What I understand for the Mossbauer s...

What I understand for the Mossbauer spectroscopy

1) Recoil-free absorption spectra, similar to the optical absorption spectra.
Here the key is that in a solid, the atoms can not move freely. In fact, the motion of atoms are described by the vibrational spectra as collective phenomena. In this case, the energy involved is quantized, and there is a lower cut off.
We can estimate the lower cut off using

E_{min}~k_BT_{Debye}/N^{1/3}

For a 300K Debye temperature and N~10^23, we get E_{min}~1e-9 J.

At the same time, we can calculate the recoil energy of a certain nucleus

E_{recoil}=\frac{p^2}{2m}=\frac{1}{2m}(\frac{h}{\lambda})^2

Using Fe⁵⁷ as an example, if it is excited by 100 keV gamma ray, the recoil energy is 3e-20, which means that no phonon can be created. Therefore, the whole crystal will recoil, leaving the recoil speed 1e-21 m/s. In contrast the single nuclear recoil speed can be as high as 500 m/s.

This is the way to get recoil free absorption.

2) discrete peaks due to separate nuclear energy levels

3) nuclear energy levels may change due to .

    A electric interaction

    a) isomer shift, the monopole effect of the environment to the nucleus
     This comes from the interaction between charge of electrons and the nucleus. Because the nucleus is so small, only the s electron that has some density at the center of the atom can have significant interaction. For example, Fe3+ has more isomer shift then Fe2+ because 3d electrons can screen 4s electron, putting them slightly out of the center of the atom.

    b) quadropole splitting, the interaction between the electric quadrapole of nucleus, i.e. the field gradient from the electrons surrounding the nucleus.
   
    B magnetic interaction
    a) Zeeman effect: E=\muB, where \mu is the magnetic moment of the nucleus.


Other remarks,

   Normally, Co⁵⁷ in Rh is used as source, because Co57 can decay into excited state of Fe57 (I=5/2) state, it will later decay  I=5/2->I=3/2 state and I=3/2->I=1/2. Because the I=1/2 is the ground state of Co57. The real useful radiation source is I=3/2->I=1/2.