In the proton-proton chain reaction in the Sun, the first step is $$p + p \rightarrow \; ^2_2{\rm He} .$$ After this, the most likely thing to happen next is that the reverse reaction occurs: the $^2_2{\rm He}$ splits up and we are back where we started. Sometimes, very much more rarely, there is a weak beta+ decay process which converts a proton to a neutron and then we get a deuteron and further reactions can occur. I know how to find the rate for the latter process, but I would like to find the rate for the first process.
My question is: In the solar core, how many times does the fuse-fission sequence $p+p \rightarrow {\rm He} \rightarrow p+p$ occur, on average, for any given proton, before we get the weak decay and a deuteron? Even an order-of-magnitude estimate from rough cross section formula would be helpful. (I have tried to find it with no luck yet.)
Edit added 19 Feb 2018: My research so far has yielded numbers between $10^{15}$ and $10^{28}$. So anyone who can pin it down better than that range (13 orders of magnitude) is making progress!