Mossbauer Intro

An Introduction to Mossbauer Spectroscopy

In general, spectroscopy uses a photon source with an adjustable energy range to bombard a sample of interest, or ‘absorber', and a particle detector counting the number of photons which passed through the absorber (see below).

In a way that is analogous to electrons that may be excited (or decay) to quantized energy levels, nuclei may also experience transitions between specific energy levels if they absorb or emit photons of precisely the needed energy. If the energy of the photons is not an energy associated with a nuclear transition, then the photons essentially pass through the absorber without interacting. Therefore, for these energies, you will observe about as many photons on the backside of the absorber as were emitted by the source in that direction in the first place.

If the energy of the photons IS an energy associated with a nuclear transition, then the nuclei in the absorber will absorb the photons and make transitions to an excited state. Eventually, the nuclei decay again, and re-emit the photons in a random direction. This means that only some of the re-emitted photons end up travelling in the direction of the detector, and fewer photons will be observed for these energies. By compiling count rates for a range of photon energies, the result is a spectrum with markedly fewer photons in areas that represent nuclear transition energies.

But wait! This model is slightly naive. The assumption that the needed 'transition energy' is the same regardless of the direction of the transition is in fact incorrect. The recoil of the nucleus as it absorbs or emits a photon dissipates some energy due to the conservation of angular momentum. This implies that the absorption energy is somewhat greater than the transition energy, and the emission energy is somewhat less. Thus, multiple peaks associated with a single transition may appear on any spectra taken, complicating the data significantly.

Fortunately, the Mössbauer method exploits the phenomenon of “recoilless resonant absorption.” In Mössbauer spectroscopy, only certain substances (solids!) are used as absorbers, and nuclei in these particular substances are embedded in a lattice. If a nucleus is embedded in a lattice, the much larger mass of the lattice functions as a momentum reservoir. In this case, the recoil of a nucleus during a transition is essentially zero (recoill-less event fraction for Fe 57 absorbers: 65%). The absorption energy and the emission energy converge to the transition energy, which means that the photons emitted by a de-exciting nucleus may then be used to excite another nucleus – this is known as resonant absorption, and is central to Mossbauer spectroscopy. The three parameters that characterize a Mossbauer spectrum are as follows:

Isomer Shift (chemical shift)

For any nuclear state, there exists some Coulomb interaction between the nucleus and the electrons of the atom. At this level, the nucleus cannot be regarded as a point charge, and in fact there is a finite probability that some electrons may even be found within the nucleus.

Different nuclear states generally have slightly different nuclear radii and/or electron density. Varying the size of the nucleus changes the probability that electrons may be found in, or overlap, the nucleus. It also modifies the Coulomb interactions between the nucleus and the electrons, which in turn changes the overall energy of the state. This means that differences in nuclear radii (and electron density) between the source's nuclei and the absorber's nuclei shifts the amount of energy required for a transition away from the expected value by a small amount.

This shift in energy is observed as a shift of the resonance peak (or peaks) away from zero velocity. (See image below.)

Quadrupole Splitting

The nucleus is stationary inside an atom - therefore, we know there cannot be an electric field at the nucleus. However, there certainly can be an electric field gradient. The interaction between the nuclear quadrupole moment and the electric field gradient near the nucleus gives rise to quadrupole splitting. The Harvard Mossbauer paper (also listed in the references section) provides a concise explanation: "If a nucleus in a particular spin state has a slight spheroidal deformation, its distribution of charge is not perfectly spherical, and the nuclear quadrupole moment, Q, is a measure of the deviation of the nuclear charge from spherical symmetry. If a nucleus has a quadrupole moment, its energy depends on its orientation with respect to the electric field gradient." In the spectra we will observe, these energies result in a pair of peaks, evenly spaced around the resonance energy.

Zeeman Effect (Magnetic Hyperfine Splitting)

A nucleus has angular momentum J and a magnetic dipole moment. When the nuclear magnetic dipole moment interacts with the internal magnetic field near the nucleus, hyperfine splitting is observed. Each state with quantum number J can be split into 2J+1 energy levels, but selection rules forbid two of the transitions (those shown in gray in the figure below), leaving six possible transitions. These, naturally, are the six peaks observed in the Mossbauer spectrum. These three effects are depicted below:

Spectroscopy using the Doppler Effect

Lastly, how can Mossbauer spectroscopy observe such tiny effects? It works because the peaks' natural line width, Γ, is related to the lifetime of the states via the Heisenberg uncertainty principle: ∆E ∆t ≥ Γ τ = h / 2π. Here, Γ is the natural line width and tau is the mean lifetime. In our experiment, the Fe 57 decay has a mean life of 141 ns which corresponds to a natural line width of 4.7 x 10^-9 eV.

Since the gamma emitted in the decay process has an energy of 14.4 keV, its natural line width corresponds to a 3 parts in 10¹² effect! To put this in comparison consider stacking sheets of copy paper, about 0.01 cm thick, all the way to the moon; removing a single sheet from this pile corresponds to a 3 parts in 10¹² effect.

To perform the spectroscopy, the energy of the of the gamma emitter is adjusted until resonances in the absorber are observed. This energy shift is created through the Doppler Effect, f = f_o ( 1 ± v/c), by moving the emitter at some velocity v. Specifically, if E_γ = h f_o ≈ 14.4 keV and ΔE = h(f - f_o) then the change in energy (as a function of velocity) is: ΔE = E_γ (v/c).

To get a better feeling of the velocities involved, consider an energy shift, ΔE, on the order of the resolution, i.e, the natural line width of the experiment, Γ = 4.7 x 10^-9 eV. To achieve such a (small) change we would only have to move our source by about 10^-4 m/sec or at 0.35 m/hr!

Next, Mossbauer Apparatus