  Realizing Majorana bound states in chains of magnetic impurities on $s$-wave
superconducting substrates relies on a fine tuning of the energy and
hybridization of the single magnetic impurity bound states and of the
spin-orbit coupling (SOC). While recent experiments investigate the influence
of the former two parameters, the effect of SOC remained experimentally largely
unexplored. Here, we present a scanning tunneling spectroscopy study of
close-packed Mn chains along the [001]-direction on Ta(110) which has almost
identical atomic and surface electronic structure compared to the previously
studied Nb(110) system, but a three times larger SOC. The dominant Shiba band
has a very similar dispersion, but its minigap, taken relative to $\varDelta$,
is increased by a factor of 1.9 with respect to the Nb case, which can be
ascribed to the stronger SOC.
