In short, what it is, and it was I think the year that Mössbauer actually got the… Mössbauer... sorry, got the Nobel Prize for the Mössbauer effect. It is, essentially, that if you have a particular type of radioactive transition, gamma ray emission it’s called, and the atom that is giving off the gamma ray is embedded in a solid, you get no recoil. You know that if you fire a gun, the gun recoils. And there are ways of minimising that, but the recoil is there. When an atom gives off a gamma ray, that is energy, and the atom recoils. And that is taken from the energy of the ray.

Now, what Mössbauer found, and this was totally unexpected, was that if the atom was in a solid, the whole of the crystal recoiled, and as the recoil energy is inversely proportional to the mass, it was negligible, because it was the whole crystal, not just the atom, which took the recoil energy. So he had the perception to realise that he was seeing the recoil-less emission of gamma rays, and their resonant reabsorption in another atom. So you have an emitter of gamma rays, and you have an atom in a sample... solid state sample of interest. The gamma rays pass through, and if the atoms in the absorber have exactly the right energy for the gamma ray, the energy will be absorbed. The trick is how to count it. 

Well, Mössbauer did it in a particular way, because it was the first time it was done, but in the course of a year or two, some electronic ways were developed, which I needn’t go into, but essentially they used the Doppler effect.