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In order to develop a laser-driven spin-polarized ³He-ion beam source available for nuclear-physics experiments as well as for the investigation of polarized nuclear fusion, several challenges have to be overcome. Apart from the provision of a properly polarized ³He gas-jet target, one of the biggest milestones is the demonstration of the general feasibility of laser-induced ion acceleration out of gas-jet targets. Of particular importance is the knowledge about the main ion-emission angles as well as the achievable ion-energy spectra (dependent on the optimal set of laser and target parameters). We report on the results of such a feasibility study performed at PHELIX, GSI Darmstadt. Both ³He- and ⁴He-gas jets (ngas ∼ 10¹⁹ cm⁻³) were illuminated with high-intensity laser pulses, IL ∼ O (10¹⁹ W cm⁻²). The main ion-emission angles could be identified (±90° with respect to the laser-propagation direction) and the ion-energy spectra for all ion species could be extracted: for the optimal laser and target parameters, the high-energy cut-offs for He ²⁺,¹⁺ ions were 4.65 MeV (with a normalized energy uncertainty of Δ ɛ​ ɛ​⁻¹ = 0.033) and 3.27 MeV (Δ ɛ​ ɛ​⁻¹= 0.055), respectively.