Problems, exercises
Mössbauer effect, ELTE, Department of Atomic Physics
1. Calibrate the velocity spectrum based on the iron sample: calculate the velocity
change per channel, taking into account that the distance of the position of the 1st and
6th (last) peak is 10,6162 mm/s. Check the consistency with the 512 channels being
equivalent to the maximum speed you set on the control panel of the moving unit.
2. Determine the isomer shift (in neV units) of the stainless steel and the
Na2FeII(CN)5NO (sodium nitroprusside) sample with respect to the iron sample!
3. Plot the the imeas line widths as a function of the wi relative intensities (i=1,2,3), and
fit the data with a linear function! Using equation (16) and the parameters of the
linear function, calculate the lifetime of the excited state, its experimental uncertainty,
and compare it to the table value (141,8 ns)! Based on the computed natural line
width, determine the effective thickness, TA, of all the three samples and check the
validity of the approximation in Eq. (16) where we neglected the second order term!
The effective width of the source is 1,62.
4. Determine the electric field gradient in the sodium nitroprusside sample (in V/m2
units)! The quadrupole moment of the excited state is Q = 0,21 barn, and  = 0.
5. The energy level shift of the nucleus due to magnetic field (Zeeman-effect) is
m
E m    I B . Determine the magnetic moment, 3/2, of 57Fe in the excited state!
I
Determine the magnitude of the magnetic field, B, in the iron sample (in T units)!
Note that the magnetic moment of the ground state is 1/2 = +0,090604 N, where N
= 3,15238·10-11 keV/T the nuclear magneton. Also note, that the ratio of the intensity
of the transitions between levels in polycrystals is I  3  1 : I  1  1 : I  1  1  3 : 2 : 1 .
2
6.
7.
8.
9.
2
2
2
2
2
These ratios are determined by group theory: the excited state with spin 3/2 decays
into a photon with spin 1 and a ground state with spin ½. The ratios above are the
squares of the respective Clebsh-Gordan coefficients.
Compare the electric field gradient measured in exercise 4 to the “Bohr-gradient”,
which is the gradient of the electric field of the electron at the location of the proton
in the ground-state hydrogen atom in the Bohr model.
Compare the magnetic field value measured in exercise 5 to the “Bohr-field”, which
is the magnetic field strength caused by the electron orbiting the proton in the groundstate hydrogen atom in the Bohr model.
Determine the maximal displacement of the source when moving it periodically!
Assuming that the distance between the sample and the source is 1 cm, by how many
% does the distance change in each period?
Design a measurement that can determine the gravitational redshift! Give your
recommendations about the height difference between the source and the absorber,
the activity of the source, the duration of the measurement, etc. in order to prove the
gravitational redshift experimentally! (The effective mass of the photon is E/c2).
Note: please provide the appropriate experimental uncertainty with all the measured and
computed quantities!