If one reads "Design of Air Frames for Nuclear Power" written by Kelly Johnson and then looks at the design of the SR-71 it is clear it was designed for nuclear power. Looking at the drawings one sees that the fuel was used to shield the pilots from radiation. The SR-71 either utilized an indirect liquid fuel reactor as its powerplant that was placed in the center of gravity of the plane or SNAP-8 sized reactors were used and mounted in the engines. Shadow shielding was all that was needed to protect the pilots once the plane was above 90,000 feet.
This is the layout that Kelly Johnson thought was best to shield the pilots of the nuclear plane. The SR-71 follows this layout. As you can see the SR-71 landing gear folds up into the fuselage. There is also about 50 feet worth of fuel between the pilot and where the reactor is. That's a lot of shield. The SR-71 also had boronated fuel on the plane. This fuel also played a role in mitigating the radiation problem.
They were working on a delta wing aircraft for the ANP all along. The Nuclear SR-71 Blackbird just makes more sense. The chemical bird was very limited. It had no legs. It could fly for about 90 minutes at mach 3 speeds before needing to refuel. The nuclear SR-71 had virtually unlimited range. Going nuclear turns the SR-71 into a superweapon.
The J-58 engine for the SR-71 was the nuclear direct cycle engine being developed under the Project PLUTO program. The payload of the plane developed under PLUTO was 25% of total mass [1]. Using the PLUTO engines, a bomber version of the SR-71 would carry 43,000 pounds, the same payload as a B-52C heavy bomber.
The J-58 had cesium in the exhaust. Cesium is a well known fission product. [2]
SOURCES:
1. "General Branch Says Ramjet Will Preclude Rocket, Airplane". Nucleonics August 1960.
2. http://large.stanford.edu/courses/2012/ph241/wessells1/#:~:text=Cesium%2D137%20is%20an%20especially,radiation%20released%20during%20nuclear%20accidents.