If one large particle splits into two is that inelastic or elastic in terms of momentum?
I don't know what you mean by "inelastic or elastic in terms of momentum". A collision (and we can think of this as the two parts of the particle as two objects colliding) is "elastic" or "inelastic" if the energy is conserved or not conserved.
Both elastic and inelastic processes conserve momentum. Momentum is always conserved. Whether a collision is elastic or inelastic depends on conservation of kinetic energy. If kinetic energy is conserved, then the collision is elastic.
In the case of a decay, there's no collision, so the term elastic versus inelastic is a ill-defined. But the kinetic energy of the particle in its rest frame will go from 0 to some non-zero value for the decay particles.
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