Integrator circuit time interval
Lucky for you there is an emerging market for IC's that became prevalent in the last few years. What you are looking for is a time of flight IC. These are mostly used for applications related to LIDAR and measuring distance. The resolution can get lower than 100ps (55ps). 

What you would need to do is take the output from the scintillators and gain it to the appropriate voltage level and/or build a comparator, for a diode based scintellator it would look something like this:


Source: https://transistorized.net/post/stdal/post79.htm 

You could then use the time of flight module TDC7201 to get the difference of the time between the detectors. 


Source: https://www.digikey.com/en/articles/techzone/2017/jan/simplifying-time-of-flight-distance-measurements