Can you say a little bit more about why you are interested in this question, and perhaps specify what you mean by economic situation here? My first thought is that there may not be sufficiently detailed information available to answer this.

The main tool for identifying the contribution of a particular industry or product to an economy is something called input-output tables. These show the relationships between industries and "end uses" (final consumption, investment and exports) based on the products each industry produces and consumes. Therefore one can estimate the direct and indirect effects of a product or industry (e.g. if households consume electricity and the electricity sector uses coal, one can estimate how much coal is used indirectly by households via electricity, and thus how much of the output of coal mining winds up as electricity).

From a brief look the US Bureau of Economic Analysis does have input-output tables dating back to the 1950s and 1960s, but they have only 85 industries, so there just isn't enough detail to pick up on nuclear in particular.

I will say that as a general rule, for a modern large economy like the USA or the USSR were in the 1950s, any particular technology or product is pretty unimportant in terms of the total economy, in large part because people tend to find alternative uses for resources (petrol states are the main exception I can think of to this general rule).