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## Section 3.4: Exploring Particle Decays

Initial particle: Mass = MeV/c2 and Speed, v/c =

Decay products: Mass1 = MeV/c2 | Mass2 = MeV/c2.

Please wait for the animation to completely load.

The animation shows the decay of one particle into two decay products  (momentum is given in units of MeV/c, mass in units of MeV/c2 and speed is in the form of v/c).  If a particle of unknown mass decays into two particles of known mass and momentum, you can discover the mass of that particle by measuring the energies of the end products. The key is to use conservation of relativistic momentum,

p = m0v/(1 − v2/c2)1/2,                        (3.6)

and energy,

E2 = p2c2 + m02c4.                       (3.7)

Restart. Using the animation, choose a mass and an initial speed of a particle that will spontaneously decay into two other particles. Pick the masses of the two decay products that you want to create. If the total mass of the two decay particles is equal to the initial particle mass, check that the momentum is conserved.   Compare momentum before and after the decay. When the decay products have different masses, notice that there are two possible scenarios: I) both particles move to the right and II) Particle 2 moves to the left while Particle 1 moves to the right. By reversing the masses of the decay products, you can see both cases (the animation is designed to always show Particle 1 heading off to the right).

Now run the animation in reverse. Notice that you see two particles colliding and creating a third particle that is more massive than the sum of the two initial particles. How is this possible?  Where does the additional mass come from?

Note that the animation obeys the laws of relativistic mechanics and thus you cannot create any possible combination of decay products from a given initial particle. For example, the animation will not let you create two decay products of total mass greater than the initial particle's mass. Why not?  You might think that if you set the initial particle speed high enough, the additional energy (in the form of kinetic energy) could be converted into rest mass energy. The easiest way to see why this cannot occur is to switch reference frames. Suppose you are in the reference frame of the initial particle. In this reference frame, the initial energy is

Einitial = Minitial c2 ,

and it would decay into two particles, each with energy given by the sum of kinetic energy and rest mass energy so

Edecay products = K1 + m1c2 + K2+ m2c2 .

For energy to be conserved, the kinetic energy (K1 + K2) would need to be negative, but relativistic kinetic energy is given by

K = [m0c2/((1 − v2/c2)1/2) ] − m0c2,                     (3.8)

which cannot be negative, any more than non-relativistic kinetic energy can. Since the kinetic energy cannot be negative, it is not possible for the combined masses of the decay products to be greater than the initial particle mass (in all reference frames).