  The Paschos-Wolfenstein (PW) relation joins neutral- and charged-current
neutrino- and antineutrino-induced cross sections into an expression that
depends on the weak mixing angle $\sin^2 \theta_W$. Contrary to the traditional
approach with partonic degrees of freedom, we adopt a model built on hadronic
degrees of freedom to perform a study of the PW relation at intermediate
energies (100 MeV to 2 GeV). With upcoming high-statistics scattering
experiments such as MINER$\nu$A and FINeSSE, a scrutiny of the PW relation is
timely. Employing a relativistic Glauber nucleon knockout model for the
description of quasielastic neutrino-nucleus reactions, the influence of
nuclear effects on the PW relation is investigated. We discuss nuclear-model
dependences and show that the PW relation is a robust ratio, mitigating the
effect of final-state interactions, for example to the 1% level. The role
played by a possible strangeness content of the nucleon is investigated. It
appears that the uncertainties arising from the poorly known strangeness
parameters and the difficulties in nuclear modelling seriously limit the
applicability of the PW relation as an intermediate-energy electroweak
precision tool. On the other hand, we show that nuclear effects may be
sufficiently well under control to allow the extraction of new information on
the axial strangeness parameter. Results are presented for $^{16} {O}$ and
$^{56} {Fe}$.
