The rate of fusion changes as the square of density but you still get fusion at vary low density's it's just less common. You might be thinking of fission?
As to PP fusion from what read. Without a large enough plasma the beta more common proton emission path >99.99% ends up costing more energy than you gain from beta-plus decay <0.01%. "The least stable is 5He, with a half-life of 7.6×10−22 seconds, although it is possible that 2He has an even shorter half-life" http://en.wikipedia.org/wiki/Isotopes_of_helium#Helium-2_.28...
As to PP fusion from what read. Without a large enough plasma the beta more common proton emission path >99.99% ends up costing more energy than you gain from beta-plus decay <0.01%. "The least stable is 5He, with a half-life of 7.6×10−22 seconds, although it is possible that 2He has an even shorter half-life" http://en.wikipedia.org/wiki/Isotopes_of_helium#Helium-2_.28...