The aim of the reported research is to contribute to investigation of new processes and methods interlinking nuclear and laser-plasma physics. With respect to requirements of nuclear experiments at medium-size high-power lasers, the selection of proper candidates for studying the excitation and decay of low-lying nuclear states is reviewed. An experimental approach to the identification of low-energy nuclear transitions is discussed, simple estimates of the ¹⁸¹Ta excitation yield in the laser-generated plasma provide a theoretical basis for planning future work. First tests and results of the experiments at the laser facility PALS are presented.