phase space

Imagine handing a fixed sum of money to a group of people and asking in how many different ways they could split it. With two people there are only so many splits; with ten people there are vastly more. Phase space is the particle-physics version of this counting: given a fixed total energy and momentum, it is a measure of how many distinct ways the outgoing particles can share that energy and momentum among themselves. More ways to share means more phase space.

Phase space matters because, as Fermi's golden rule makes precise, a reaction rate is the squared amplitude (the dynamics) multiplied by the available phase space (the kinematics). The phase-space factor knows nothing about the forces involved; it only counts room. It depends strongly on the masses of the outgoing particles and on how much energy is available: producing light particles leaves lots of leftover energy to be divided many ways, so there is generous phase space; producing particles whose combined mass nearly uses up all the available energy leaves almost no room, so the phase space, and hence the rate, is squeezed toward zero right at threshold.

This is why a process can be suppressed not because the underlying interaction is weak, but simply because there is little room for the products to exist. Near the energy threshold for making a heavy particle, the rate creeps up slowly from zero purely as a phase-space effect. Disentangling phase space from dynamics is a routine and essential step in interpreting any measurement: a small rate might mean a feeble force, or it might just mean a cramped phase space, and only by computing the phase space can you tell which.