an additional source of background radiation is x-ray fluorescence in the shielding material.
for a lead shield, x-ray energies are 12 keV and 80 keV.
these x-rays can hinder the accurate examination of photons in a spectrum!
to minimize these effects, the cave should be lined with a material which absorbs lead x-rays. In this case, a 1mm thick sheet of cadmium would be appropriate.