The on-going developments in laser acceleration of protons and light ions, as well as the production of strong bursts of neutrons and multi-[Formula: see text] photons by secondary processes now provide a basis for novel high-flux nuclear physics experiments. While the maximum energy of protons resulting from Target Normal Sheath Acceleration is presently still limited to around [Formula: see text], the generated proton peak flux within the short laser-accelerated bunches can already today exceed the values achievable at the most advanced conventional accelerators by orders of magnitude. This paper consists of two parts covering the scientific motivation and relevance of such experiments and a first proof-of-principle demonstration. In the presented experiment pulses of [Formula: see text] at [Formula: see text] duration from the PHELIX laser produced more than [Formula: see text] protons with energies above [Formula: see text] in a bunch of sub-nanosecond duration. They were used to induce fission in foil targets made of natural uranium. To make use of the nonpareil flux, these targets have to be very close to the laser acceleration source, since the particle density within the bunch is strongly affected by Coulomb explosion and the velocity differences between ions of different energy. The main challenge for nuclear detection with high-purity germanium detectors is given by the strong electromagnetic pulse caused by the laser-matter interaction close to the laser acceleration source. This was mitigated by utilizing fast transport of the fission products by a gas flow to a carbon filter, where the [Formula: see text]-rays were registered. The identified nuclides include those that have half-lives down to [Formula: see text]. These results demonstrate the capability to produce, extract, and detect short-lived reaction products under the demanding experimental condition imposed by the high-power laser interaction. The approach promotes research towards relevant nuclear astrophysical studies at conditions currently only accessible at nuclear high energy density laser facilities.