# Energy in nuclear decays

After a nuclear decay is it a necessity that the total energy of the products is more than the energy of the original particle before decaying? (NB: by 'energy' I don't intend to include mass-energy as well, unless by definition the term 'total energy' happens to include that in the realm of particle physics)

I was told that this might depend on whether the total mass of the products is less than the mass of the decaying particle. I'm not sure of the veracity of this claim.

I've heard the Higgs Boson can decay to heavier particles than itself. But, I'm not sure about other decays, such as the one I described, which is not a Higgs Boson.

For example, is the statement "the mass energy of the original particle is equal to the total energy of the decay products" false?

• Particle physicists do tend to include mass in "energy" most (but not quite all) of the time. But I can take it that you are interested in the relationship between the pre- and post-decay kinetic energies, no? – dmckee May 10 '14 at 17:49
• @dmckee yes, particularly in whether the last statement I quoted is true/false – hb20007 May 10 '14 at 17:53
• If you examine the situation in the rest frame of the progenitor, then it should be absolutely clear that the kinetic energies can't be the same. From that I would conclude that the question is asking you about all the energy contributions, including the masses. – dmckee May 10 '14 at 18:29
• @dmckee oh, I think you're right then – hb20007 May 10 '14 at 19:46

• @hb2007 Energy (and also momentum) is conserved in all references frames. The arithmetic is easier in the rest frame of the decaying particle, but observers in all inertial reference frames will agree that total energy is conserved. In fact, in special relativity, energy and momentum make a four-vector $(E,\vec p)$ that transforms just the same way as the more familiar combinations of time and position coordinates $(t, \vec x)$. – rob May 10 '14 at 20:37