
The Mössbauer Effect has since been applied to measure electromagnetic moments of excited nuclear states, observation of dynamic processes in condensed matter and even spectroscopy on extraterrestrial samples of Martian soil [2,3] . Some examples of the applications of Mössbauer Spectroscopy follow:
Mössbauer Spectroscopy of Biological Molecules and Systems
Iron is abundant in many biological molecules, such as hemoglobin, myoglobin, cytochrome c and ferredoxins. The 57Fe isotope is useful for analysis of biological systems because the Mössbauer Effect essentially resonates with and detects any Fe present in the system, regardless of oxidation state or whether the molecule it is bound in is paramagnetic, diamagnetic or involved in magnetic coupling.
The Mössbauer Effect has permitted analysis of biological molecules to levels not previously possible. For example, biological literature up to 1978 suggested that the MoFe protein of nitrogenase had between 14 – 36 Fe atoms. Through Mössbauer Spectroscopy, this figure was improved to 30 ± 2 atoms in 1978, and indeed confirmed to be 30 Fe atoms in 1992.
Mössbauer Spectroscopy has also been used to probe whole cells in addition to proteins. For example, Figure 4 shows the Mössbauer spectra of whole E. Coli cells at 4.2K under different conditions.
Figure 4: Mössbauer Spectra of E. Coli cells under different conditions
There is a slight effect on the nuclear transition energy levels based on the ionisation state and chemical bonding of the ion; this effect is known as isomer shifts. This effect may be measured using the Mössbauer Effect, and an example of the effect of ionisation level on the isomer shifts on iridium compounds relative to iridium metal is shown below in Figure 3.
Figure 3: Isomer shifts in iridium compounds relative to iridium metal, reflecting chemical bonding and valence states 
Mössbauer Spectroscopy of the Rare Earths
Prior work has been done by Brix, et al on the isomer shift of 151Eu in different Europium compounds, when activated by a SmF3 source. The Mössbauer velocities and measurement temperatures are listed in Table 1 below :
Dysprosium has been descrbied, along with many other rare earth metals, as being trivalent. Work by Nowik, Ofer and Wernick  on 161Dy using the Mössbauer Effect in binary metal alloys suggests that the valency of Dysprosium actually varies, and is affected by both the electronegativity and size of the second metal it is paired with in the alloy10, see Table 2.
Other Isotopes Suitable for the Mössbauer Effect
Two criteria are required for an isotope to be a candidate for the Mössbauer Effect. Firstly, it must have a γ-transition to a ground state that is relatively stable or with a convenient half-life. Secondly, a sizable portion of the γ-rays must be emitted free of thermal, Doppler or recoil energy loss; this criteria is satisfied if the nucleus may be bound in a solid (not necessarily crystalline) form. At this time, only 18 elements are practical candidates for Mössbauer-related research . A Mössbauer periodic table is shown in Figure 5.
Of these isotopes, we can supply: 57Fe, 61Ni, 149Sm, 151Eu, 161Dy.
Figure 5: Mössbauer Periodic Table 
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