  The formalism describing (anti)neutrino-nucleus reaction cross-sections in
neutral- and charged-current processes is improved. Compact formulae for the
single-particle transition matrix elements, based on the multipole expansion
treatment of the relevant hadronic currents and the use of harmonic oscillator
basis, are presented. As an application, the nucleus $^{127}I$, a promising
target for detection of solar- and supernova-neutrinos as well as of cold dark
matter candidates, is considered. Our matrix elements refer to exclusive
processes of the charge-changing $^{127}I(\nu_l,l^-)^{127}Xe^{\star}$ reaction
and especially to the transition ${5/2}^+ \to {3/2}^+$ leading from the ground
state of $^{127}$I to the lowest excitation of $^{127}$Xe nucleus.
