Momentum computed tomography of low-energy charged particles produced in collisional reactions

The momentum distributions of secondary particles in collisional reactions carry rich information about the interaction dynamics. Traditional spectrometer measurements are always limited to certain aiming directions or a small solid angle. The velocity map imaging device is developed only for certain symmetric momentum distributions, while the reaction microscope is restricted to low count-rate experiments. They all fail in imaging arbitrary momentum distributions of high-intensity particle showers. We propose the momentum computed tomography (MCT) to overcome this situation, which pursues a projection-reconstruction solution to the measurement problem. We lay down the projection theory both in the continuum and discretized forms in the context of a general parameterized MCT model. The reconstruction problem is formulated under the maximum a posteriori framework and the compressed sensing scenario. It is solved with an indefinite preconditioned alternating direction method of multipliers. Numerical experiments are carried out to illustrate the MCT working principles.