  Deciphering the conditions under which neutron captures occur in the Universe
to synthesize heavy elements is an endeavour pursued since the 1950s, but that
has proven elusive up to now due to the experimental difficulty of generating
the extreme neutron fluxes required. It has been evoked that laser-driven
(pulsed) neutron sources could produce neutron beams with characteristics
suitable to achieve nucleosynthesis in the laboratory. In this scheme, the
laser first generates an ultra-high-current, high-energy proton beam, which is
subsequently converted into a dense neutron beam. Here we model, in a
self-consistent manner, the transport of laser-accelerated protons through the
neutron converter, the subsequent neutron generation and propagation, and
finally the neutron capture reactions in a gold ($^{197}$Au) chosen as an
illustrative example. Using the parameters of present-day available lasers, as
well as of those foreseeable in the near future, we find that the final yield
of the isotopes containing two more neutrons than the seed nuclei is
negligible. Our investigation highlights that the areal density of the
laser-driven neutron source is a critical quantity and that it would have to be
increased by several orders of magnitude over the current state of the art in
order to offer realistic prospects for laser-based generation of neutron-rich
isotopes.
