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The discovery of chirped pulse amplification has led to great improvements in laser technology, enabling energetic laser beams to be compressed to pulse durations of tens of femtoseconds and focused to a few micrometers. Protons with energies of tens of MeV can be accelerated using, for instance, target normal sheath acceleration and focused on secondary targets. Under such conditions, nuclear reactions can occur, with the production of radioisotopes suitable for medical application. The use of high-repetition lasers to produce such isotopes is competitive with conventional methods mostly based on accelerators. In this paper, we study the production of 67Cu, 63Zn, 18F, and 11C, which are currently used in positron emission tomography and other applications. At the same time, we study the reactions 10B(p,α)7Be and 70Zn(p,4n)67Ga to put further constraints on the proton distributions at different angles, as well as the reaction 11B(p,α)8Be relevant for energy production. The experiment was performed at the 1 PW laser facility at Vega III in Salamanca, Spain. Angular distributions of radioisotopes in the forward (with respect to the laser direction) and backward directions were measured using a high purity germanium detector. Our results are in reasonable agreement with numerical estimates obtained following the approach of Kimura and Bonasera [Nucl. Instrum. Methods Phys. Res., Sect. A 637, 164–170 (2011)].