Alxhan said:
How many ways the nuclear waste can be transmuted?
Since transmutation is a nuclear process, it require a nuclear reaction, which could be induced by neutrons, protons, or other particles.
Neutron reaction may include capture (n, γ), an inelastic collision (n,n'), or a spallation reaction, e.g., (n,p), (n,α), . . . The outcome of a neutron reaction is dependent on the energy and the target nucleus.
Protons may also be used, in which case, one might observe a (p,n) reaction or some spallation reaction depending on the proton energy and target nucleus.
For practical purposes, one would seek to minimize the energy input into the reacting particle. It is relatively easy to generate protons and neutrons. Accelerator driven spallation systems have been proposed.
One might also separate isotopes chemically for transmutation with different reactions.