An Approximation for the rp‐Process

Hot (explosive) hydrogen burning or the Rapid Proton Capture Process(rp-process) occurs in a number of astrophysical environments. Novae and X-raybursts are the most prominent ones, but accretion disks around black holes andother sites are candidates as well. The expensive and often multidimensionalhydro calculations for such events require an accurate prediction of thethermonuclear energy generation, while avoiding full nucleosynthesis networkcalculations. In the present investigation we present an approximation schemeapplicable in a temperature range which covers the whole range of all presentlyknown astrophysical sites. It is based on the concept of slowly varyinghydrogen and helium abundances and assumes a kind of local steady flow byrequiring that all reactions entering and leaving a nucleus add up to a zeroflux. This scheme can adapt itself automatically and covers situations at lowtemperatures, characterized by a steady flow of reactions, as well as hightemperature regimes where a $(p,\gamma)-(\gamma,p)$-equilibrium is established.In addition to a gain of a factor of 15 in computational speed over a fullnetwork calculation, and an energy generation accurate to more than 15 %, thisscheme also allows to predict correctly individual isotopic abundances. Thus,it delivers all features of a full network at a highly reduced cost and caneasily be implemented in hydro calculations.