1. Gamma attenuation demands high density substance to be added.
2, Neutron attenuation demands lightweight mass chemical elements in the substance's formula like carbon, boron, oxygen, etc.
3. A wide range of hydrogenated, neutron-absorbing materials allows neutron slowdown and capture. For fast neutrons good retarders are hydrogen, carbon or oxygen-rich compounds. Organic compounds?!
4. Literature points out that unlike lead, heavy (not much?) materials such as iron, cast iron and steel may be used as gamma shields in mixed fields or as structural materials and can also help to slow down fast neutrons.
5. Heavy metals must be avoided. They become radioactive if irradiated with neutrons. But they are the best to reduce gamma.
6. The better material to fulfill both your needs is high density organic polymers, but do the specific concrete features allow?
7. Considering that concrete is a mix of cement (with iron oxide), quartz sand and (rock) gravel, maybe the amount an increase in the iron content of the cement and/or a substitution of some of the rock by (cast-iron or steel) gravel would solve the problem.
7. Considering that concrete is a mix of cement (with iron oxide), quartz sand and (rock) gravel, maybe an increase in the iron content of the cement and/or a substitution of some of the rock by (cast-iron or steel) gravel would solve the problem.