Since the train in moving so fast, the actual time interval where measurement is possible would be very small. You would have to repeat the measurement countless times in order to gather enough data. You would also need a very long vacuum chamber to prevent the gamma-rays from scattering before reaching the scatterer.
Maybe we could let the train move on a circular track so that it passes the scatterer multiple times. This would also reduce the size of the vacuum chamber. However, this would probably also have its complications.