p p annihilations at rest occur from initial states with J PC =0 −+, 1 −−, 1 +−, 0 ++, 1 ++, 2 ++. These initial states are S- and P-wave atomic levels of protonium atoms that are populated by the atomic cascade which follows the atomic capture of the antiproton. Each of the six fractions F J PC of annihilations from initial states of protonium with quantum numbers J PC depends on the density of the target where antiprotons are brought to rest, and is not known individually at present at any target density. Here we show that the values of the six annihilation fractions F J PC can be determined by measuring at four target densities the values f J PC channel of the frequencies of annihilations for six exclusive annihilation channels. The same measurements would provide, for the channels exploited for the F J PC determination, the values B J PC channel of the branching ratios of annihilation from each J PC type of initial states from which the channels are allowed.