  The instanton vacuum picture is used to study hadronic matrix elements of the
twist-3 (dimension-4, spin-1) QCD operators measuring the quark spin density
and spin-orbit correlations. The QCD operators are converted to effective
operators in the low-energy effective theory emerging after chiral symmetry
breaking, in a systematic approach based on the diluteness of the instanton
medium and the $1/N_c$ expansion. The instanton fields induce
spin-flavor-dependent "potential" terms in the effective operators,
complementing the "kinetic" terms from the quark field momenta. As a result,
the effective operators obey the same equation-of-motion relations as the
original QCD operators. The spin-orbit correlations are qualitatively different
from naive quark model expectations.
