  Ultra-intense MeV photon and neutron beams are indispensable tools in many
research fields such as nuclear, atomic and material science as well as in
medical and biophysical applications. For astrophysical applications aimed for
laboratory investigations, neutron fluxes in excess of 10$^{21}$ n/(cm$^2$ s)
are required. Such ultra-high fluxes are unattainable with existing
conventional reactor- and accelerator-based facilities. Currently discussed
concepts for generating high-flux neutron beams are based on ultra-high-power
multi-petawatt lasers operating at >10$^{23}$ W/cm$^2$ intensities. Here, we
present a novel efficient concept for generating $\gamma$ and neutron beams
based on enhanced generation of direct laser accelerated electrons in
relativistic laser interactions with a long-scale near critical density plasma
at 10$^{19}$ W/cm$^{2}$ intensity. New experimental insights in the
laser-driven generation of ultra-intense well-directed multi-MeV beams of
photons with >10$^{12}$ ph/sr and a ultra-high intense neutron source with
>6$\times$10$^{10}$ neutrons per shot are presented. More than 1.4\%
laser-to-gamma conversion efficiency above 10 MeV and 0.05\% laser-to-neutron
conversion efficiency were recorded, already at moderate relativistic laser
intensities and ps pulse duration. This approach promises a strong boost of the
diagnostic potential of existing kJ PW laser systems used for ICF research.
