  The process of nuclear excitation by electron capture in plasma environments
generated by the interaction of ultra-strong optical lasers with solid-state
samples is investigated theoretically. With the help of a plasma model we
perform a comprehensive study of the optimal parameters for most efficient
nuclear excitation and determine the corresponding laser setup requirements. We
discern between the low-density plasma regime, modeled by scaling laws, and the
high-density regime, for which we perform particle-in-cell calculations. As
nuclear transition case study we consider the 4.85 keV nuclear excitation
starting from the long-lived $^{93\mathrm{m}}$Mo isomer. Our results show that
the optimal plasma and laser parameters are sensitive to the chosen observable
and that measurable rates of nuclear excitation and isomer depletion of
$^{93\mathrm{m}}$Mo should be already achievable at laser facilities existing
today.
