What are the properties of proton+proton fusion reaction

$p + p → 2H + e^+ + ν\_e + 0.42 MeV$

making it hard to replicate on Earth? 

If we aim beam of protons to a can of water, won't we observe some number of these p-p fusions?

Do we have p-p fusion events on some well known accelerator like LHC or old ones?