performing an x-/gamma-ray transmission experiment seems to be easy; but it is not at all...
I think you will suffer from dead time effects of the detector when dealing with low sample thicknesses. In this case your count rate might be too high to have a sufficient linear response of the detector output with respect to the countrate.
In order to solve that issue you should reduce the intensity of the radiation by
a) taking larger distances between the x-ray/gamma source and the detector, or
b) use a filter (e.g. some mm of Al, or Cu, etc. ; depending on the photon energy) in your beam path; please take your reference photon flux including the filter attenuation, or
c) make use of a small diameter pinhole diaphragm to reduce the intensity, or
d) skip the data for low thicknesses and start with thicknesses d larger than do ( d > do). Your primary intensity Io will now be Io = I(do) and your thickness dependence now is I(d')= I(d-do). Your sample section 'do' now can be regarded as the additional filter.
In addition, please ensure that unconditionally
e) your detector is sufficiently shielded at its sides and its back in order to prevent pick up of scattered radiation*) from these directions, and
f) make use of sufficient collimation**) of the incoming radiation in front of the detector in order to prevent pick up of scattered radiation by the detector port (e.g. coming from the walls of your cabinet or from any means of sample support, etc.).
Other issues, which will affect your measurements will be
g) insufficient monochromaticity of your radiation ( e.g. having multiple gamma lines present in your spectrum), and
h) cosmic radiation, which will lead to a significant background countrate in the case of large sample thicknesses.
For a further discussion of precautions you may share more details of your setup ... (e.g. x-ray/gamma source, photon energ(y)ies, estimated primary photon flux, type of detector)
*) when dealing with gammas you will have a very lot of Compton scatter radiation...
**) the detector must only 'see' the sample, but nothing else ...
In case a) you will have trouble with the monochromaticity...
What is about the detector; do you use an energy resolving one (e.g. HpGe)?
In such a case you should be able to establish energy dependent attenuation curves and each curve, which is associated with a gamma line energy should give a thickness dependence according to the Lambert-Beer law (but with different attenuation coefficients according to different gamma energies).
One needs more information to conclude but generally at high energies the primary suspect would be Compon scattering. More material provoke more scattering, and lower energy scattered photons have better chance being absorbed in the detector.
I assume you suffer from the lack of sufficient monochromaticity.
In either case (Cs and Ba) you will have the characteristic x-ray fluorescence K-alpha+beta present in your spectrum. For small thicknesses (up to a few mm) of your sample Ba- and Cs-K-radiation of your sources is able to pass the sample(s) and reach the detector...
So, to model your attenuation curve you have to take your gamma line(s) as well as the K-fluorescence lines into account...
...and the properties of the detector (e.g. photon counting type without energy weighting such as HPGe, or integrating detector using photon energy integration such as scintillation type of detector).
Things are not so easy as they might appear...
You may share spectra of your sources...
You should discuss all these things with your supervisor...